Dynamic Optical Components by Combining Plasmonic Metasurfaces with Piezoelectric MEMS

University of Southern Denmark Dynamic Optical Components by Combining Plasmonic Metasurfaces with Piezoelectric MEMS Vaagen Thrane, Paul Conrad DOI: 10.21996/eac24207-cb4c-4b1e-a8ed-6a8ffc3e717f Publication date: 2025 Document version: Final published version Document license: CC BY-NC-SA Citation for pulished version (APA): Vaagen Thrane, P. C. (2025). Dynamic Optical Components by Combining Plasmonic Metasurfaces with Piezoelectric MEMS . [Ph.D. thesis, SDU]. Syddansk Universitet. Det Tekniske Fakultet. https://doi.org/10.21996/eac24207-cb4c-4b1e-a8ed-6a8ffc3e717f Go to publication entry in University of Southern Denmark's Research Portal Terms of use This work is brought to you by the University of Southern Denmark. Unless otherwise specified it has been shared according to the terms for self-archiving. If no other license is stated, these terms apply: • You may download this work for personal use only. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying this open access version If you believe that this document breaches copyright please contact us providing details and we will investigate your claim. Please direct all enquiries to [email protected] Download date: 22. Sep. 2025 UNIVERSITY OF SOUTHERN DENMARK Doctoral Thesis Dynamic Optical Components by Combining Plasmonic Metasurfaces with Piezoelectric MEMS Author: Paul Conrad Vaagen Thrane Supervisor: Prof. Dr. Sergey I. Bozhevolnyi Co-supervisor: Dr. Christopher A. Dirdal A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Centre for Nano Optics Mads Clausen Institute February 2025 ii Dynamic Optical Components by Combining Plasmonic Metasurfaces with Piezoelectric MEMS Paul Conrad Vaagen Thrane February 2025 This work is licensed under a Creative Commons “Attribution-NonCommercial-ShareAlike 4.0 International” license. iii Abstract Optical metasurfaces offer an incredible wealth of opportunities to control light in new ways. Comprised of sub-wavelength sized structures they enable effective material properties not present in naturally occurring substances, and which can be tailored by design to control all properties of light. Dynamic metasurfaces - metasurfaces that can adjust their properties during use - are especially promising, and there is currently a large ongoing effort by the research community to identify and develop these devices. This thesis presents studies on one such system. By replacing the metallic substrate in gap surface plasmon metasurfaces with a piezoelectric MEMS mirror, we realize metasurface structures coupled to a micro-cavity with a variable length. This results in a dynamic reflective metasurface with fast response down to 5 µs, high efficiency of 50-90 %, full 2πphase control, and we demonstrate the concept for several interesting use cases in near IR frequencies. Through the introductory chapters and included articles, the design, fabrication, assembly and characterization of these devices is presented, and their merits and drawbacks are discussed in light of other developments in the field. Being based on two recent, but by now well established technologies, the final conclusion is that the platform represents a suitable and cost-effective platform for realizing dynamic metasurfaces. iv Resum´e Optiske metaflader tilbyder en utrolig rigdom af muligheder for at kontrollere lys p˚a nye m˚ader. Best˚aende af strukturer i sub-bølgelængde størrelse muliggør de effektive materialegenskaber der ikke er til stede i naturligt forekommende stoffer, og som kan skræddersys ved design til at kontrollere alle lysets egenskaber. Dynamiske metaflader - metaflader der kan justere deres egenskaber under brug - er særligt lovende, og der er i øjeblikket en stor igangværende indsats fra forskningssamfundet for at identificere og udvikle disse enheder. Denne afhandling præsenterer studier af et s˚adant system. Ved at erstatte det metalliske substrat i gap surface plasmon metaflader med et piezoelektrisk MEMS-spejl, realiserer vi metaflade-strukturer koblet til en mikro-kavitet med variabel længde. Dette resulterer i en dynamisk reflekterende metaflade med hurtig respons ned til 5 µs, høj effektivitet p˚a 50-90 %, fuld 2πfasekontrol, og vi demonstrerer konceptet for flere interessante anvendelsestilfælde i nær IR-frekvenser. Gennem de indledende kapitler og inkluderede artikler præsenteres design, fremstilling, samling og karakterisering af disse enheder, og deres fordele og ulemper diskuteres i lyset af andre udviklinger p˚a omr˚adet. Baseret p˚a to nyere, men nu vel etablerede teknologier, er den endelige konklusion, at platformen repræsenterer en god og omkostningseffektiv platform til realisering af dynamiske metaflader. v Preface and Acknowledgements This thesis is the result of close collaboration between the research groups at the Centre for Nano Optics at the University of Southern Denmark and the Micro-Optics group at SINTEF in Norway, respectively led by my supervisor for this work, Prof. Dr. Sergey I. Bozhevolnyi, and my co-supervisor Dr. Christopher A. Dirdal. During the course of this work I have also visited Prof. Dr. Olav Solgaard, at the Ginzton Laboratory, Stanford University. This work has received funding from the Research Council of Norway under project number 323322; the ATTRACT program (European Union Horizon 2020 Research and Innovation Program 101004462); and the European Innovation Council under project number 101185769. The work presented in this thesis would in no way have been possible alone, and there are a lot of people I am grateful for and who have made it all possible. First of all, my supervisor Sergey is an expert at refocusing overambitious students on the most important tasks at hand. I am afraid I have not always made his job easy, but I can sincerely say I am immensely grateful for all his insightful suggestions, clear guidance, support and kindness. Being for the most part located on opposite sides of Skagerrak has complicated some things, and I hugely appreciate the large effort Sergey has made to make me an integrated part of his group nonetheless. They are a very welcoming group and I have had the great pleasure of collaborating with many of its members, I thank them all and hope we will keep the collaboration going. I am immensely grateful for my local supervisor too, Christopher, who has likewise made a lot of accommodations to facilitate the project. His enthusiasm, motivational support and organizational skills have somehow made it possible to juggle the many tasks within this project and others. In extension of him, I am also thankful to SINTEF for letting me have this opportunity. My gratitude furthermore goes out to Olav and his students at Stanford, a group of highly intelligent people best characterized by their kindness and inclusiveness. Olav additionally has a knack for sparking interest and ideas, and I greatly value the time he devotes to help us students with our projects. The idea for this project would never have existed if it had not been for Thor Bakke and the other people involved in developing the MEMS we have been using, which includes many of my fantastic colleagues at SINTEF. Some of my colleagues have not been involved, but they are fantastic too and I vi thank them for making my workplace great. My colleague and friend Runar is especially awesome, and I want to thank him for that, as well as his wife Line for being awesomest. My family and many great friends also deserve a mention, without them this work might have been possible - but not by me. I thank them with all my heart. If I get the impossible task of naming just a few, I am forever grateful for Anne-Line, H˚akon, Marie and Kristian, to whom I know I can always go for support - or just a stupidly long ski excursion if that is what I need. Last but certainly not least, I would like to thank Chao Meng, who I have had the great pleasure of collaborating with these last years and who I consider a close friend. I greatly value his immense kindness, and admire his brilliance for experimental work which has made this project possible. Contents Abstract iii Resum´e iv Preface and Acknowledgements v 1 Introduction 1 1.1 Motivation ............................. 1 1.2 Aims of this thesis ......................... 2 1.3 Thesis outline ............................ 3 2 Static metasurfaces 5 2.1 Overview and state of the art ................... 5 2.1.1 The transition to flat optics ................ 5 2.1.2 Categories of metasurfaces ................. 7 2.1.3 Applications ........................ 16 2.1.4 Challenges ......................... 17 2.2 Metasurface design ......................... 18 2.3 Metasurface fabrication ...................... 23 3 Active metasurfaces 27 3.1 Overview and state of the art ................... 27 3.1.1 MEMS metasurfaces .................... 29 3.2 Piezoelectric MEMS ........................ 31 3.3 Combining piezoelectric MEMS and metasurfaces ........ 35 3.4 MEMS metasurfaces, a comparison ................ 46 4 Conclusion and outlook 51 vii viii CONTENTS 5 Articles 53 5.1 Dynamic piezoelectric MEMS-based optical metasurfaces . . . 53 5.2 Full-range birefringence control with piezoelectric MEMS-based metasurfaces ............................ 66 5.3 MEMS Tunable Metasurfaces Based on Gap Plasmon or Fabry–P´erot Resonances ............................. 74 5.4 MEMS-tunable topological bilayer metasurfaces for reconfigurable dual-state phase control .................. 82 5.5 Metasurface Polarimeter for Structural Imaging and Tissue Diagnostics ............................... 94 References 113 2.1. OVERVIEW AND STATE OF THE ART 7 Figure 2.1: aA prism can be used to shift the direction of an optical beam of light. bA blazed grating - a type of diffractive optical element - can do the same, but wrapping the phase by 2πenables considerable miniaturization. c Optical metasurfaces can be used to make diffractive optical elements, but are not limited to this. countless design choices like combinations of materials and geometries - only limited by your imagination and your fabrication techniques - translate into a huge variety of different behaviors in the effective material. There have been demonstrated numerous ways of controlling both phase and amplitude, and by introducing anisotropic geometries it is relatively straightforward to do this independently for orthogonal polarization states. As a specific example, metasurface based diffractive lenses have already shown better numerical aperture, efficiency and polarization control than more traditional approaches [11], and more progress is expected on control of chromatic effects and tunability. But how do they work? The following section will give a brief overview of different types of metasurfaces and their operational principles. 2.1.2 Categories of metasurfaces The degrees of freedom in materials, geometries, targeted wavelengths and all the various configurations for different applications makes classification of metasurfaces a challenge, but there are some main categories that give a good overview for most of the concepts used to date [12–16]. Perhaps the most instructive way of categorizing is by how the metasurface imparts a phase delay to the electromagnetic wave. For a traditional lens this is done by varying the path length different rays of light have to traverse through the lens, taking into account how the light refracts at the surfaces. As we have mentioned regular diffractive optics does the same but wraps the phase by 2π. With metasurfaces it is likewise possible to change the phase by varying the 8CHAPTER 2. STATIC METASURFACES optical path distance, but instead of varying the physical distance through the material this is done by varying the local effective refractive index seen by the propagating light. Another technique is to make use of the phase delay that comes in connection with a resonance, we shall briefly discuss both of these options after looking at a third way to control the phase. Geometric phase When converting one state of polarization into another there is a contribution to the phase change which is dependent on how the polarization is changed called the geometric phase, or often the Pancharatnam-Berry phase. It arises due to the geometry, and more specifically the curvature, of the parameter space describing the degrees of freedom - which for polarization can be represented by the Poincar´e sphere [17]. As such, it is not limited to polarization effects but also appears in other areas like the spin of an electron which similarly can be described by a Bloch sphere, while also being relevant for more complicated systems [18]. To illustrate the most used example, we look at transmission through a birefringent material, with ordinary and extraordinary axes aligned in the orthogonal ˆxand ˆydirections as described by a Jones matrix J(0) = 1 0 0eiδ, where we assume perfect transmission amplitude, and ignore the dynamic phase change by pulling out eiδxand set δ=δy−δxbeing the phase difference between the two linear eigenpolarization states upon transmission. Following the same procedure as for example in [19] we can rotate the basis by an angle θand change to a circular polarization basis with unit vectors ˆ l= (ˆx+iˆy)/√2 and ˆr= (ˆx−iˆy)/√2 giving a new Jones matrix ˜ J(θ) = 1 2(1 + eiδ)1 0 0 1+1 2(1 −eiδ)0e−i2θ ei2θ0.(2.1) From this equation it becomes immediately apparent that if the incident light is circularly polarized, and we design the material to act as a half-waveplate with δ=π, then we can impart a phase of 2θto the cross-polarized light by varying the amount of rotation θ. The usefulness of this comes from the fact that with metasurfaces it is possible to vary the direction of the birefringence locally across a surface as indicated in Figure 2.2. This way, a blazed grating can for example be realized by gradually varying θalong one direction of the surface. 2.1. OVERVIEW AND STATE OF THE ART 9 Figure 2.2: aand b, a polarization state going through two elements with eigenpolarization direction rotated compared to each other. In both cases the polarization is changed from circular to the opposite handedness, but there is a difference in the phase of the transmitted light which is dependent on the orientation of the eigenpolarization axes. cSEM image of a geometric phase metasurface made by Christopher Dirdal at SINTEF. Note that the two orthogonal circular polarization states acquire opposite phases, and these types of metasurfaces are therefore inherently polarization dependent. For some applications this can be used as an advantage, while for other applications it might mean a reduced efficiency. For example, in [20] the authors demonstrate a lens which is focusing for one helicity while being defocusing for the orthogonal one. Advantages with this technique include the fact that the phase is not as directly wavelength dependent as with some of the other effects, and might therefore be more broadband. Furthermore, these metasurfaces often only need one nanostructure geometry with an even fill factor, which can make it easier to optimize fabrication and get high phase resolution with very even amplitude. In the above discussion we assumed perfect transmission and chose δ=π, however, it is possible to vary the birefringence to control both phase and amplitude. If assuming only one circular polarization state is incident and filtering out any light not converted to the orthogonal polarization afterwards, Equation (2.1) tells us that the amplitude of the transmitted light will be dependent on the degree of birefringence and the phase will be a combination of the dynamic and geometric phase, this has been demonstrated in [21]. It is worth noting that one can also use elliptic or circular eigenpolarization states, which makes it possible to independently control elliptic or linear states 10 CHAPTER 2. STATIC METASURFACES Figure 2.3: aIn-plane view of silicon pillars that function as an effective medium for light with wavelength 1.55 µm. bTop view of similar silicon pillars - the varying diameter of the pillars changes the effective refractive index and thus the phase delay upon transmission. Metasurfaces made by Christopher Dirdal at SINTEF. of polarization [17]. However, this can require more complicated unit cell structures [22,23]. Another technique that similarly gives control over general polarization states but with potentially simpler fabrication, is by combining the geometric phase with other phase control techniques like the truncated waveguide method [24]. Truncated waveguides Figure 2.3 is an illustration of dielectric pillars protruding from a surface. The phase shift for light propagating through such a metasurface can be understood as propagation through a media with effective refractive index in between those of the pillars and surrounding media ϕ=2π λneff h, with hbeing the height of the pillars and neff the effective refractive index. Keeping the height of all pillars the same to simplify fabrication, variation of the phase can then be achieved by altering the diameter or shape of the pillars to change neff . This effective refractive index can be estimated as the fundamental mode index of a single step-index circular waveguide model [25], 2.1. OVERVIEW AND STATE OF THE ART 11 with the largest errors being due to multiple reflections at both ends of the pillar [26]. For normal incidence and with isotropic structures such metasurfaces will be polarization independent, but it is straightforward to make polarization dependent components by for example using elliptic or rectangular cross-sections, which can be combined with the geometric phase to control general polarization states [24]. Whether they are polarization dependent or independent, the phase is directly dependent on the wavelength as well as being sensitive to the incidence angle, and most of these metasurfaces have been designed for single wavelength applications. Nonetheless, there are many different techniques being pursued to increase the bandwidth or get control over the spectral and angular dispersion for other purposes [27]. A couple examples include increasing the complexity of the unit cell with multiple or more complicated pillars, giving more parameters to adjust independently [28,29], adding a reflective back surface [30] and cascading several metasurfaces [31]. For the truncated waveguide method in general, advantages include high efficiency when using lossless dielectric materials, and localized modes that reduce cross-talk between neighboring structures and simplifies design. On the other hand, a drawback is the relatively tall structures that must be made, roughly around one wavelength depending on the refractive index contrast between the pillar and surrounding material. This leads to aspect ratios and varying fill factors that can be challenging to fabricate, especially when wanting to ramp up production past single prototypes. It is also possible to use dielectric structures with smaller aspect ratios, these do not function the same way but rather make use of resonances [26]. Resonant phase As physicists often do [32] we shall contemplate the forced harmonic oscillator ¨x+ Γ ˙x+ω2 0x=1 mF(t), with Γ being a damping term. Assuming a time-harmonic behavior, with the same frequency as the driving force we can write (−ω2+iΓω+ω2 0)x0eiωt =1 mF0eiωt, which can be slightly rewritten to emphasize that the inertial, damping and restoring terms have different phases with respect to the driving force x=x0eiωt =F0eiωt/m eiπω2+eiπ/2Γω+ω2 0 .(2.2) 12 CHAPTER 2. STATIC METASURFACES Clearly, when driving the oscillator way below the resonance frequency ω≪ω0 the ω2 0term dominates (we are assuming the damping term is small), which means the oscillations are in phase with the driving force. Meanwhile, at the resonance the inertial and restoring terms cancel, delaying the oscillation phase by a quarter of a period, which turns to half a period for ω≫ω0when the driving force is so fast that the inertial term dominates. These considerations still apply when taking into account the radiation reaction force by adding a damping term proportional to ... x[12,33,34]. If we take Equation 2.2 to be describing a charge in a potential being driven by an applied electrical field, we can use it to find the polarization field which gives us the well known Lorentz model of the dielectric response - see for example [35]. In this case, however, we are interested in this because it suggests another way to design a metasurface: Make a resonant system where you can vary ω0, for a certain ωthe phase of light scattered by this resonance can then be controlled. For example, a thin metallic bar being hit by an EM wave polarized along it’s long axis will have an electric dipole resonance with resonant wavelength about twice the length of the bar [13], and adjusting this length will therefore change the phase of the scattered light. Note that this estimate is not accurate at optical frequencies, where metals can no longer be considered as perfect conductors. The problem with this simple approach is that it only allows controlling the phase to within a value of π, while full control of the scattered field requires a phase range of 2π. A couple main techniques have been developed to achieve full phase range and high efficiency. Firstly, dielectric particles with a high refractive index and a transverse size approximately equal to the wavelength in that material can be designed to have overlapping electric and magnetic resonances which have the same amplitude and are in phase. This condition, known as the first Kerker condition [36], results in cancellation of the back-scattered field enabling high transmission efficiency in addition to the 2πphase shift. Yet, when varying the size/shape of these structures to change the phase the transmission is affected [37,38], because the dipole resonances are no longer perfectly overlapped, in addition to coupling between neighboring structures affecting the total response [39]. For these reasons the truncated waveguide approach results in higher efficiency while this resonant approach gives more enhanced fields, and can be easier to fabricate as the aspect ratios are not as large [40]. Meanwhile, for phase controlling plasmonic metasurfaces we can categorize them roughly in two methods, one that can be used for transmission and one that works in reflection. The transmissive ones combine resonant effects with the geometric phase to get full phase coverage. Two common configurations are using v-shaped antennas or split ring resonators, with one symmetric mode 2.1. OVERVIEW AND STATE OF THE ART 13 Figure 2.4: aIllustration of a metasurface comprised of a reflective substrate, a dielectric spacer and plasmonic nanoantennas of varying sizes. bSimulation of a gap surface plasmon resonance, yellow areas are gold, while the rest is air. The blue indicates areas with no field enhancement while red indicates large field enhancement. cSEM image of a polarization independent blazed grating metasurface. dSEM image of a polarization dependent blazed grating metasurface, notice the anisotropic structures. The scale bar is for both SEM images. The metasurfaces were made by Chao Meng at SDU. and one antisymmetric mode, and where the asymmetric geometry allows the antisymmetric mode to couple with incident light [41]. Although they are simple to fabricate, being dependent on the geometric phase they are polarization dependent and the efficiency is dictated by the cross-polarization efficiency, which is limited for these kinds of structures - experimental demonstrations are have had around 10 % efficiency while theoretically the limit is 25 % largely due to symmetric forward and backwards scattering [42–46]. More complicated configurations such as dielectric structures covered with a thin layer of metal deposited on top have shown higher efficiency up to around 40 %, with larger efficiencies being possible due to canceling the back-scattering using several resonances [42,43]. A simple and efficient way of breaking the forward/backward symmetry is to add a reflective surface, in which case your metasurface obviously will work in reflection, bringing us to gap surface plasmon metasurfaces. Gap surface plasmon metasurfaces These metasurfaces consist of a small plasmonic antenna separated from a ground plane by a dielectric spacer, see Figure 2.4. When the dielectric spacer 14 CHAPTER 2. STATIC METASURFACES is thin enough, surface plasmon polaritons [47] on the two metal-dielectric interfaces can interact through near field coupling [48]. As a result, the system acts as a Fabry-P´erot cavity for the gap surface plasmon modes with the cavity size being determined by the length of the antenna [49]. In principle higher order modes are possible, but we shall stick to the lowest order antisymmetric mode, where the currents in the antenna and ground plane go in opposite directions and the system acts as a magnetic dipole. If the parameters are chosen appropriately, see Section 2.2, this results in a deeply sub-wavelength resonator that can be easily tuned by adjusting the length of the antenna, which has a strong scattering cross-section and a large phase range [7,48, 50]. This system can be used with the geometric phase, but in contrast to the transmissive plasmonic structures it does not need geometric phase to achieve full 2πphase range. One way of understanding this is that away from the resonance the system acts as a mirror, applying a πphase shift to the reflected electric field, while at resonance the system acts as a magnetic dipole and thus as a magnetic mirror - applying the πphase shift to the magnetic field and thus the electric field is reflected with zero phase. Continuing past the resonance will continue changing the phase until the electric field is again reflected with πphase [13,51]. In practice however, some of the phase range is usually sacrificed in order to have less absorption losses at the resonance, this trade-off is done by adjusting the dielectric layer thickness and has the added advantage of broadening the resonance, thereby simplifying fabrication as the size tolerances become larger. Significantly more than 2πphase range is also possible, by introducing several detuned resonators for each unit cell [52]. Furthermore, it is straightforward to control the phase independently for orthogonal linear polarization states, as we shall demonstrate in Section 2.2, by adjusting the two in-plane dimensions of the antenna, elliptic or circular eigenpolarization states are also possible with more complicated unit cell structures [53]. We should note that for larger separations between the ground plane and plasmonic antenna the near field coupling ceases and instead we get a Fabry-P´erot resonance between the ground plane on one side, and the metasurface nanostructures on the other [48,54]. This will be discussed in more detail in Chapter 3, a comprehensive review is also found in [55]. It is also worth noting the analogy to reflectarrays [56–58], which share many characteristics but have some implementations which are not currently feasible on the nanoscale (and at optical frequencies) such as connecting structures with individually tunable varactors [59]. Although they are limited to working in reflection, there are several advantages with gap surface plasmon metasurfaces. Other than simple fabrication, they can be broadband and efficient, an example being 80% efficiency and 2.1. OVERVIEW AND STATE OF THE ART 15 150 nm bandwith at 850 nm using gold [50], in addition to working for a large range of incidence angles. The bandwidth can also be extended by introducing more complicated resonators, at the expense of efficiency [60]. The losses are mainly due to absorption, and can be used to control amplitude in addition to phase, or to make narrowband as well as broadband absorbers [48]. By using gold, the metasurfaces can also benefit from established methods of biofunctionalization to make sensors [61]. Material-wise, though gold is suitable for fabrication, biosensing and its chemical stability, it does however have a lot of absorption in the visible frequencies and consequently the efficiency suffers at these wavelengths. Silver is a good low-loss option [62], but lacks chemical stability and like gold is not compatible with CMOS processing. Aluminium is a CMOS compatible alternative [63] with more losses than silver, but less losses than gold at shorter frequencies, and is chemically protected by the naturally forming oxide layer. Finally, other possibilities are also being developed, such as conductive oxides [64]. For example, titanium nitride is CMOS compatible and has been used to make plasmonic nanostructures with characteristics similar to those made of gold but with lower losses when using wavelengths around 500 nm [65]. Other kinds of metasurfaces The above mentioned categories focus on how phase is imparted, while it is also possible to make metasurfaces that do not aim to control the phase but rather focus on the amplitude of the reflected or transmitted light. A well known analogy to more traditional diffractive optics is the Fresnel binary zone plate where, instead of a varying phase profile, a binary grating is used to make a focusing lens by selectively letting through parts of a beam that will interfere constructively at the desired focal spot. In [66] this principle is implemented to make an achromatic metasurface lens for visible light. This is accomplished by cascading three separate metasurface layers, each layer consisting of an array of plasmonic nanodisks. In addition to separately varying the nanodisk diameters and spacings, the authors also use different materials (gold, silver and aluminium) in each layer to optimize the combined lens for red, green and blue wavelengths. Another example is found in [67] where an array of gold disks are separated from a ground plane by a thin dielectric spacer, but instead of being optimized for phase control the structures are tailored for absorption. By deliberately analyzing and taking into account the amount of damping in their materials, the authors achieve near perfect absorbance over a broad range of angles and with minimal dependence on polarization. Notably, the absorbance is very sensitive to the refractive index of the surrounding dielectric 16 CHAPTER 2. STATIC METASURFACES media, and the system is therefore demonstrated as a plasmonic sensor. Another type of metasurface that does not fit the categories above is what can be classified as a nonlocal metasurface. So far we have only discussed arrays of structures where the response is local, which is to say that the response is only determined by the structures in the immediate vicinity - often with minimal cross-talk between neighboring structures. In many cases this is on purpose as it makes design simpler. However, systems where there scattering at one location is dependent on fields and structures over a broad area can give a high degree of control over the spectral and angular properties [68]. Furthermore, such metasurfaces can be utilized to greatly increase the effective interaction length between matter and light passing through a thin metasurface, which can be used to increase nonlinear effects [69]. Thus, metasurfaces can be used not only to change the phase, amplitude and polarization of light, but also the wavelength. It should be noted that nonlinear effects can also be enhanced in other ways such as through field enhancement [70,71]. 2.1.3 Applications The number of possible applications for optical metasurfaces is seemingly endless, with an ever growing list of promising alternatives [4,14,15]. No exhaustive overview shall be attempted here, but rather a few selected topics with some examples will be mentioned to give an impression of the breadth of the research field. Metasurface lenses [28,72] and related components like axicons [28] enable miniaturization of optical systems which is of great importance for both imaging and projection systems for consumer electronics, but also higher-end markets such as endoscopes [73]. For emerging applications like augmented reality, off-axis optical components are especially interesting as it allows to combine these projection and imaging systems seamlessly and unobtrusively into the line of sight [74,75]. Pattern projection is a similar high-volume market where metasurfaces are already being used in dot-projection for 3Dmeasurements commercially [3] and with further optimization already demonstrated [76]. More generally of course, metasurfaces are not limited to projecting dots and one can imagine much more sophisticated techniques utilizing all the research done on hologram generation [77,78]. Together with beam steering, for example for lidar [79], these areas are expected to account for the majority of the market in the near future [3]. Sensors are another big category, and we have already discussed the plasmonic refractive index sensor in [67]. Another example can be found in [80], where a hyperspectral system for biosensing is presented. The scheme con- 2.3. METASURFACE FABRICATION 23 Figure 2.9: aDark field microscope image of the exposed and developed resist for a series of dose tests, with close up dark field and clear field images in b and c. Note that this is an earlier design than that shown in Figures 2.8,2.10 and 2.11, and has an elliptic aperture. 2.3 Metasurface fabrication The fabrication process starts with a die from a polished silicon wafer, on which a 3 nm titanium, 120 nm gold, 3 nm titanium, and 60 nm SiO2are deposited using evaporation (Tornado 400 Cryofox). The titanium layers are to ensure good adhesion. Subsequently, a 100 nm layer of poly(methyl methacrylate) (PMMA A2, MicroChem) is deposited using spin coating. This PMMA layer functions as electron beam resist and is patterned with a SEM (JEOL JSM-6500F field-emission SEM with a Raith Elphy Quantum lithography system), before being developed. After this process, the PMMA should cover the substrate everywhere except for at the locations where the nanobricks are intended to be. Note that when combining the metasurfaces with MEMS as described in Chapter 3, the nanostructures are fabricated on a glass substrate (Borofloat 33, Wafer Universe), and the PMMA is coated directly on the glass. Since there is no conductive gold layer in this case, to prevent charge buildup during exposure a 40 nm thick conductive polymer layer (AR-PC 5090, Allresist) is spin coated on top of the PMMA prior to e-beam exposure and removed prior to PMMA developement by rinsing in DI water. Following development, the structures are inspected in an optical microscope, see Figure 2.9, before another 3 nm titanium adhesion layer and 50 nm gold are deposited (Tornado 400 Cryofox). Finally, the chip is submerged overnight in acetone which desolves the PMMA and completes the lift-off process. SEM images of resulting structures are shown in Figure 2.10. 24 CHAPTER 2. STATIC METASURFACES Figure 2.10: SEM images of metasurface lenses for collimation of a fiber output. aMetasurface lens with diameter 30 µ.bClose up image of structures in a. cMetasurface lens with unsuccessful lift-off, large parts of the circle is covered by connected gold (bright areas). Figure 2.11 is an image of the collimating metasurface lens being tested. The samples were tested using a super-continuum laser with a variable filter (SuperK Extreme, NKT Photonics). The angular dispersion was measured to be around 0.05 degrees per nm as expected from Equation 2.3, while the divergence of the resulting beam was estimated to 1 degree by comparing with the output from a fiber with known divergence as seen in the Fourier image plane. Additionally, one sample was tested with a 100 fs, 250 mW laser for 20 minutes without showing any signs of degrading. Although this preliminary study shows great promise for enabling a miniature system for temporal focusing in 2-photon microscopes, for a next iteration it would be advantageous to increase the dispersion by using a metasurface where one can control the chromaticity such as demonstrated in [30], conversely, the same type of metasurface could be used to reduce angular dispersion for applications where it is undesirable. 2.3. METASURFACE FABRICATION 25 Figure 2.11: One of several metasurface lenses is illuminated at an angle by a single mode fiber (dark shape protruding from the left). The illuminated metasurface collimates the light and reflects it in the normal direction towards the camera (bright circle), the unilluminated metasurfaces can be seen as dark circles. A low intensity and wide beam is used to light up the field of view. An alignment marker (cross) can be seen at the bottom of the picture. 26 CHAPTER 2. STATIC METASURFACES Chapter 3 Active metasurfaces 3.1 Overview and state of the art For passive metasurfaces the optical behavior is locked at the time of fabrication. Active metasurfaces, on the other hand, have the ability to adjust the optical response at some later point. This change can be controlled on purpose by an external system, or it could occur as a result of some physical process for which the metasurface is designed to measure or react to. The last case is evidently useful for sensing purposes, while the former has many technological applications such as varifocal lenses, multiplexing, beam steering and polarization control. The large interest and participation in the rapidly expanding field is therefore of no surprise, and there have been temendous amounts of developments over the last couple years [53,103–105]. To achieve dynamic functionality, we start from the basic principles of static metasurfaces but incorporate some characteristic that can be altered postproduction. An example could be how a localized surface plasmon resonance changes frequency as the refractive index surrounding the antenna is altered, which could be due to the presence of some measurand or by controlling the properties of the media in some other way. Another alternative is to alter the geometry of the system, notably, this is the method used for the articles in Chapter 5. As the reader by now surely is getting accustomed to, we shall summarize this field in a brief manner with a limited set of examples, by touching upon some of the main principles used to acquire tunability, while saving MEMS-based systems for the next section. If you want to actively switch a refractive index, liquid crystals are a great 27 28 CHAPTER 3. ACTIVE METASURFACES option. They consist of anisotropic molecules that can be aligned and controlled by applying an external voltage, which changes the refractive index of the material (by changing the orientation of the ordinary and extraordinary optical axes). This principle can be used to make tunable metasurfaces functioning both in transmission and reflection, as well as for controlling phase and amplitude [106,107], and has even been used for tunable nonlinear effects [108]. Advantages include the large optical efficiency and change in refractive index that are possible, as well as a mature and reliable technology platform. The main disadvantage with liquid crystals is that the time it takes to reorient the molecules limits switching speed to around 1 kHz [105], although research into new types of molecules could improve this to some degree [109]. Another effect with large refractive index change is the switching between crystal and amorphous phases in some materials such as GeSbTe (GST) and VO2For GST, for example, this is accompanied by a 50 % reduction of the refractive index, depending on the wavelength. This is already used in optical memory storage at really fast operation speeds. However, it is turning out to be difficult to realize the same rewriting speeds for metasurfaces, as it is not possible to include the same protective layers and electrodes [110]. Nonetheless, high quality metasurfaces with ∼70 −80 % efficiency have been demonstrated for both materials, and for switching speeds on the order of 1 kHz [111,112]. It is worth noting that the switching from crystal to amorphous state is usually much faster than opposite, and can be used for example for optical limiting in high-power applications [113]. In some noncentrosymmetric crystals the refractive index can be altered in proportion to an applied electric field. Called the Pockels effect, this change only requires a slight displacement of the ions in the crystal lattice and can be used to modulate the refractive index with switching speeds well into the GHz range [114]. The catch, however, is that these materials, for example LiNbO3, PZT and BaTiO3are challenging to use in nanofabrication processes, and the typical refractive index change is small. High speed demonstrations are therefore often based on short spectral shifts of narrowband resonances for amplitude modulation [115]. A further alternative for such high-speed devices is using electrical doping, also referred to as plasma dispersion effect or Drude effect [114,115], which can be used to alter the plasma frequency of conductive oxides by changing the density of free charge carriers [116,117]. The effect can also be used to adjust the properties of 2D materials such as graphene [61]. In both cases the effect can be strong, but in both cases the effectiveness of these systems is limited due to the very thin region of the property changes - by the very nature of 2D materials and by shielding effects in conductive oxides [114]. Similar charge doping can also be used to adjust the refractive 3.1. OVERVIEW AND STATE OF THE ART 29 index of multiple quantum well systems, in this case the problem is opposite: The thickness can be increased by adding more layers, but the refractive index change is limited [105]. Moving away from refractive index modulation and instead looking at how the geometry can be altered, one very tempting idea is to place the metasurface structures on a stretchable material, thereby making the period directly tunable [118,119]. Current demonstrations are limited in the sense that it is hard to imagine a robust, compact system for reliable and high speed operation. Nonetheless, they enable drastically different tuning opportunities than other methods, like complete restructuring of the geometry [120] and could be very relevant for applications such as sensors for monitoring structure deformations [62]. A different deformation technique which is easier to implement control systems for is thermal deformations. The thermal deformation of a single material is not much over nanoor microscale distances, but when combining several materials with different thermal expansion coefficients together, it is possible to make structures that move considerably upon temperature changes due to internal stress. Thin bimaterial structures can thus be used to change angles [121,122] or lateral positions [123] of structures relative to each other. It is also possible to integrate heating into the device itself [124], and to use deformations due to structural changes [125]. Finally, within the field of nanokirigami [126] there is a long list of microand nanostructures with complex deformation patterns that could have very interesting optical behavior, and that might be controlled using MEMS-techniques. The structures in [126] for example show a strong circular dichroism that vanishes when they are compressed using an optical fiber, while the structures in [127] show a large change in reflectance when deformed by a pneumatic pressure difference. 3.1.1 MEMS metasurfaces In MEMS metasurfaces, the mechanical movements of MEMS are used to alter the optical response of the metasurface in some way. There are several advantages with this approach to designing active metasurfaces. Firstly, by not requiring the optical change to originate in some material effect you are more free in the choice of materials [128,129]. Furthermore, the mechanical movements can be used to make large changes in both phase and amplitude, and can be integrated with high efficiency metasurfaces. To drive these movements there are four main actuation techniques, namely electromagnetic, piezoelectric, electrothermal and electrostatic [130]. Electromagnetic based MEMS generate a magnetic field in order to interact with an external magnetic field, achieving large movements at the expense of a less compact system. 30 CHAPTER 3. ACTIVE METASURFACES In some cases this might be advantageous for MEMS only intended to function as mirrors [131], but for metasurfaces these large movements are often not required. Piezoelectric MEMS are more compact, but also have less range and a more complicated fabrication procedure, they are presented in the next section. Electrothermal MEMS can demonstrate large movements with strong forces, but have limited speed and use more power. Interestingly, they can also offer complicated folding patterns, as demonstrated in [124] using a bimorph structure that folds in multiple directions. Meanwhile, electrostatic MEMS utilizes capacitive forces between electrodes to move. They represent the most common type of MEMS, as they are relatively simple to design and fabricate, have rapid response times, low power consumption and large flexibility with both in-plane and out-of-plane forces available using comb drives and capacitive plates. Drawbacks include nonlinearity of the driving force, limited movement range and requiring high voltages to operate. In addition to these four main operation modes which are usually actuated electronically, it is possible to design MEMS intended to be optically activated, which can be especially exciting for integration with metasurfaces. For example, by making a MEMS that absorbs and reacts to one sets of wavelengths while monitoring it in another wavelength, several groups have demonstrated imaging in mm and THz wavelengths [132–134]. The ”engines” mentioned above can be used to generate an amazingly diverse set of mechanical behaviors, but many of the most common can be categorized into the following: •Cantilevers are simple to realize and can have both large angular and out-of-plane motion, an interesting example is presented in [135], where cantilevers with very large motion are used to cover or expose plasmonic structures which could be used as a rare-earth-mineral-free color display. •Piston motion, or a motion where a structure is translated in the outof-plane direction is especially relevant for many optical applications, and has been used to demonstrate high-speed modulation of absorption frequency in both the visible [136] and infrared wavelength ranges [137]. •Curving membranes are used in MEMS mirrors for varifocal reflective lenses [138], and might be relevant for combining with metasurfaces. •In-plane translation, which for example has been used to make a MEMSbased Alvarez lens [139]. •In-plane rotation is another interesting modality, and has recently been 3.2. PIEZOELECTRIC MEMS 31 used in a MEMS device together with piston motion to probe the interaction between layers of 2D materials [140]. •Tip/tilt motion is another common type of movement, which is useful for MEMS mirror scanners and thus has seen a lot of optimization for large deflection angles. By integrating a metasurface lens on such a mirror, a focusing profile can be integrated efficiently and in the same optical plane as the angle deflection [141]. Before moving on to piezoelectric MEMS we will mention that for long wavelengths, MEMS based devices can be used as individual metasurface pixels [142,143]. However, they are too big to do so for the visible and near infrared wavelengths, which requires new development of movable structures for sub-µm sized devices [128]. A promising development in this direction can be seen in [144], where electron beam lithography and ion beam etching is used to make spiral structures with a ∼2µm period that can be deformed electrostatically. The structures are controlled collectively but can be designed with individual characteristics, and the extremely light weight results in a large modulation frequency above 10 MHz. Figure 3.8 at the end of this chapter contains a comparison of the efficiency and switching speed for some selected metasurface demonstrations related to the effects presented here, both for MEMS and the other active metasurface modalities. 3.2 Piezoelectric MEMS A piezoelectric material changes the internal polarization when a stress is applied, and conversely becomes strained when an electric field is applied across the material [145]. As such, these materials are very useful for electromechanical transduction, and bulk piezoelectrics are often used for applications requiring small but very accurate displacements. These bulk piezoelectric devices usually need high voltages to operate, as the effect is proportional to the electrical field, and a strong field translates to a large voltage if the electrodes are far apart. On the other hand, if the electrodes are close together the opposite is true, and thin-film piezoelectrics can therefore be employed to actuate MEMS without the large voltages common in other applications. One material often used for this purpose is lead zirconate titanate, or PZT, which has considerably larger piezoelectric response than most other materials - especially for certain multi-phase polycrystalline structures [5]. Figure 3.1 is a schematic example of a PZT-based MEMS cantilever. An electrode-PZTelectrode stack is deposited on a substrate and parts of this substrate is etched 32 CHAPTER 3. ACTIVE METASURFACES away to form a thin membrane. When a voltage is applied across the PZT, the material - which is clamped to what is left of the substrate - experiences an outof-plane expansion and an in-plane contraction. The membrane is thin in the out-of-plane direction, however, the electrodes typically cover a much larger area and the in-plane stresses therefore add up to a large in-plane stress on one side of the membrane, causing the cantilever to bend. The resultant large mechanical movement at low voltages is one of the main advantages with these thin-film based piezoelectric MEMS, together with the low leakage current resulting in ultra-low power operation on the order of 10-100 nW depending on the electrode surface area and applied voltages. The disadvantage with PZT is that it has considerable hysterisis, and thus accurate control requires some kind of feedback system [146]. An example of the type of material stack used to fabricate the MEMS mirrors in this work is shown in the insert of Figure 3.1. The starting point is a silicon on insulator wafer which has a buried silicon oxide layer between the silicon handle wafer and the silicon device layer. This device layer will form the passive part of the membrane, while the buried oxide is used as a stopping layer for the deep reactive ion etching used to remove the handle wafer and free the membrane. On top of the device layer, a silicon oxide layer is thermally grown to isolate the electrodes from the silicon while additionally acting as a stress-compensation layer. If adjusted to the correct thickness this oxide layer minimizes the inherent stress of the final membranes, or alternatively it can be used to create some nonzero intrinsic membrane curvature. On top of the oxide, the bottom electrode consists of a thin titanium adhesion layer, a platinum electrode and a thin layer of LaNiO3. The platinum forms a suitable flat surface for the PZT while also acting as a chemical barrier between PZT and silicon, and the LaNiO3forms a seed layer for the PZT deposition in addition to improving device lifetime by preventing the build up of a passive layer in the PZT [5]. Thereafter, PZT is deposited using either pulsed laser deposition or chemical solution deposition, typically with a thickness between 1 and 2 µm. Finally, a titanium and wolfram adhesion layer and gold top electrode are deposited on top, these do not need a LaNiO3layer as long as the applied field is always going from the top to the bottom electrode. More details on the stack and the many considerations can be found in [5]. Shown in Figure 3.2 is a typical case for how a piezoelectric MEMS mirror can be designed. Four cantilevers with piezoelectric thin films suspend a silicon mass that has a reflective coating to act as a mirror. By applying voltages to specific areas of each cantilever, this mirror can then be moved in a pistonmotion along the direction normal to the mirror surface, or it can be tilted by moving some cantilevers in one direction and some in the other. Moving the 3.3. COMBINING PIEZOELECTRIC MEMS AND METASURFACES 39 Dynamic waveplate During the demonstration of the switchable metasurfaces mentioned above it became clear that certain anisotropic nanostructures give a phase upon reflection that for one polarization state changes drastically when adjusting the air gap, while for the orthogonal polarization state it remains unaltered. The evident idea was then to use this behavior in order to realize a waveplate with an adjustable phase delay between the two eigenpolarization states, with the associated problem being the polarization dependent absorption at certain mirror-metasurface spacings, when the light interacts strongly with the metasurface structures. A solution was found by choosing a set of nanostructure dimensions and a lattice periodicity that give strong coupling between resonators for one polarization state and with minimal interaction for the orthogonal one, the resulting device is presented in [101] found in Chapter 5. This strong coupling gives near perfect reflection at the metasurface layer for the resonance wavelength, and has been explored in several similar settings but with static cavities, and with a larger focus on the related occurring effect of perfect absorption [55,149,150]. Meanwhile, the orthogonal polarization state is transmitted through the metasurface and is reflected by the mirror. Simply stated, one polarization state is reflected at the metasurface and the other at the mirror, with the separation distance giving a relative phase shift between the two, while a more accurate treatment needs to include additional reflections through the Fabry-P´erot equation. In this way, we were able to make a dynamic waveplate with a stable, high and largely polarization-independent reflection amplitude with full 2πbirefingence tunability. A transmissive version would be interesting, but there are some fundamental challenges. Looking at a simplified version of the Fabry-P´erot equations for transmission and reflection, here assuming a cavity with symmetric reflection and transmission coefficients on both sides equal to rand t, and with a propagation phase shift across the cavity of ϕ, we have rtotal =r+t2rei2ϕ 1−r2ei2ϕ, ttotal =t2eiϕ 1−r2ei2ϕ. For the reflective dynamic waveplate it was relatively straightforward to make |r| ≈ 1 for one polarization and let the orthogonal polarization experience the phase shift from the cavity, avoiding large changes in the amplitude by minimizing |r2|. However, in transmission both polarizations will necessarily experience the propagation phase across the cavity at least once. It is of course 40 CHAPTER 3. ACTIVE METASURFACES possible to make one polarization state interact strongly with the cavity and the other not, but this strongly affects the transmission amplitude of the interacting polarization state, thus reducing efficiency - and perhaps even more problematically introducing uneven efficiencies between the different polarization states. A solution might be to not work in the Fabry-P´erot regime but rather using near field coupling, for example using a system along the lines of [43], where an array of plasmonic antennas are in close proximity to a metal layer with an array of holes. Nonetheless, it is unclear how one would keep a low reflection for all settings and simultaneously achieve a full 2πphase range. Fabry-P´erot operation Article 3 in Chapter 3, [151], compares the characteristics of the MEMSmetasurface platform when operating in the gap surface plasmon and FabryP´erot operation regimes. The efficiencies at the design wavelength are shown to be very similar, with only slight degradation when going to larger cavity lengths. Optimal structure sizes for the polarization independent blazed grating which was investigated are also nearly identical, within normal fabrication uncertainties at optical wavelengths. The main difference pertains to the bandwidth, which gets reduced at larger cavity lengths due to the wavelength dependence of the Fabry-P´erot resonances. Comparing the near field operation with operating at the first Fabry-P´erot resonance, the bandwidth was found to fall from around 20 % to 7 %. Tunable metalens doublet Utilizing the same type of MEMS, but in a different configuration, the device in [152] consists of two dielectric metasurface lenses operating as a transmissive doublet, in a way similar to what is done in [153]. One metasurface lens is mounted in a MEMS frame, basically a MEMS mirror with the mirror part removed, see Figure 3.5. This allows the distance between the two lenses to be altered, thereby changing the total focal length of the system. The two metasurface lenses are identical, and consist of silicon pillars placed in a geometric phase pattern. Thus, the circularly polarized light incident on the first lens is cross-polarized before hitting the next lens. As the metasurface is based on the geometric phase, this cross-polarized light would have experienced a flipped phase but for the fact that this second lens is flipped, reversing the rotation angles of the nanostructures, as seen from the side of the incoming light. In this way a MEMS displacement of 7 µm is converted to a focal lenght shift of 250 µm. 3.3. COMBINING PIEZOELECTRIC MEMS AND METASURFACES 41 Figure 3.5: One of two metasurface lenses combined to form a doublet. The aperture of the square metalens seen in the center of the photo is 1.5 mm. The other metalens (not shown) was kept static, while the one shown in the picture is placed in a MEMS frame that can be translated by about 7 µm to change the separation of the two lenses - thus adjusting the total focal length of the doublet. The lower left insert is a SEM image of the silicon pillars used to implement the geometric phase lens. The device was documented in [152]. 42 CHAPTER 3. ACTIVE METASURFACES Dynamic linear polarizer During the discussion of the dynamic waveplate above, it was mentioned that strong coupling was investigated in similar systems in connection with perfect absorption. In [154] this is used to create a variable linear polarizer, where the reflection of one linear polarization state is constantly around 98 %, while for the orthogonal state it is varied from 95 % to 7 %. The extinction ratio is thus adjusted from 1 to 13, with the simulations suggesting an extinction ratio above 60 could be possible with more accurate fabrication and mounting. Looking at other investigations, [149] was for example able to achieve 3 % reflectance, which would correspond to an extinction ratio tunability of 32 in our case. Large circular dichroism The waveplate and linear polarizer presented above have linear polarization states as eigenstates for the metasurface, meaning that if one of these states are incident the reflected state is the same but with an altered phase and/or amplitude. In [53] an asymmetric unit cell consisting of four separate plasmonic resonators is used to make a reflective device that can function as a standard mirror when the MEMS is in a specific position. Meanwhile, at a second MEMS position there is a large circular dichroism where one circular polarization state is fully absorbed while the orthogonal state is reflected and cross-polarized, as compared with the reflection from a mirror. The article explores the effect in the framework of exceptional points [155], where there is a simultaneous degeneracy in both the eigenstates and eigenvalues. Mode switching laser In Section 2.1.3 the use of static metasurfaces for mode control in laser cavities was mentioned. This is demonstrated with an active metasurface in [156], where a reflective MEMS-metasurface is used to make a laser in which the emitted light can be switched between a Gaussian mode and a mode with orbital angular momentum. The metasurface uses a similar nanostructure geometry as for the dynamic waveplate, but with dimensions scaled to function at a wavelength of 1030 nm, these structures are then rotated to impart a geometric phase according to the desired degree of orbital angular momentum. Thus, when moving the MEMS mirror the behavior of each individual metasurface cell can be switched between that of a half-waveplate and a mirror, giving the intended effect. Amplification is done using a polarization maintaining fiber, which is connected to a free-space cavity incorporating the 3.3. COMBINING PIEZOELECTRIC MEMS AND METASURFACES 43 MEMS-metasurface. By using the reflective device at a slightly oblique incidence (7◦) it is possible to have a Gaussian mode for coupling into the fiber on one side of the MEMS-metasurface, while keeping a orbital angular momentum carrying state on the other side, where an output coupler emits the laser output. Bilayer metasurfaces With a single metasurface layer combined with a MEMS mirror it is possible to switch between mirror behavior and that which is built into the metasurface. For some cases, such as the dynamic waveplate, this might entail several useful functionalities or even a continuous range. However, you only have independent control over one designed behavior. For example, when using a blazed grating metasurface, adjusting the cavity spacing will only alter the diffraction order efficiencies. By adding a second metasurface layer, this limitation is removed and it is possible to incorporate two independent functionalities, this is done in [157] - which is included in Chapter 5. The basic principle is depicted in Figure 3.6, where it is explained how a metasurface can be placed at the node of a standing wave pattern, formed when a monochromatic beam is normally incident on the metasurface-mirror system. In this case the system acts as a standard mirror, and the metasurface can even be invisible in a microscope image. When moving the mirror, the metasurface is no longer at the node and the designed functionality is switched on. Going back to having the metasurface at the node, it is also possible to add a second metasurface which will interact with the field, resulting in whatever behavior this second metasurface is designed for. Changing the mirror position now, however, will cause the field to interact with both of the layers, even when the separation between the two is set equal to λ/4, though this reduces cross-talk. To account for these interactions, including all the multiple reflections and transmissions, a transfer matrix method is used [150]. The article documents how this is done successfully for several different combinations of metasurface functionalities, with a key takaway being that the realized quality is better for the functionality only dependent on one of the metasurface layers. Also notable is the switching speed achieved, using a small MEMS mirror rise and fall times of around 5 µs are measured. Metasurface polarimeter Contrary to the title of this thesis, the last development is not an active metasurface but rather an integrated system based on a principle first described 44 CHAPTER 3. ACTIVE METASURFACES Figure 3.6: At normal incidence, the reflection of a monochromatic wave at a metallic interface causes a standing wave pattern between the incoming and reflected wave. Placing a metasurface in the extrema of the standing wave pattern as in awill give very different results than placing in the minima b, where the field in practice does not see the metasurface. In that way, cis practically identical to the case in a, but if the cavity length is altered the field will interact with both metasurfaces. An example of this using a single layer metasurface is shown in the two images: dAt one cavity length the metasurfaces (two large and six small circles) are visible; dwhen the MEMS is used to change cavity length the metasurfaces are no longer visible, although the alignment marker (cross) is still visible on the bottom left due to a slight tilt of the mirror. A thorough review on such cavity effects can be found in [55]. 3.3. COMBINING PIEZOELECTRIC MEMS AND METASURFACES 45 Figure 3.7: Showcasing of a metasurface polarimeter at SPIE Photonics Europe 2024. The metasurface polarimeter is documented in [158]. in [6], where a metasurface is used to split an incoming beam into six diffraction spots, the intensities of which are used to determine the polarization state of the incoming beam. The system, consisting of a metasurface, beam-splitter, camera and alignment components is presented in [158], to be found in Chapter 5. The design wavelength is chosen to be 640 nm, to make it suitable for integration in a setup for digital polarimetric histopathology [159]. This technique analyzes polarization changes from light scattered by tissue, with the goal of speeding up and improving medical diagnostic procedures. At 640 nm the absorption of gold starts being noticeable, and reduced efficiency is clearly shown in the simulations for shorter wavelengths. Still, at the nominal wavelength the system works well and is benchmarked against a commercially available polarimeter with good results, accurately determining the Stokes-components and the degree of polarization within 2 %. However, for efficient use in the digital histopathology setup with real tissue samples, it was determined that the metasurface polarimeter lacks sufficient dynamic range, and it is therefore suggested to replace the image sensor with individual diodes. In addition to improving dynamic range, this would greatly improve acquisition speed - especially compared to traditional polarimeters that employ a physically rotating quarter-waveplate. 46 CHAPTER 3. ACTIVE METASURFACES 3.4 MEMS metasurfaces, a comparison Table 3.1 is an overview of some key parameters for the piezoelectric MEMS metasurfaces discussed in the previous section. Regarding the efficiencies they are all significant, with the exception of the varifocal lens doublet, but this was in no part due to the MEMS as both the silicon chips lacked antireflection coating on the backside, and the cross-polarization efficiency of the structures in both lenses had room for improvement. The other efficiencies vary quite a bit, from 30 % for the bilayer metasurfaces to 95 % for the dynamic linear polarizers, reflecting the large range of different effects demonstrated. Similar results or better are expected if moving to longer wavelengths, where one has the combined factors of less (unwanted) plasmonic losses, as well as higher tolerance on what constitutes a short cavity length for improved bandwidth. For shorter wavelengths in the visible, one quickly runs into large resistive losses in gold, although the metasurface polarimeter demonstrates it is still a viable option for red light. Using aluminium, silver or conductive oxides as discussed in Section 2.1.2 could be an option for these wavelengths. Alternatively one could also switch to dielectrics, the metasurfaces in [30] for example consist of dielectric pillars in close proximity to a metallic mirror, and are used to freely design both the reflected phase and chromatic dispersion of light. The study is for wavelengths between 1440 nm and 1590 nm and uses high dispersion silicon meta-atoms, but the design could be scalable to the visible, especially if considering switching to silicon rich nitride - where one can tune the deposition process parameters to trade refractive index contrast and dispersion for less absorption [40]. When it comes to switching speed, the devices are all based on similar MEMS and have roughly the same switching speeds of aroud 100-400 µs with two exceptions. For the linear polarizer we suspect there was some defect in the MEMS causing slightly slower response, meanwhile, for the bilayer metasurfaces a smaller mirror (500 µm diameter) with shorter membrane was used, resulting in a switching speed of only 5 µs. Note that this MEMS could be used with any of the other concepts to achieve the same rate. Except for the varifocal doublet metalenses made using nanoimprint lithography, all the metasurfaces have been made using e-beam lithography with a total diameter of around 100 µm. For demonstration purposes the MEMS mirror diameter has therefore not been a limiting factor, but this might be the case for real-world applications, where one can end up with trade-off considerations between switching rate and the free aperture size. Regarding the limits of this platform, we have worked with diameters from 100 µm to 5 mm, and with mm-sized apertures the switching speed of these mirrors lies in the range of 3.4. MEMS METASURFACES, A COMPARISON 47 Table 3.1: An overview of some main characteristics of the developed MEMS and metasurface components. The component abbreviations refer to the previous sub-sections and stand for: gap surface plasmon (GSP), dynamic waveplate, Fabry-P´erot based metasurface, tunable lens doublet, linear polarizer (LP), circular dichroism (CD), mode switching laser, bilayer metasurface and metasurface polarimeter. The categories are efficiency, switching time (ts), design wavelength (λ), bandwidth (BW) and minimum cavity length (min(Ta)). a100 nm bandwidth is for the functionality where only one metasurface contributes, the other functionality has a shorter bandwidth. bBandwidth is strongly skewed towards longer wavelength than the design wavelength, due to strong absorption of gold in the visible frequencies. Eff. % ts[ms] λ[nm] BW [nm] min(Ta) Ref. GSP 56 0.4 800 160 50 nm [148] Waveplate 75 0.4 800 100 2.2 µm [101] FP 40 - 800 100 - [151] Doublet low ∼0.1 1550 - - [152] LP 95 2 831 <10 3.4 µm [154] CD 50 0.2 810 <10 1.5 µm [53] Mode switching 80 0.1 1030 - 465 nm [156] Bilayer 30 0.005 800 100a1.7 µm [157] Polarimeter 50 Static 640 >100b- [158] 48 CHAPTER 3. ACTIVE METASURFACES 10-20 kHz. There is room for some improvement with adjustments such as thinning the handle wafer section of the mirror mass, and trading movement range for higher resonance frequency by making a stiffer membrane. In the limit of these adjustments the MEMS will start to resemble a PMUT (piezoelectric micromachined ultrasound tranducer), and from a recent review article [160] it seems likely that relevant designs will be restricted to the 100 kHz range, although the combination of large aperture and short deflection is outside the scope of mainstream PMUT research. Note however, that if going to smaller apertures PMUTs are able to go high up in frequency while giving sufficient movement for switching of metasurfaces. To reach MHz frequencies with MEMS using large apertures it probably necessary with dedicated designs such as presented in [136], where the metasurface functionality is built into a suspended silicon structure that can be moved electrostatically. In order to reach high modulation frequencies this structure is also limited to having a small aperture, but the electrostatic actuation gives a device which can be more easily patterned into an array without too much non-functional area. Figure 3.8 compares a selection of active metasurfaces in the efficiencyswitching speed space, including the MEMS metasurfaces from Table 3.1, while highlighting what kind of basic principle is used for modulation. In this view the advantages of the demonstrated platform are clear, it can be used to realize active metasurfaces with high efficiency and with rapid response times. It is not suitable for ultra-fast modulation, but unlike some of the faster effects the MEMS-based approach provides full phase and amplitude tunability, and with good bandwidth for many functionalities. Compared to other MEMS metasurfaces the method of mounting a metasurface together with a general MEMS is quite attractive, as it allows the relatively complex MEMS production to be decoupled from the specific application the metasurface is designed for. In this way one production run of MEMS can be used for various applications, which has been especially useful for prototyping - this selling point might be more important for piezoelectric than for electrostatic MEMS, due to the more complicated fabrication. Disadvantages, on the other hand, include the collective modulation, or the lack of pixel-by-pixel control which applies to most other concepts too. By using a reflective mirror on the MEMS, the demonstrated devices are also limited to working in reflection, for applications where this is appropriate, however, it is an advantage since it improves efficiency. Losses in the visible frequencies are also a challenge, but should be possible to address by using other materials. Furthermore, due to hysterisis in the piezoelectric material, some kind of feedback mechanism is necessary for accurate control, this adds a layer of complexity but can be done in several ways, for example with piezoresistive elements, capacitive measurements or optical read out [146]. Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 2 of 11 ultraflat MEMS mirror serving as a moveable back reflector (Fig.1A). OMSs and MEMS mirrors are designed and fabricated in separate processing paths and then combined, ensuring thereby the design freedom on both sides and reducing the fabrication complexity. The choice of the piezoelectric MEMS to be combined with the GSPbased OMS is dictated by specific advantages of the former, including continuous out-of-plane actuation capability and low voltage/power operation (53), which enable the development of continuously tunable/ reconfigurable MEMS-OMS components with ultracompact sizes and low power consumption. With this platform, we experimentally demonstrate dynamic polarization-independent beam steering (Fig.1B) and reflective 2D focusing (Fig.1C). By electrically actuating the MEMS mirror and thus modulating the MEMS-OMS distance, polarization-independent dynamic responses with large modulation efficiencies are demonstrated. Specifically, when operating at a wavelength of 800 nm, the beam steering efficiency (in the +1st diffraction order) reaches 40 and 46% for the respective transverse magnetic (TM) and transverse electric (TE) polarizations (electric field parallel/perpendicular to the reflection plane, respectively), where 76 and 78% are expected from simulations, while the beam focusing efficiency reaches 56 and 53% (64 and 66% expected from simulations). Furthermore, the dynamic response of the investigated MEMS-OMSs is characterized with the respective rise/fall times of ~0.4/0.3 ms, characteristics that can be further improved by using MEMS mirrors optimized for bandwidth in the megahertz range. For example, by using MEMS actuated membranes to ensure ~30MHz of switching speeds (54–56). RESULTS Operational principle Similar to the conventional GSP-based OMSs (6–8,57), the proposed MEMS-OMS configuration represents a metal-insulator-metal (MIM) structure composed of a bottom thick gold layer atop a silicon substrate (MEMS mirror), an air spacer, and a top layer with 2D arrays of gold nanobricks on a glass substrate (OMS structure). The air spacer gap ta can be finely adjusted by actuating the MEMS mirror (Fig.2A). When the air gap is small (ta<200 nm), the optical responses of OMS unit cells are determined by the GSP excitation and resonance in the MIM configuration (57,58) and thus by nanobrick dimensions (8,57). To progress further toward the design of dynamically controlled MEMS-OMSs, several geometrical OMS parameters must be determined. First, we set the operating wavelength at 800nm and choose the OMS unit cell size of 250nm that should be substantially smaller than the operating wavelength (8,57). Assuming the smallest achievable air gap is between 20 and 50 nm, the nanobrick thickness tm is then optimized to achieve a wide phase coverage with large reflection amplitudes, resulting in the choice of tm=50nm (fig. S1). The nanobrick lateral dimensions, side lengths, are chosen to be equal to ensure the polarization-independent optical response. Analysis of the complex reflection coefficients of the OMS conducted for increased air gaps reveals that the phase gradient for different nanobrick side lengths progressively decreases, with the reflection phase and amplitude becoming independent on the nanobrick length at an air gap of ta=350nm (Fig.2,BandC). This drastic transformation in the optical response is related to strong dependencies of the GSP excitation (at normal incidence) and GSP reflection at nanobrick terminations on the air gap: Both decrease rapidly for increased air gaps, thereby attenuating and eventually eliminating the GSP resonance. The observed transformation of the reflection phase response (Fig.2C) implies a simple and straightforward approach to realize dynamically controlled MEMS-OMSs: For a given smallest air gap (for example, 20 nm), one can design any conceivable GSP-based OMS (59), whose functionality can then be switched on and off by moving the MEMS mirror. Hereafter, we demonstrate this approach by realizing dynamically controlled polarizationindependent beam steering and reflective 2D focusing. Polarization-independent dynamic beam steering: Design The MEMS-OMS design for realizing dynamically controlled polarization-independent beam steering requires the choice of the number N of unit cells in the OMS supercell that, in turn, determines the steering angle  for the given unit cell size =250 nm, refractive index of silica glass n=1.46, and light wavelength =800 nm: sin =/nN (6,8,57). Bearing in mind experimental conditions, we chose an OMS supercell consisting of 12 cells so that the steering angle is =10.5° in glass (corresponding to 15.5° in air), facilitating the characterization of well-separated 0th/±1st diffraction orders Fig. 1. 2D wavefront shaping with the MEMS-OMS. (A) Schematic of mirror-like light reflection by the MEMS-OMS before the actuation, i.e., with the initial gap of ~350 nm between the OMS nanobrick arrays and MEMS mirror. Incident light is specularly reflected by the MEMS-OMS regardless the OMS design. (B and C) Schematic of demonstrated functionalities, (B) anomalous reflection and (C) focusing (depending on the OMS design), activated by bringing the MEMS mirror close to the OMS surface, i.e., by decreasing the air gap to ~20 nm. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 3 of 11 with a 20×/0.42 objective. Following the approach described above, the phase response calculated with the air gap ta=20nm for different nanobrick lengths is used to select the 12 nanobricks (Fig.2C, red circles) and arrange them into an array along the x direction (Fig.2,DandE) to mimic the reflection coefficient of an ideal blazed grating: r(x)=Aexp(i2x/sc) (6,8,57), where A≤1 is the reflection amplitude, and sc=12 is the grating (supercell) period. The available phase range at ta=20nm is slightly more than 270° (the red dashed line in Fig.2C), implying that it is impossible to design a supercell with 12 different unit cells ensuring a constant phase gradient (the latter requires the phase range of 11×30°=330°). One possible approach to deal with this problem is to increase the phase (discretization) steps to 90° (fig. S2, A to E), so that the required phase range would decrease to 3×90°=270°, resulting in the possibility to compose the supercell from duplicated (sc=4×2=8) or triplicated (sc=4×3=12) cells (8). Our simulations suggested another approach, in which two unit cells were left out empty, i.e., without nanobricks, while the other 10 nanobricks cover the available phase range of 270°, thus ensuring better sampling of the phase profile and improving the efficiency of diffraction to the desired +1st order (fig. S2, F to L). Note that, in the absence of absorption, one might opt for another approach, such as doubling only the cells with extreme (minimum and maximum) phase responses (60). The reflected electric field (x/y components) calculated for thus designed MEMS-OMS under the TM/TE incident light at 800-nm wavelength with ta=20nm manifests smooth wavefronts traveling in the direction of the +1st diffraction order (Fig.2F and fig. S2J, left). For increased air gaps, the phase gradients produced by the supercell nanobricks progressively decrease as expected (Fig.2,BandC), with the phase gradient becoming zero and the reflected field returning to the specular reflection at an air gap of ta=350nm (Fig.2G and fig. S2J, right). Here, we remark that our simulations presented Fig. 2. Polarization-independent dynamic beam steering: Design. (A) Schematic of the OMS unit cell including the air gap and gold mirror. (B) The complex reflection coefficient r calculated as a function of the nanobrick side length Lx and air gap ta with other parameters being as follows:  = 800 nm, tm = 50 nm,  = 250 nm, and Ly = Lx. Coloration is related to the reflection amplitude, while the magenta lines represent constant reflection phase contours. (C) Reflection phase (dashed lines) and amplitude (solid lines) dependencies on the nanobrick length Lx for two extreme air gaps: ta = 20 nm (red) and 350 nm (blue). Circles represent the nanobrick sizes selected for the OMS supercell designed for dynamic beam steering. (D) Top view and (E) cross section of the designed MEMS-OMS supercell. (F and G) Distributions of the reflected TM electric field (x component) at 800-nm wavelength for air gaps of ta = 20 and 350 nm, respectively. (H) Diffraction efficiencies of different orders (|m| ≤ 1) calculated as a function of the air gap ta for TM/TE incident light with 800-nm wavelength. (I) Diffraction efficiencies of different orders (|m| ≤ 1) calculated at the air gap ta = 20 nm as a function of the wavelength for TM/TE incident light. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 4 of 11 hereafter are concerned with the air gaps limited by 350nm since, for larger air gaps, a MEMS-OMS would function in a completely different regime determined by multiple and periodic positions of Fabry-Pérot resonances (see Discussion). The associated decrease in the +1st order diffraction efficiency and increase in the 0th order one as a function of the air gap, are practically linear, promising large modulation efficiencies available with the actuated MEMS-OMS (Fig.2H). Thus, +1st/0th-order diffraction efficiencies are expected to change from ~77/0 to 0/96% (for both TM and TE polarizations) when changing the air gap from 20 to 350nm. Redistributions of the power between diffracted orders for gradually varying air gaps are interconnected with the corresponding modifications in the reflected fields, undergoing gradual transition (fig. S3) between those primarily diffracted (at ta=20 nm) and those primarily reflected (at ta=350 nm). The designed MEMS-OMS is expected to exhibit the broadband operation similar to that known for conventional GSP-based OMSs (7,8,57). We note that the MEMS-OMS performance at large air gaps is equivalent to that of a mirror, with the value of a suitably large air gap being proportional to the operating wavelength (see the consideration of the Fabry-Pérot–based operation in Discussion). With this caveat in mind, the MEMS-OMS overall performance is determined by that at the smaller air gap of ta=20 nm, suggesting a 1-dB bandwidth of ~150nm near the operating wavelength of 800nm (Fig.2I). Note that, while the reflected field distribution for the air gap of 20nm (Fig.2F and fig. S2J, left) is not ideal for a number of reasons: insufficient phase range, unequal amplitude reflection coefficients, etc. (7,8,57), the performance of the MEMS-OMS at the design wavelength of 800nm is practically ideal with only the +1st diffraction order being nonzero (Fig.2I and fig. S2, H and I), i.e., this nonideal wavefront formation is of no practical importance for the device operation. As a final comment, it should be mentioned that, given the possibility of small air gap adjustments around the designed air gap of ta=20 nm, the diffraction efficiencies for different wavelengths could be enhanced, thus improving the effective bandwidth of the MEMS-OMS device (fig. S2, K and L). Polarization-independent dynamic beam steering: Characterization The MEMS-OMS for polarization-independent dynamic beam steering designed above (Fig.2) was assembled from a separately fabricated OMS, an ultraflat MEMS mirror (53), and a printed circuit board (Fig.3A; for details, see Materials and Methods along with fig. S4, A to D). The possibility of fabricating the MEMS mirror and OMS separately simplifies the design and fabrication processes, for example, by allowing the two components to be produced in separate processing lines with different minimum linewidth capabilities. The fabricated MEMS mirror and OMS were characterized individually using an optical microscope and scanning electron microscope (SEM) (Fig.3,BandC). When joining the MEMS mirror and OMS, it is important to avoid any particles that can obstruct the mirror from getting close enough to the OMS. Because the mirror (i.e., 3mm in diameter) was much larger than the OMS (i.e., 30 m by 30 m in size), the OMS was fabricated on top of a 10-m-high pedestal, the idea being that any particles smaller than 10m outside the pedestal will not prevent the OMS and MEMS mirror from coming into contact. This pedestal did not affect the fabrication of the nanobricks, featuring overall consistency with the design apart from slightly rounded corners and minor size deviations (Fig.3C) that are not expected to produce noticeable deterioration in the OMS performance (8). After assembling the MEMS-OMS, the MEMS-OMS separation was estimated using white light interferometry (Zygo NewView 6000) to be ~2m (fig. S4E), which is well within the ~6-m-large moving range of the MEMS mirror (see Materials and Methods along with fig. S4F). Following that, we estimated the smallest achievable separation between the MEMS mirror and OMS substrate surface (crucial for efficient modulation) by using a multiwavelength interferometry (fig. S5). We found by actuating the MEMS mirror that, for several assemblies, this gap (tm+ta) can be as small as ~100nm (fig. S5), corresponding to ta~50 nm, and these samples were then selected for further optical characterizations. To characterize the MEMS-OMS performance, we used a wavelength-tunable (~700 to 1000 nm) laser with the corresponding optical, polarization, and imaging components (see Materials and Methods along with fig. S6). The MEMS mirror is electrically actuated to modulate the optical response of the MEMS-OMS observed visually in both direct object (OMS surface) and Fourier image planes (Fig.4A). In the direct object images, this effect of power redistribution is seen in the appearance (at nonzero actuation voltages) of well-pronounced interference fringes formed due to the interference between the residual specular reflection and the +1st-order diffracted Fig. 3. MEMS-OMS assembly. (A) Typical photo of the MEMS-OMS assembly consisting of the OMS patterned on a glass substrate, an ultraflat thin-film MEMS mirror, and a printed circuit board (PCB) for electrical connection. (B) Optical microscopy and (C) SEM images of the OMS representing the 30 m by 30 m and 250-nm-period array of differently sized gold nanobricks designed for dynamic beam steering, fabricated atop a 10-m-high pedestal on the glass substrate, and used in the MEMS-OMS assembly. Photo credit: Chao Meng, University of Southern Denmark. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 5 of 11 beam. For both polarizations, the redistribution of radiation power between the 0th and +1st diffraction orders are well pronounced, reaching the maximum contrast at 3.75 V with the diffraction efficiencies of 40/46% for the respective TM/TE polarizations (Fig.4,AandB). The experimentally obtained diffraction efficiencies (Fig.4B) are noticeably smaller than those expected from the simulations (Fig.2H), discrepancies that are somewhat expected and attributed to additional absorption in gold nanobricks because of surface scattering and grain boundary effects as well as increased damping associated with a nanometer-thin titanium adhesion layer between gold-glass interfaces (8). Note that there is also a minor difference to be expected because of different media considered when determining the theoretical and experimental efficiencies (see Materials and Methods). The high-contrast dynamic beam steering, induced by actuating the MEMS mirror with the alternating voltages of 0 and 3.75 V at a slow switching speed, is clearly seen in the movie captured by the charge-coupled device (CCD) camera (movie S1). The MEMS-OMS operation is found to be polarization independent and broadband, exhibiting the 1-dB bandwidth of ~150nm (Fig.4C). By actuating the MEMS mirror with a periodic rectangle signal and detecting the spatially separated 0th/+1st order of diffraction fields, one observes relatively fast switching with the rise/fall times of ~0.4/0.3 ms, respectively (Fig.4D). The response speed is related to the intrinsic oscillation frequency of the MEMS mirror, thus being dependent on the MEMS design parameters such as geometry, weight, stiffness, and so on (53–56). Note that the standard thin-film MEMS mirror used is rather large (~3mm in diameter; Fig.3A), with its surface area orders of magnitude larger than that of the OMS area (~30 m by 30 m in size; Fig.3B), considerably slowing down the dynamic response. Bearing in mind the possibility of optimizing the MEMS mirror for fast switching speeds, one should expect that reaching operation bandwidths in the megahertz range, indeed, current state of the art in thin-film piezoelectric MEMS, can achieve ~30MHz of switching frequencies (54–56). In terms of stability and repeatability of operation, thin-film piezoelectric MEMS can survive more than 1011 cycles at full 20 V of ac cycles for standard operating conditions (23°C, 35% relative humidity), drifting by ~10% during its lifetime (61), although the repeatability within ~1nm is feasible with accurate position feedback by, e.g., optical, capacitive, or piezoresistive sensing. As far as the vibration instability is concerned, it is important that the MEMS device and glass plate resonances are not excited, which is usually the case once resonance frequencies are above 1kHz. The current MEMS device has a resonance frequency of ~4kHz and that of the glass plate is much higher. Consequently, no vibration is expected under normal circumstances and no instability was observed. Concluding the presentation of the demonstrated MEMS-OMS for polarization-independent dynamic beam steering, we would like to note that, although the experimentally observed performance (Fig.4) is somewhat inferior to that expected from our simulations (Fig.2), the experimental performance can be improved. The deterioration can be attributed partly to fabrication imperfections and to the smallest air gap ta that was achieved in practice. It seems that the air gap decreases with applying the actuation voltage only up to ~3.75 V, resulting thereby in increasing +1st and decreasing 0th order diffraction efficiencies, whereas for larger voltages, the MEMS Fig. 4. Polarization-independent dynamic beam steering: Characterization. (A) Optical images at the direct object (DI) and Fourier image (FI) planes of the reflected light from MEMS-OMS under actuation voltages of Va1 = 0.00 V (top) and Va2 = 3.75 V (middle) for TM/TE normally incident light with 800-nm wavelength. Reflected light from unstructured substrate (bottom) in the MEMS-OMS device is also recorded as a reference. (B) Diffraction efficiencies of different orders (|m| ≤ 1) measured as a function of the actuation voltage for TM/TE incident light with 800-nm wavelength. (C) Diffraction efficiencies of different orders (|m| ≤ 1) measured as a function of the wavelength for TM/TE incident light. (D) Response time of the different diffraction orders (m = 0/+1) measured by actuating the MEMS mirror with a periodic rectangle signal. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 6 of 11 mirror starts to move slightly away from the OMS, probably because of the residual contaminants on the substrate or bending at the pedestal edges that prevent the MEMS mirror from moving further closer to the OMS surface. Both better fabrication accuracy and smaller air gaps are feasible and expected to be realized in further experiments. Polarization-independent dynamic 2D focusing: Design The MEMS-OMS design for realizing dynamically controlled polarization-independent 2D beam focusing in reflection requires the choice of diameter D and focal length f of the OMS lens that, in turn, determines the numerical aperture (NA) for the given refractive index in the image space n=1.46 at an incident wavelength of =800 nm: NA=nsin[tan−1(D/2f)]. To realize strong focusing, we chose D=14 m and f=15m, so that NA ≈ 0.62 is expected, which should be adequate to enable high-efficiency reflective 2D focusing (7). Following the same design approach used in demonstrating MEMS-OMS for dynamic beam steering, we use the phase response calculated with air gap ta=20nm for different nanobrick lengths (the red dashed line in Fig.2C) to extract the proper unit cells and arrange them into a circular region with D=14m (Fig.5A), approximating a hyperboloidal phase profile (7,9)  2D = 2 _  n(f − √ _ x 2 + y 2 + f 2 ) in the xy plane (Fig.5B). The above phase profile is also discretized with the step size =250nm along both x and y directions, matching the unit cell size (=250 nm). In contrast to the previous work, we do not limit the choice of unit cells to a discrete design space [i.e., unit cells with discrete phase steps of 45° (7)]. Instead, appropriate lengths of the nanobricks are chosen from the entire space of simulation results (the red dashed line in Fig.2C), thus ensuring better sampling of the 2D phase profile with minor deviations (fig. S7, A and B) from the required one (Fig.5B). The deviation between the required and available phase profiles results mostly from the achievable phase coverage of ~270°, a limitation that could be circumvented by including more complex unit cell elements such as detuned GSP resonators (62) that can also be constructed square-like to ensure the polarization-independent operation or by using cross-like nanobricks, allowing for a wider phase coverage (57). Bearing in mind high computational demands when simulating 2D focusing (and thus aperiodic) OMSs, we estimate the focusing performance by simulating the corresponding (reduced to a 1D aperiodic configuration) OMS (fig. S7, C and D), which is designed Fig. 5. Polarization-independent dynamic 2D focusing: Design. (A) Top view of the OMS designed for dynamic 2D focusing. (B) The phase profile required to focus radiation with focal length of 15 m at 800-nm wavelength. (C and D) Distributions of the reflected intensity for TM incident light with 800-nm wavelength at air gaps of ta = 20 and 350 nm, respectively. (E and F) Distributions of the reflected TM electric field (x component) at 800-nm wavelength for air gaps of ta = 20 and 350 nm, respectively. (G and H) Focusing efficiencies calculated as a function of the operating wavelength  and air gap ta for TM/TE polarizations. The green, black, and cyan lines indicate the cases of  = 750, 800, and 950 nm, respectively. (I) Focusing efficiencies calculated as a function of the air gap ta for TM/TE polarizations with respective 750-, 800-, and 950-nm wavelengths. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 7 of 11 to provide a 1D hyperboloidal phase profile  1D = 2 _  n(f − √ _ x 2 + f 2 ) , while the D, f, and  are the same as that of the above-designed OMS with the 2D phase profile. The reflected intensity distributions calculated for this simplified MEMS-OMS under TM/TE incident light at 800-nm wavelength with ta=20nm manifest high focusing quality with a diffraction-limited spot situated at the focal length of ~15 m (Fig.5C and fig. S7E). For increased air gaps, the phase gradients produced by nanobricks with different lengths progressively decrease (Fig.2,BandC), approaching zero at an air gap of 350 nm, with the reflection transformed into specular reflection (Fig.5D and fig. S7F). The associated reflected electric fields calculated near the focus display smoothly converging and planar wavefronts at air gaps ta=20nm (Fig.5E and fig. S7G) and 350nm (Fig.5F and fig. S7H), respectively, implying a high-efficiency operation of the actuated MEMS-OMS. Taking into account the possibility of adjusting the air gap to maximize the focusing efficiency at other (than the design) wavelengths, we evaluated the focusing efficiencies achievable at different wavelengths with varied air gaps (Fig.5,GandH). The maximum achievable focusing efficiencies at the design wavelength of 800nm are estimated to be ~64/66% (TM/TE) for the air gap of ~20nm as expected. For other wavelengths, the polarizationindependent focusing behavior is well maintained, while the corresponding maximal focusing efficiencies are expected to achieve at slightly different air gaps. To better visualize this feature, the focusing efficiency as a function of the air gap is explicitly plotted for distinct wavelengths of 750, 800, and 950nm (Fig.5I), showing for all wavelengths a nearly linear decrease of the efficiency for increasing air gaps without noticeable changes in the reflected field distributions (fig. S7, I to L). Polarization-independent dynamic 2D focusing: Characterization The MEMS-OMS for polarization-independent dynamic reflective 2D focusing designed as described above (Fig.5) was assembled following the fabrication and precharacterization processes similar to those used when assembling the dynamic beam steering MEMS-OMS. Optical microscopy and SEM are used for monitoring the possible contaminants on the OMS surface and the fabrication quality (the upper-left inset of Fig.6A and fig. S8). To characterize the dynamic focusing MEMS-OMS, we electrically actuated the MEMS mirror and observed corresponding optical responses in the direct object plane (Fig.6B). Since the MEMSOMS was designed to exhibit a very short focal length of ~15 m, it was not possible to directly access the focal plane using a beam splitter (BS) and a low-divergent incident laser beam. Instead, the focusing effect was verified by illuminating the MEMS-OMS with a focused incident beam and placing the MEMS-OMS surface plane B at a distance of ~2f (the double focal length of the MEMS-OMS) away from the incident beam focal plane A (see inset in Fig.6A). According to the ray optics, the beam reflected by the OMS (when close to the MEMS mirror) will then be focused again at the focal plane of the objective (plane A in the bottom-right inset of Fig.6A). At the same time, the reflection from the unstructured substrate surface (outside the OMS area) would be strong diverging (see the bottom-right inset in Fig.6A). If one moves the MEMS-OMS surface to plane A, then the reflection behavior will be reversed: The reflection by the OMS will be diverging (after the objective) and the reflection by the unstructured surface collimated. This procedure was successfully used and described in detail in the previous experiment conducted with the static focusing OMS (7). In the current case with the dynamic focusing MEMS-OMS, it is expected for the MEMS-OMS arrangement to switch between the focusing configuration, when the applied voltage would bring the OMS very close to the MEMS mirror, and the mirror reflecting configuration for relatively small applied voltages that would correspond to sufficient large OMS and MEMS mirror separations. To observe this transformation, we monitored the reflected light from the MEMS-OMS positioned at plane B while actuating the MEMS mirror. For both polarizations, the switching of the reflected light between the mirror (at Vb1=10.00 V) and focusing (at Vb2=14.50 V) cases was clearly visualized (Fig.6B), with the focusing efficiencies reaching their maxima of ~56/53% at Vb2=14.50 V for the respective TM/TE light incidence at the wavelength of 800nm (Fig.6A). At the same time, the reflection from the unstructured substrate surface was not influenced with the applied voltages, revealing, however, that the reflection from the substrate at plane A is notably similar to the TM/TE reflection from the OMS at plane B, with the applied voltage being Vb2=14.50 V (Fig.6B). The latter evidences a rather high efficiency and excellent quality of polarizationindependent focusing by the MEMS-OMS at Vb2=14.50 V. The dynamic evolution of the reflected field from the MEMS-OMS positioned at plane B, induced by actuating the MEMS mirror with stepwise increased voltages from 10.00 to 14.50 V, is clearly observed with a CCD camera (movie S2). Because of the usage of the same Fig. 6. Polarization-independent dynamic 2D focusing: Characterization. (A) Focusing efficiencies measured as a function of the actuation voltage for TM/TE incident light with 800-nm wavelength. The upper-left inset is a typical SEM image of the OMS representing 14-m-diameter and 250-nm-period array of differently sized gold nanobricks designed for dynamic 2D focusing. Scale bar, 2 m. The bottom-right inset illustrate the measurement method in which the incident beam is focused at plane A (focal plane of the objective) and impinging on the unstructured substrate or OMS area of the MEMS-OMS at plane B (2f distance away from the focal plane of the objective), resulting in respective divergent or focused reflected fields. (B) Optical images of the reflected light from the unstructured substrate and OMS area of the MEMS-OMS positioned at plane B with actuation voltages of Vb1 = 10.00 V and Vb2 = 14.50 V for TM/TE incident light at 800-nm wavelength. The reflected light from the unstructured substrate and OMS area of the MEMS-OMS positioned at plane A was also recorded as a reference. Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 8 of 11 MEMS component as that in the dynamic beam steering MEMS-OMS, similar response time of ~0.4 ms is expected. It is lastly worth noting that, according to the current state of the art in thin-film piezoelectric MEMS techniques (54–56), MEMS-OMS components with a few megahertz of switching bandwidth should be feasible and expected for further developments. DISCUSSION We have developed the electrically driven dynamic MEMS-OMS platform by combining a thin-film piezoelectric MEMS mirror with a GSP-based OMS. This platform offers controllable phase and amplitude modulation of the reflected light by finely actuating the MEMS mirror. We have designed and experimentally demonstrated MEMS-OMS devices operating in the near-infrared wavelength range for dynamic polarization-independent beam steering and reflective 2D focusing, both exhibiting efficient (~50%), broadband (~20% near the operating wavelength of 800 nm), and fast (<0.4 ms) operation. Note that the operation bandwidth can be markedly increased when using the circularly polarized light whose transformation relies on the OMS, making use of the geometrical (PancharatnamBerry) phase (17). The operation of both devices relies on the phase response transformation when changing the MEMS-OMS separation by adjusting the applied voltage within the range of ~4 V. The same operation principle can be used to design a MEMS-OMS for dynamically controlling any functionality available for conventional GSP-based OMSs, from polarization control/detection to vector/ vortex beam generation (59): For a given smallest air gap, one designs the GSP-based OMS exhibiting a required functionality that can then be switched on and off by moving the MEMS mirror toward and away from the OMS surface. Moreover, the nontrivial modification of the size-dependent phase response with the MEMS-OMS separation (Fig.2B), which can accurately be adjusted by electrical MEMS actuation, suggests a possibility of realizing more sophisticated dynamic functionalities. One functionality of particular interest to commercial applications is the possibility of switching between multiple diffraction orders to allow for quasi-continuous beam steering (for use in, e.g., LIDAR applications). Thus, we have also designed and experimentally demonstrated the MEMS-OMS device for polarization-independent dynamic beam steering between three (0th, 1st, and 2nd) diffraction orders, corresponding to reflection angles of 0°, 5.2°, and 10.5° in glass (i.e., 0°, 7.7°, and 15.5° in air) under normally incident light with 800-nm wavelength. The OMS configuration (fig. S9) consisted of two OMSs with different supercells with sc1=12 and sc2= 24 optimized at two distinct air gaps and interleaved by adopting a random-interleaving strategy (63). The experimental characterization (fig. S10) has confirmed the intended dynamic MEMS-OMS response: With the actuation voltage increasing, the +1st and +2nd diffraction orders became visible, succeeding one another, in accordance with our simulations (fig. S9, K and L). Another promising direction for further research and development is to circumvent the necessity of bringing the MEMS mirror very close (~100 nm) to the OMS surface. For large MEMS-OMS separations, one can make use of localized plasmon resonances because of excitation of short-range surface plasmon polaritons (SR-SPPs) in thin metal films (58). Our preliminary simulations showed that the SR-SPP resonances hybridize with the Fabry-Pérot resonances (supported with wavelength-large air gaps) (64,65) and open a similar to the considered above route to modify the OMS phase response by controlling the air gap (fig. S11, A to C). Note that at certain air gaps (separated by half of the wavelength), the reflected phase becomes independent on the nanobrick size (fig. S11, A and B), resulting thereby in the mirror-like behavior (fig. S11, D and E). In between these air gaps, there are gaps at which the phase does depend on the nanobrick size (see a dashed line at the gap of 1250nm in fig. S11B). At these gaps, the nanobrick sizes can be chosen in a manner enabling one to realize a phase-gradient metasurface (fig. S11, F and G). Switching between these two distinct air gaps results therefore in switching between the mirror-like and gradient metasurface behavior, which is similar to switching between the same types of responses of the dynamic GSP-based metasurfaces. With this approach, the MEMS-OMS can be operated near the air gap of ~1 m or more, as demonstrated with our simulations of dynamic beam steering (fig. S11, D to L), thus avoiding the problem of realizing nanometer-sized air gaps. Overall, we believe that diverse functionalities with dynamically reconfigurable performances can be realized using the developed MEMS-OMS platform, thus opening fascinating perspectives for successful realization of high-performance dynamically controlled devices with potential applications in future reconfigurable/adaptive optical systems. MATERIALS AND METHODS Simulation methods All numerical simulations were performed using COMSOL Multiphysics 5.5. We modeled one individual glass-Au-air-Au unit cell (Fig.2A), where periodic boundary conditions were applied in both x and y directions, and linearly x-polarized light at the design wavelength of 800nm was normally incident onto the unit cell from the upper glass layer. The permittivity of Au is described by the interpolated experimental values (66), and the glass layer is taken as a lossless dielectric with a constant refractive index of 1.46. Then, the complex reflection coefficients (Fig.2B) were calculated as a function of nanobrick lengths Lx, and air gap ta with other parameters being as follows: =800 nm, tm=50 nm, =250 nm, and Ly=Lx to ensure the polarization-independent optical responses. To design the MEMS-OMS for dynamic beam steering, the phase response calculated with the air gap ta=20nm for different nanobrick lengths is used to select the lengths of 12 nanobricks (Fig.2C) for approximating the reflection coefficient of an ideal blazed grating: r(x)=Aexp(i2x/sc) (6,8,57), where A≤1 is the reflection amplitude, and sc=12 is the grating (supercell) period. Reflected light directed to different diffraction orders are monitored, with different air gaps ta and incident wavelengths  for estimating the dynamic diffraction efficiencies and operation optical bandwidths, respectively (Fig.2,D to I, and fig. S2, F to L). Here, the diffraction efficiencies are defined as the ratios of the light intensities (in glass) in the corresponding diffraction orders to the incident (in glass) light intensity. MEMS-OMS for dynamic beam focusing is designed and simulated in a similar fashion. Nanobricks from the phase response calculated with the air gap ta=20nm for different nanobrick lengths (Fig.2C) are selected to approximate a 1D hyperboloidal phase profile of  1D = 2 _  n(f − √ _ x 2 + f 2 ) (7,9) within a 14-m-diameter region in the xy plane (fig. S7, C and D). Reflected fields are monitored to visualize the dynamic beam focusing and estimate corresponding focusing efficiencies as a function of the gap sizes ta and incident Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. Adv. 2021; 7 : eabg5639 23 June 2021 SCIENCE ADVANCES | RESEARCH ARTICLE 9 of 11 wavelengths , for both TM and TE polarizations (Fig.5,C to I, and fig. S7, E to L). Here, the focusing efficiencies are defined as the ratio of the light power from the corresponding focal spot (in glass) to the incident (in glass) light power. Note that both diffraction and focusing efficiencies obtained in our simulations should not be directly compared to the experimental values that were measured in air because of the reflections at the glass-air interface. Considering the fact that all optical fields propagate at directions close to the normal to the OMS surface and disregarding multiple reflections, one can estimate the expected difference between the quantities obtained for the fields in air and in glass as air≈0.93glass, i.e., the difference amounts to ~7%. Fabrication and assembly of the MEMS-OMS devices The OMSs for developing MEMS-OMS for dynamic beam steering/ focusing were fabricated using standard electron beam lithography (EBL), thin-film deposition, and lift-off techniques. First, a 100-nm-thick poly(methyl methacrylate) (2% in anisole; MicroChem) layer and a 40-nm-thick conductive polymer layer (AR-PC 5090, Allresist) were successively spin-coated on a 16mm by 16mm glass substrate (Borofloat 33 wafer, Wafer Universe). Note that the glass substrate was preprocessed to have a 10-m-high circular/cross-shaped pedestal on one side using optical lithography and wet etching. The OMSs were then defined on the pedestal of the glass substrate using EBL (JEOL JSM-6500F field-emission SEM with a Raith Elphy Quantum lithography system) and subsequently developed in 1:3 solution of methyl isobutyl ketone and isopropyl alcohol. After development, a 1-nm Ti adhesion layer and a 50-nm Au layer were deposited using thermal evaporation. The Au nanobricks were lastly formed atop the pedestal on the glass substrate after a lift-off process (Fig.3 and fig. S8). Owing to the large size of the MEMS mirror (~3mm in diameter) in comparison to the OMS (30 m by 30 m in size), the pedestal on the glass substrate is very practical for reducing the possible contaminants between the MEMS mirror and OMS surface, thus promising high-efficiency modulation of the MEMS-OMS devices. The MEMS mirror, which is very similar to the previously reported ultraplanar, long-stroke, and low-voltage piezoelectric micromirror (53), is fabricated using standard semiconductor manufacturing processes (fig. S4A) and incorporating thin-film lead zirconate titanate (PZT) for actuation. First, a platinum-bottom electrode, a 2-m-thick PZT film, and a top electrode consisting of TiW/Au were deposited on a SOI wafer (fig. S4A, first panel). Then, a central circular aperture of 3mm was opened by using deep reactive ion etching of silicon and etching of the buried oxide (fig. S4A, second panel). An annulus trench is etched into the backside of the wafer, thereby releasing the circular plate. Last, the wafer backside is sputtered with Au (fig. S4A, third panel) for acting as the ultraflat MEMS mirror that is of vital importance in developing dynamic MEMS-OMS. After the fabrication of both OMS and MEMS mirror, we move to the assembly and packaging processes for making MEMS-OMS devices (fig. S4A, fourth panel). Before assembly, the surface topography of the MEMS mirror and glass substrate were measured by a white light interferometry (Zygo NewView 6000), so as to select favorable areas on both sides with the least amount of contaminants and surface roughness that might obstruct the MEMS mirror from getting close enough to the OMS. Then, the MEMS mirror was glued to the glass substrate upon which the OMS has been structured (fig. S4, B to D). Getting the mirror and OMS parallel was done by adjusting the tilt of the MEMS mirror using the piezoelectric electrodes. The spacing between the MEMS mirror and the glass substrate (ta+tm) was measured to be commonly ~2m after mounting (fig. S4E), well within the 6-m moving range of the MEMS mirrors (fig. S4F). Last, the MEMS-OMS was glued to a printed circuitry board, and gold wire bonding is used to connect electrically to the MEMS electrodes for enabling simple connection to a voltage controller used to actuate the MEMS mirror. After the MEMS-OMS assembly, we applied multiwavelength interferometry to estimate the smallest achievable separation between the MEMS mirror and OMS surface (fig. S5). We found by actuating the MEMS mirror that, for several assemblies, this gap (tm+ta) can be as small as ~100nm corresponding to ta~50 nm, and these samples were then selected for further optical characterizations. Optical characterization of MEMS-OMS To characterize the performances of the MEMS-OMS for dynamic 2D wavefront shaping, we used a fiber-coupled wavelength-tunable Ti:sapphire laser (Spectra-Physics 3900S; wavelength range, 700to 1000 nm), whose light was directed through a half-wave plate (AHWP05M-980, Thorlabs), a Glan-Thompson polarizer and a first BS (BS1; BS014, Thorlabs) successively, and then focused by an objective (Obj, M Plan Apo, ×20/×50 magnifications; Mitutoyo) onto the MEMS-OMSs. The reflected light was collected by the same objective and directed via BS1 and a second BS (BS2; BS014, Thorlabs) to two optical paths terminated with two CCD cameras (DCC1545M, Thorlabs) for visualizing respective direct object and Fourier plane images (fig. S6). Note that the objective of ×20/0.42 and ×50/0.55 are used for measuring respective MEMS-OMS for dynamic beam steering and focusing. During the measurement, the MEMS mirror was electrically actuated to modulate the optical responses of the MEMS-OMS devices. To characterize the MEMS-OMS for dynamic beam steering, we measured both diffraction efficiencies and response time with the experimental setup shown in fig. S6. For estimating the diffraction efficiencies, we recorded the intensity of spatially separated 0th/±1st diffraction orders using a CCD camera at the Fourier plane for the laser beam being on the OMS area, which is then normalized with the reflection intensity from an unstructured substrate in the MEMS-OMS components. The response time of the MEMS-OMS was evaluated by actuating the MEMS mirror with a periodic rectangle signal from a function generator (TOE 7402, TOELLNER). The spatially separated diffraction orders at the Fourier plane could be selected by an iris and then projected to a photodetector (PDA20CS-EC, Thorlabs), which was connected to an oscilloscope (DSOX2024A, Keysight) for visualizing and recording the corresponding modulated signals. In the response time measurement, we recorded the 0th/+1st diffraction orders of the MEMS-OMS components, showing overall good repeatability and stability of the actuated MEMS-OMS components with the periodically electrical signals (Fig.4D). SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/7/26/eabg5639/DC1 REFERENCES AND NOTES 1. N. Yu, F. Capasso, Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014). 2. D. Lin, P. Fan, E. Hasman, M. L. Brongersma, Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014). Downloaded from https://www.science.org on April 26, 2022 Meng et al., Sci. 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Acknowledgments Funding: This project has received funding from the ATTRACT project funded by the EC under grant agreement 777222, the University of Southern Denmark (SDU2020 funding), the VKR Foundation (Award in Technical and Natural Sciences 2019 and grant nos. 00022988 and 37372), and the EU Horizon 2020 research and innovation program (the Marie Skłodowska-Curie grant agreement no. 713694). Author contributions: C.D. and S.I.B. conceived the idea. C.M. and F.D. performed the numerical simulations. C.M. and C.W. fabricated the OMS samples, P.C.V.T. and J.G. fabricated the MEMS mirror and assembled MEMS-OMS devices, and C.M. and P.C.V.T. conducted the optical measurements. C.M. and M.T. performed the response time measurement. All authors contributed to the manuscript writing. C.D. and S.I.B. supervised the project. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Submitted 15 January 2021 Accepted 11 May 2021 Published 23 June 2021 10.1126/sciadv.abg5639 Citation: C. Meng, P. C. V. Thrane, F. Ding, J. Gjessing, M. Thomaschewski, C. Wu, C. Dirdal, S. I. Bozhevolnyi, Dynamic piezoelectric MEMS-based optical metasurfaces. Sci. Adv. 7, eabg5639 (2021). Downloaded from https://www.science.org on April 26, 2022 and Video S5), as well as for different incident LP states (θ LP =60°, 75°, 105°, 120°) and fixed DWP orientation θ DWP =45° (Fig. 4c, SupplementaryFig.S14,andVideoS6).Thepolarizationtrajectories onthePoincarésphereareseento be differently tilted for different DWP orientations having the common point, the incident LP state |y>(Fig. 4b), while being parallel to the plane (S 1 ,S 3 )andreflecting the incident LP state (Fig. 4c). Note that, for any given point on the Poincaré sphere, one can identify suitable orientations of the DWP and incident LP state enabling closed polarization trajectories to pass this point, so that a multitude of polarization modulation capabilities can be realized with the same DWP. Finally, we would like to emphasize that all experimental results agree exceedingly well with the simulations without any fitting parameters, demonstrating convincingly that the fabricated DWP behaves according to the design and that the modeling approach developed is well suited for use in the future MEMS-OMS component developments. Discussion To summarize, capitalizing on our development of the MEMS-OMS platform22 we have demonstrated the electrically driven DWP operating in reflection with high polarization conversion efficiencies (~75%), broadband operation (~100 nm near the operating wavelength of 800 nm), fast responses (<0.4 ms) and full-range birefringence control that enables completely encircling the Poincaré sphere along trajectories determined by the incident light polarization and DWP orientation. It should be noted that, given the access to nmsized air gaps, one can exploit the same design principle to realize the DWP with gap surface plasmons being generated22,aregimethat promises a broader operation wavelength range (~160 nm) although probably at the expense of a lower efficiency (~50%)22.Importantly, the general approach developed can also be applied to design a DWP operating in transmission by using a partially transmitting MEMS mirror and placing an OMS in the middle of an FP cavity25.Given that a multitude of polarization modulation capabilities can be realized with the same DWP, we believe that the demonstrated electrically driven DWP configuration with full-range birefringence control opens fascinating perspectives for successful integration of high-performance compact dynamic polarization components into future miniaturized reconfigurable/adaptive optical networks and systems26,27. Methods Numerical calculations. All numerical simulations were done using COMSOL Multiphysics version 5.6. The model is composed of a rectangular volume with a square footprint with sides Λ=250 nm and periodic boundary conditions were employed for both uand vdirections. The DWP unit cell is divided into two parts of air and glass, with one gold nanobrick placed against the glass region. The corners of the nanobrick are rounded with a 5 nm radius. The refractive index of air is set as 1 and that of glass as 1.46 for all wavelengths, while the gold permittivity was interpolated as a function of wavelength from experimental tabulated values28. Using this model, the complex reflection and transmission coefficients for the glass/OMS/air interface are calculated for both propagation directions (i.e., a normal incident from glass or air) and for light linearly polarized along both uand vseparately. These are used to calculate the total reflection coefficient rFP by including the gold substrate with the FP equation19–21 rFP ¼r12 þt12t21r23ei2kn2Ta 1r21r23ei2kn2Ta ð1Þ |y> |x> Vm -8 -6 -4 |l> |r> Vm Time (ms) -2 02468 0 6 12 Intensity (mV) 0 6 12 14 17 20 Voltage Vm (V) -4 -3 -2 Time (ms) -1 01234 0 10 20 Intensity (mV) 0 10 20 17 19 21 Voltage Vm (V) ZWP HWP c dQWP TQWP QWP TQWP QWP TQWP QWP TQWP ZWP HWP ZWP HWP ZWP HWP b |r> |l> DI FI DI FI DI FI DI FI a |x> |y> Vm(HWP)=17.1 V Vm(TQWP)=14.4 VVm(QWP)=19.1 V Vm(ZWP)=20.2 V Fig. 3 Polarization conversion dynamics. a,bOptical images of the reflected light at the direct image (DI) and Fourier image (FI) planes for the fixed input linear polarization (LP) state |y>(θ LP =90°) and dynamic wave plate (DWP) orientation (θ DWP =45°) at λ=800 nm, showing polarization modulation between orthogonal (a) LP states (|x>, |y>), corresponding to zero-wave plate (ZWP)/half-wave plate (HWP) transformation, by changing the actuation voltage V m from 20.2 to 17.1 V, and (b) circular polarization (CP) states (|r>, |l>), corresponding to quarter-wave plate (QWP)/three-quarters-wave plate (TQWP) transformation, by changing the actuation voltage V m from 19.1 to 14.4 V. For the FIs, the light is filtered using an iris letting through only light reflected from inside the orange dashed circles (shown in DIs). The leftmost column in (a,b) indicates the polarizer orientations used for filtering the respective polarization states in the reflected light. Scale bars in the DIs and FIs are 10 μm and 0.02k 0 , respectively. c,dTemporal evolution of the reflected light power for cZWP/HWP and dQWP/TQWP transformations, measured by actuating the MEMS mirror with a periodic rectangular signal and filtering respective polarization states. NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29798-0 ARTICLE NATURE COMMUNICATIONS | (2022) 13:2071 | https://doi.org/10.1038/s41467-022-29798-0 | www.nature.com/naturecommunications 5 Here, r mn (t mn ) denotes the reflection (transmission) coefficients for light incident on material nfrom material mand the materials are numbered 1, 2, 3 for respectively glass substrate, air, and gold substrate, n 2 represents the refractive index of the air (i.e., medium 2 between the OMS layer and gold substrate), and kis the wavenumber in a vacuum. Note that the effect of the OMS on the interface between the air and glass substrate is included in r 12 ,r 21 ,t 12 , and t 21 , and that even for normal incidence r FP are polarization-dependent due to the anisotropy of the OMS layer. The reflection coefficient r 23 from the air/gold interface is calculated directly using the Fresnel equation. An illustration of the DWP geometry is shown in Supplementary Fig. S2 together with plots explaining the behavior of the total reflection coefficient r FP with varying T a . For air gaps much smaller than the wavelengths, there is near-field coupling between the nanobricks and the gold substrate in addition to the FP resonances1,20, requiring numerical simulations including also the gold substrate in COMSOL. The results obtained using the FP equation were confirmed to give the same results as COMSOL simulations with the whole glass/nanobrick/air/gold substrate model when T a > 100 nm for a wavelength of λ=800 nm. As a final comment, to compare with the measurements, the imaginary part of the gold permittivity is increased by three times in the simulations of Figs. 2,4and Supplementary Figs. S7, S9–S14, accounting for the surface roughness and grain boundary effects of the fabricated gold nanobricks as well as the increased damping associated with the titanium (Ti) adhesion layers between the gold/glass interface. Fabrication. The OMS for developing MEMS-OMS DWP were fabricated using electron-beam lithography (EBL), thin-film deposition, and lift-off techniques. First, a 100-nm-thick poly(methyl methacrylate) (PMMA A2, MicroChem) layer and a 40-nm thick conductive polymer layer (AR-PC 5090, Allresist) were successively spin-coated on the glass substrate (Borofloat 33 wafer, Wafer Universe). Note that the glass substrate was preprocessed to have a 10-μm-high circular pedestal using optical lithography and wet etching, and the OMS pattern was defined on the pedestal using EBL (JEOL JSM-6500F field-emission SEM with a Raith Elphy Quantum lithography system). After development, the OMS layer was formulated by depositing a 1-nm Ti adhesion layer and a 50-nm gold layer (Tornado 400, Cryofox) followed by lift-off in acetone (Supplementary Fig. S4). The pedestal on the glass substrate is very effective for reducing the possible contaminants between the MEMS mirror and OMS surface, thus improving the stability and repeatability of the DWP components. The MEMS mirror is fabricated using standard semiconductor manufacturing processes (Supplementary Fig. S3), in which thin-film lead zirconate titanate (PZT) is incorporated for longstroke, low-voltage electrical actuation. For use in the MEMS-OMS component, the ultra-flat MEMS mirror was sputtered with a 100 nm gold layer. After the gold deposition, the MEMS mirror surface is inspected with white light interferometry (Zygo NewView 6300), showing overall good flatness and roughness all over the whole MEMS mirror (i.e., ~3 mm diameter) (Supplementary Fig. S3). The MEM-OMS-based DWP component (Supplementary Fig. S4) was assembled by gluing the MEMS mirror with the glass substrate upon which OMS is structured and then glued to a printed circuit board (PCB), followed by a gold wire bonding process between the MEMS mirror and PCB for enabling simple electrical connection to a voltage controller used to actuate the MEMS mirror. Characterization. The experimental setup is shown in Supplementary Fig. S8. A collimated fiber-coupled supercontinuum laser (SuperK Extreme, NKT) was directed through an HWP (AHWP10M-980, Thorlabs), a mirror, a linear polarizer (Pol 1 ; LPNIR050-MP2, Thorlabs), two beam splitters (BS 1,2 ; CCM1-BS014, Thorlabs) successively, and then focused onto the DWP samples by an objective (Obj; M Plan Apo, ×20/0.42NA, Mitutoyo). The combination of HWP and Pol 1 is used for altering the input LP states as well as the intensity. The reflected light was collected by the same objective and passed through two beam splitters (BS 2,3 ; CCM1-BS014, Thorlabs) and a tube lens (TL; TTL200-S8, Thorlabs), generating the first direct image plane where an iris is placed for filtering out the reflected light within the DWP area. The first direct image is then transformed by a relay lens (RL; AC254200-B-ML, f=200 mm, Thorlabs) to the corresponding Fourier image and captured by a CCD camera (CCD; DCC1545M, Thorlabs), according to a 2fconfiguration. Note that a flip lens (FL; AC254-100-B-ML, f=100 mm, Thorlabs) is used for switching between the direct and Fourier images, and a Stokes analyzer composed of a QWP (AQWP10M-980, Thorlabs) and a linear polarizer (Pol 2 ; LPNIR050-MP2, Thorlabs) is implemented before the CCD camera for performing full Stokes polarimetry23. Two beam splitters are configured for crosscompensating the polarization-dependent phase shifts in the beam splitters for both incidence and reflection routes. To obtain the wavelength-resolved full Stokes parameters, we replaced the CCD camera with a fiber-coupled spectrometer (QE Pro, Ocean Optics) and conducted measurements at the Fourier image plane. By rotating the QWP and Pol 2 ,we recorded polarization-resolved spectra of I x (λ), I y (λ), I a (λ), I b (λ), I r (λ), I l (λ), and the stokes parameters (s 1 ,s 2 ,s 3 ) are calculated as s 1 =(I x (λ)–I y (λ))/(I x (λ)+I y (λ)), s 2 =(I a (λ)–I b (λ))/(I x (λ)+I y (λ)), s 3 =(I r (λ)–I l (λ))/(I x (λ)+I y (λ)). For a reasonable comparison with the simulations, the stokes parameters (s 1 ,s 2 ,s 3 ) are normalized to the polarized proportion of the reflected light beam: S1;2;3¼s1;2;3 DOP, and the degree of polarization (DOP) is defined as DOP ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 1þs2 2þs2 3 p.The polarization conversion efficiency (Fig. 2and Supplementary Figs. S9–S11) is defined as the ratio of the reflected light power in a specific polarization channel (i.e., |x>, |y>, |a>, |b>, |r>, |l> ) to the incident linearly |y> polarized light power. The coordinates system used is indicated in the lower-left inset of Fig. 1a, with z being the optical axis, xand yare transverse axes in the laboratory frame of abc θDWP=75° θDWP=60° θDWP=30° θDWP=15° θLP=60° θLP=75° θLP=105° θLP=120° y u v 45° x 60° 75° 105° 120° Input Polarization: DWP Orientation: θDWP=45° Input Polarization: |y> (θLP=90°) DWP Orientation: θDWP=45° Input Polarization: DWP Orientation: |y> (θLP=90°) v y x 30° 60° 75° 15° v u v u v u u Increasing T a Increasing Ta Increasing T a S1S2 S3 x(fast) y(slow) QWP z x u v 45° y S1S2 S3 S1S2 S3 Fig. 4 Versatile polarization transformations. a–cCalculated (lines) and measured (circles) polarization trajectories on the Poincaré sphere realized at the wavelength of 800 nm by tuning the air gap T a for different dynamic wave plate (DWP) orientations, illustrating the diversity of possible polarization transformations: acontinuous linear polarization (LP) rotation realized by combining the DWP with a conventional quarter-wave plate (QWP) with the incident LP state |y> and DWP orientation θ DWP =45°, bvarious elliptical polarization transformations realized for different DWP orientations with the fixed incident LP state |y>, and cvarious elliptical polarization transformations realized for different incident LP states with the fixed DWP orientation θ DWP =45°. The green stars in (a–c) indicate respective incident LP states. ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29798-0 6NATURE COMMUNICATIONS | (2022) 13:2071 | https://doi.org/10.1038/s41467-022-29798 -0 | www.nature.com/naturecommunications reference, while uand vare transverse axes oriented along the long and short sides of the rectangular nanobricks. The angle between uand xis denoted θ DWP , while the angle between the x-axis and the polarization direction of LP incident light is denoted θ LP . To estimate the switching speeds between different orthogonal LP and CP bases (i.e., different DWP status), the setup described above is modified by replacing the input laser and CCD camera with a cw Ti:sapphire laser (Spectra-Physics 3900 S, wavelength range: 700 to 1000 nm), and a photodetector (PD; PDA20CS-EC, Thorlabs), respectively. The signals from the PD are acquired with an oscilloscope (DSOX2024A, Keysight). In the measurement, the MEMS-OMS-based DWP is actuated with periodically alternating voltages and different polarizations (i.e., |x>, |y>, |r>and|l>) can be filtered by the Stokes analyzer. Data availability All data that support the findings of the study are provided in the main text and Supplementary Information files. Raw data are available from the corresponding authors upon reasonable request. Received: 16 December 2021; Accepted: 31 March 2022; References 1. Ding, F., Pors, A. & Bozhevolnyi, S. I. Gradient metasurfaces: a review of fundamentals and applications. Rep. Prog. Phys. 81, 026401 (2018). 2. Shaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019). 3. Wang, Q. et al. Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photon 10,60–65 (2016). 4. Li, S. Q. et al. Phase-only transmissive spatial light modulator based on tunable dielectric metasurface. 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P.T. acknowledges Jon Vedum for helping with the control electronics for the MEMS mirrors. Author contributions P.C.V.T. and C.M. performed the simulations and designed the OMS, fabricated and assembled the MEMS-OMS-based DWP samples. C.M. constructed the experimental setup, performed the measurements, and analysed the data. All authors contributed to the project idea, discussion of the results obtained and writing the manuscript. S.I.B. supervised the project. Competing interests The paper authors along with Jo Gjessing and Christopher Dirdal from SINTEF are inventors on a related patent application filed by the University of Southern Denmark and SINTEF under United Kingdom Patent Application No. 2113182.6. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-022-29798-0. Correspondence and requests for materials should be addressed to Fei Ding or Sergey I. Bozhevolnyi. Peer review information Nature Communications thanks the other anonymous reviewer(s) for their contribution to the peer review of this work. Peer review reports are available Reprints and permission information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. © The Author(s) 2022 NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-29798-0 ARTICLE NATURE COMMUNICATIONS | (2022) 13:2071 | https://doi.org/10.1038/s41467-022-29798-0 | www.nature.com/naturecommunications 7 74 CHAPTER 5. ARTICLES 5.3 MEMS Tunable Metasurfaces Based on Gap Plasmon or Fabry–P´erot Resonances Thrane P.C.V., Meng C., Ding F. and Bozhevolnyi S.I. MEMS Tunable Metasurfaces Based on Gap Plasmon or Fabry–P´erot Resonances. Nano Letters (2022). MEMS Tunable Metasurfaces Based on Gap Plasmon or Fabry−Perot Resonances Paul C. V. Thrane, § Chao Meng, § Fei Ding, and Sergey I. Bozhevolnyi* Cite This: https://doi.org/10.1021/acs.nanolett.2c01692 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Tunable metasurfaces promise to enable adaptive optical systems with complex functionalities. Among possible realizations, a recent platform combining microelectromechanical systems (MEMS) with gap-surface plasmon (GSP) metasurfaces offers high modulation efficiency, broadband operation, and fast response. We compare tunable metasurfaces operating in GSP and Fabry−Perot (FP) regions by investigating polarization-independent blazed gratings both numerically and experimentally. Peak efficiency is calculated to be ∼75% in both cases (∼40% in measurements), while the operation bandwidth is found larger when operating in the GSP region. Advantages of operating in the FP region include relaxed assembly requirements and operation tolerances. Additionally, simulation and experimental results show that coupling between neighboring unit cells increases for larger air gaps, resulting in deteriorated efficiency. We believe the presented analysis provides important guidelines for designing tunable metasurfaces for diverse applications in miniaturized adaptive optical systems. KEYWORDS: Metasurface, Tunable, MEMS, Gap Surface Plasmon, Plasmonic, Fabry−Perot, Intercell Coupling ■INTRODUCTION Metasurfaces have successfully demonstrated a wide range of optical effects and components, 1−5 with a lot of recent research focusing on developing metasurfaces with tunable properties to enable adaptive optical components and with several different techniques being followed, each having their own advantages and disadvantages. 6−9 One method to achieve this tunability is, for instance, to include materials that undergo a phase change. GeSbTe can, for example, change from having a crystal structure to an amorphous state depending on the temperature, with the two states having very different permittivity. 10 By incorporating resistive heaters, it is thus possible to make metasurface elements that can change their resonances quite significantly with a drawback being that demonstrated devices have slow switching time. 11 Faster responses have been demonstrated using the electro-optic effect in lithium niobate 12,13 or by modulating the free carrier density using electric 14 or optical 15 signals, with an issue being that the permittivity changes are limited to thin accumulation or depletion layers giving low modulation ranges. 7 The effect can be enhanced by using ε-near-zero materials 16 or by using 2D materials such as graphene 17 or black phosphorus. 18 Liquid crystals enable larger and more efficient modulation by changing the refractive index around the nanostructures 7 but again have slower responses due to the time it takes to rotate the molecules. 19 Metasurfaces can also be adjusted through mechanically altering the system, with demonstrated concepts including embedding the nanostructures in a stretchable polymer 20 or incorporating the metasurface with MEMS. 21 MEMS based tunable metasurfaces can achieve high efficiency modulation while still switching fast enough for many applications depending on the specific mechanical implementation, with most systems being able to operate in the range from one kHz up to several hundred kHz. 22 For visible and near-IR frequencies the individual meta-atoms are so small that individual actuation by MEMS is challenging, while collective modulation of all meta-atoms is more straightforward. One such recently demonstrated platform 23 consists of a gold MEMS mirror 24 and a glass substrate with gold nanostructures, where the air gap between the nanostructures and mirror can be controlled accurately. The system is designed to function as a reflective optical metasurface (OMS) for light with wavelength λ= 800 nm when the air gap is less than 50 nm. For these small separations there are GSP resonances 25 due to the near field coupling of the nanostructures and mirror. By moving the mirror away, these GSP resonances disappear, switching off the metasurface Received: April 27, 2022 Revised: August 12, 2022 Letterpubs.acs.org/NanoLett © XXXX The Authors. Published by American Chemical Society A https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX Downloaded via SINTEF on August 18, 2022 at 17:07:21 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. functionality and replacing it with that of a standard mirror. The experimentally demonstrated efficiency of this system was 50%, with switching times less than 0.4 ms. In this work we describe how the same MEMS-OMS platform can function also for larger air gaps owing to hybrid plasmonic FP resonances. 26,27 This configuration has recently been used to achieve efficient and fast 0−2πbirefringence control in reflection. 28 Not only is fabrication easier at larger air gaps since any particle or unevenness may obstruct the MEMS mirror from getting close enough for the GSP resonances, but larger gaps could also help reduce the trade-off between aperture size and switching speed by alleviating squeeze film air damping in the system. 29 Additionally, the amount of simulations required for design is reduced through the use of the analytic FP equation, removing the need to simulate the response for every air gap separately. We show also that the simulated peak efficiency is around 75% for metasurfaces working in both GSP and FP regions, while the bandwidth is larger for the GSP metasurface with around 2 times the bandwidth when comparing with the metasurface working at the first FP resonance. For larger air gaps there is progressively more coupling/cross-talk between neighboring nanostructures due to scattering and multiple reflections in the FP cavity, resulting in a gradual decrease in metasurface efficiency. This is a result of the metasurface design being based on simulations where the unit cells are placed in arrays of identical structures, whereas the actual metasurface may generally consist of varying meta-atoms. We verify this effect both numerically and experimentally. ■RESULTS AND DISCUSSION To compare plasmonic metasurfaces designed to work in the GSP and FP regions, we first calculate the complex reflection coefficient for different nanostructure geometries at two nanostructure−substrate separations corresponding to the two regions. Figure 1a and Figure 1b illustrate the MEMSOMS and its constituent unit cells used in this work. Specifically, the periodically repeated unit cell has a side length Λand consists of a gold nanobrick with thickness tmand side lengths Lxand Lyand separated from a gold substrate by an air gap Ta. In physical implementations there needs to be a dielectric substrate supporting the nanobricks; this has been omitted in the simulations except when comparing with the experimental measurements discussed later. To design the dynamic MEMS-OMS, we set the working wavelength at λ= 800 nm and choose the unit cell size of 250 nm to avoid any high-order diffraction and excitation of surface waves. Meanwhile, the optimal nanobrick thickness tmis found to be 50 nm, ensuring large reflection amplitudes and wide phase coverage. 23,30 Figure 1c and Figure 1d show electric field plots for two configurations of the unit cell, while Figure 1e and Figure 1f show the reflection coefficients as a function of Lxand Lyfor Figure 1. MEMS-OMS unit cell design within respective GSP and FP regions. (a, b) Schematic illustration of the MEMS-OMS metasurface and unit cell. A gold brick with side lengths Lxand Lyand thickness tmof 50 nm is situated a distance Taaway from a gold substrate. The unit cell has a square footprint with side lengths Λ= 250 nm. (c, d) The norm of the electric field in the xz plane at the center of the nanobricks for x-polarized excitation at normal incidence with separation distances of Ta= 20 nm and Ta= 430 nm, respectively. The nanobrick geometries are indicated as black squares in (e) and (f). (e, f) Absolute value of the complex reflection coefficients calculated as a function of nanobrick dimensions Lxand Ly at the wavelength of λ= 800 nm for (e) Ta= 20 nm and (f) Ta= 430 nm. The color maps represent the reflection amplitude for x-polarized excitation at normal incidence, while the blue and black contour lines indicate the reflection phases acquired for xand y-polarized excitations, respectively. Blue circles indicate nanobrick geometries for composing the polarization independent MEMS-OMS blazed gratings optimized in respective GSP and FP regions. The phase and reflection amplitudes of these nanobricks are shown in Figure S1. Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX B two different values of Tafor normally incident x-polarized excitation at λ= 800 nm. At Ta= 20 nm, there is a GSP resonance around Lx= 150 nm with near field coupling between the substrate and nanobrick as can be seen in the plot of the electric field in Figure 1c. At Ta= 430 nm, there is a less sharp resonance centered around Lx= 160 nm, due to a hybrid plasmonic/FP resonance between the substrate and the layer of nanobricks since the near-field coupling between the nanobricks and substrate is negligible, as shown in Figure 1d. As can be seen by comparing the phase contours in Figure 1e and Figure 1f, the range of available reflection phases are slightly larger for the case where Ta= 20 nm; however the difference is not significant enough to give larger efficiencies for the blazed grating designs presented later. The phase profiles for these gratings are shown in Figure S1. The transition between these GSP and FP regions is displayed in Figure 2, where the reflection coefficients for different brick sizes are shown as a function of Ta. The first FP resonance is located around Ta= 350 nm with Ta+Tm/2 close to λ/2, with a difference corresponding to the phase change upon reflection on the gold mirror. At this separation the system acts as a gold mirror with the reflection coefficient being independent of Lxand Ly, since at this separation distance the nanostructures are centered in the interference minimum from the superposition of incident and relected fields. For slightly larger air gaps the reflection is very dependent on the nanobrick dimensions (e.g., Ta= 430 nm Figure 2. Complex reflection coefficients as a function of air gap and nanobrick dimensions. The color map represents the reflection amplitudes for normally incident x-polarized light, while the contour lines indicate the reflection phases. The three subfigures represent three different cases of the nanobrick dimensions, namely, (a) square bricks (Lx=Ly), (b) constant Lx= 100 nm, and (c) constant Ly= 100 nm. The light is normally incident and with wavelength 800 nm. Figure 3. Dynamic MEMS-OMS blazed gratings designed for respective GSP and FP regions. (a) Supercell sketches of the 12-element polarization-independent dynamic MEMS-OMS blazed gratings. Outlines of the nanobrick dimensions optimized for Ta= 20 nm and Ta= 430 nm are indicated with black squares and orange dashed lines, respectively. (b, c) Calculated diffraction efficiencies into the specular (m= 0) and first diffraction order (m= +1) as a function of wavelength with the optimal air gap for each grating, for xand y-polarized excitations. (d, e) Calculated diffraction efficiencies as a function of air gap Taat λ= 800 nm for xand y-polarized excitations. Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX C as shown in Figure 1f) and then gradually returns to mirror-like behavior at the second FP resonance located around Ta+Tm/2 close to λ, with the pattern repeating for subsequent FP apart by a spaced separation of λ/2, again with a small correction due to the phase change upon multiple reflections on the gold mirror. This can be accurately described with the FP equation: 26 r r t t r r r e 1 e i kn T i kn T tot 12 12 21 23 2 cos( ) 21 23 2 cos( ) 2 a 2 2 a 2 = + (1) where the total reflection coefficient rtot is given as a function of the reflection and transmission coefficients rij and tij, with the light incident on region jfrom region iand the subscripts 1, 2, and 3 respectively referring to the regions above the nanobricks, between the nanobricks and substrate, and the substrate. Note that the reflection and transmission coefficients in general are dependent on the polarization and incidence angle of the light. With mirror-symmetric nanostructures and both regions 1 and 2 consisting of the same material (e.g., air), we have r12 =r21,t12 =t21, and n2= 1. Tacos(θ2) is the effective air gap for light traversing the gap with an angle θ2and can be simplified as Tafor normal incidence. By simulating the structures without any gold substrate, the reflection and transmission coefficients rij and tij are determined for each nanobrick geometry. Equation 1 is then used to calculate the total reflection coefficient as a function of Ta, thus avoiding the requirement of simulating the full structure for every air gap separation. This method gives correct results except for very small air gaps, in this case Ta< 80 nm = λ/10, where near-field Figure 4. Effect of coupling via mirror substrate on grating efficiency: comparison of simulations and experimental measurements. (a) Supercell of a MEMS-OMS dynamic blazed grating with 12 meta-atoms optimized for the GSP region. (b) Diffraction efficiencies as a function of air gap Ta. For these simulations the gold nanobricks are placed on a glass substrate, which is the case for the fabricated OMS shown in (c). The OMS is placed in close proximity (<3 μm) to a piezoelectric MEMS gold mirror. The air gap can then be changed by applying voltages on the MEMS. The measured diffraction efficiencies are shown in (d). The air gap values in (d) have been added by measuring the approximate relationship between air gap and voltage as described in Figure S7. In both (b) and (d) the upper (lower) plot is for x-polarized (y-polarized) excitation. The nanobrick thickness is 50 nm, and the wavelength is 800 nm. Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX D coupling and corresponding GSP excitation must be taken into account. The difference between the results from eq 1 and fullwave simulations including the substrate can be clearly observed for small gap sizes in Figure S2. After analyzing the polarization-dependent responses of the unit cell in both GSP and FP regions, we start to implement functional metasurfaces. Figure 3 compares the performance of two blazed metasurface gratings, one optimized for Ta= 20 nm and the other for Ta= 430 nm. As illustrated in Figure 3a, the metasurface gratings consist of a periodic array of 12 elements, with the first 2 elements empty while the other dimensions are chosen and marked with blue circles in Figure 1e and Figure 1f to provide large reflection amplitudes and an approximately linear phase gradient along the x-direction. In general the metasurface can be designed to control two orthogonal polarization states independently by using anisotropic elements, but the blazed grating is made polarization independent by choosing isotropic elements with Lx=Ly. Figure 3b and Figure 3c show the diffraction efficiencies of the two gratings for xand y-polarized light as a function of wavelength, where the polarization independent behavior can be observed. The efficiencies of the +1 diffraction order at the design wavelength of λ= 800 nm are similar for both gratings, with the values approaching 75%. However, the operating bandwidth is different. The grating working at Ta= 20 nm has an efficiency above 60% in the wavelength range between 760 and 900 nm, while for the grating working at Ta= 430 nm the corresponding wavelength range is only spanning from 770 to 825 nm. This reduced bandwidth is due to the fact that the FP resonance is narrower than the GSP resonance. At higher order FP resonances, the bandwidth will be reduced even further as the resonance requires the air gap to be an integer multiple of half wavelengths. Conversely, this effect might be used to design highly chromatic metasurfaces by choosing a large air gap. Figure 3d and Figure 3e compare the diffraction efficiencies of two metasurface gratings for xand y-polarized light as a function of Taat the design wavelength of 800 nm. Impressively, both metasurface gratings achieve more than 65% reflection in the +1 diffraction order when the air gap is Ta= 20 nm and Ta= 430 nm due to the similarity of the metaatoms. But there is a clear gain in efficiency by tailoring the meta-atoms for the relevant air gap, which is true for both polarization states. One may expect the same responses for metasurface blazed gratings with repeating FP regions. However, in our simulations and experimental results we observe a decrease in the +1 order efficiency at higher order FP resonances in combination with more reflection into other diffraction orders, which can be understood as increased coupling or cross-talk between neighboring nanostructures via reflections in the gold substrate. Figure 4a shows another 12-element blazed grating optimized for Ta= 20 nm. As earlier, the choice of nanobrick dimensions is based on simulations where the nanobricks are placed in an array of identical neighbors, while in practical applications the neighbors may have any geometry. This has been shown to not significantly affect the performance of GSP metasurfaces as long as the phase gradient is not too large. 25 However, as can be seen in the reflection amplitude for the diffraction orders plotted in Figure 4b, the efficiency of the grating degrades as Taincreases, with light going into unwanted diffraction modes other than the desired +1 diffraction order, falling from 72% at Ta= 430 nm to 66% at the fourth FP resonance due to increased coupling between elements within the supercell via the mirror substrate. In Figure S3, the same effect is visible for a grating made of 8 unit cells. With fewer meta-atoms the neighboring nanobricks are less similar in size, resulting in a larger drop in efficiency going from around 70% at Ta= 430 nm to less than 50% at the fourth FP resonance. The reflected field distributions for a blazed grating at several different air gap separations are shown in Figure S4.Figure 4c and Figure 4d show experimental measurements of a fabricated metasurface paired with a piezoelectric MEMS mirror, showing the same gradual decrease of the maximum diffraction efficiency from around 38% at the first FP resonance to 30% at the fourth FP resonance for both polarization states, together with increased intensity in the +2 diffraction order. This coupling issue is especially important when making high NA lenses or other components requiring large deflection angles, where the large phase gradient will require nanobricks that differ significantly from their neighbors. Details and some discussion of the fabrication and optical characterization can be found in Figures S5 and S6, while Figure S7 describes the measurements done to determine the relationship between air gap and voltage applied to the MEMS mirror. It should be noted that the minimal air gap achieved with the measured sample was ∼150 nm, sufficient for FP operation but not optimal for GSP operation. Closer separations can be achieved 23 but likely requires significantly more effort to be produced with high yield and might be harder to realize with larger apertures. To conclude, we show how the recently developed MEMS-OMS platform is not limited to working in the GSP region. For larger air gaps the FP resonances enable the system to still function as a metasurface, with slightly smaller phase range and similar efficiencies if the nanostructure geometries are optimized to work at the relevant air gap. The main advantage of allowing for larger air gaps is alleviating issues with thin film damping for high speed operation, as well as simplifying fabrication tolerances as decreasing the air gap below 50 nm is a very challenging problem, requiring flat parallel surfaces free from any particles or irregularities that may obstruct the MEMS movement. Meanwhile, working in the GSP region gives better bandwidth and fewer issues with coupling between meta-atoms, which causes the system to change behavior between different FP periods when having metasurfaces comprised of nonidentical meta-atoms. Ultimately, the choice between two different, albeit similar, operation regimes of the considered MEMS-OMS platform should be made by carefully considering all implications of their advantages and drawbacks, highlighted in this work, to targeted functionalities and particular applications in optical systems. ■METHODS The simulations were done using COMSOL Multiphysics 5.6 with the Wave Optics module. The refractive index for gold was interpolated from experimental values 31 for both the gold substrate and gold nanobricks. When simulating individual nanobricks, the unit cell is set to have periodic conditions in both xand y-directions, while the gold substrate is backed by a perfect electrical conductor condition and the air region is padded with a perfectly matched layer. When using eq 1 the coefficients r12,r21,t12, and t21 are determined by simulating the nanobricks without the gold substrate, with perfectly matched layers backing the domains on both sides of the nanostructure in the z-direction. r23, the reflection coefficient for the gold substrate for light with normal incidence, is determined by Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX E r n n n n 23 2 3 2 3 = + n2being the refractive index of the layer above the substrate (in this case air, n2= 1) and n3the refractive index of gold. The light was set to be normally incident for all simulations, and the results were calculated independently for light linearly polarized in the xand y-directions. When simulating gratings with large air gaps and many nanobricks, the simulation volume was reduced by simulating half the unit cell and replacing the periodic boundary conditions in the y-direction by perfectly magnetic or electric conductors depending on the incident polarization state. For the simulations in Figure 4, the nanobricks were placed on a lossless dielectric material with refractive index 1.46. Fabrication of the MEMS metasurface devices is done by individually manufacturing MEMS micromirrors and glass substrates containing the metasurfaces, before manually gluing the MEMS chips and glass substrates together in a cleanroom environment. A description and discussion of this process can be found in Figure S5. Additional details can also be found in refs 24 and 32 for MEMS fabrication and refs 23 and 28 for the MEMS−metasurface combination. Optical characterization is done by sending laser light with wavelength 800 nm through a linear polarizer, half wave plate (used to switch between two linear polarization states), and beam splitter and then focusing onto the sample using a microscope objective. The light is reflected back into the objective and is redirected by the beam splitter, before tube lens, iris (in image plane for spatial filtering), and two lenses that relay the light onto a CMOS camera. The last lens can be flipped in and out of the optical path to switch between capturing the direct and Fourier images. The direct object image is used to ensure the signal is collected from only the metasurface area, while the intensity in the different diffraction orders is measured by integrating the intensity of the corresponding areas in the Fourier plane image. Details on the equipment and a diagram of the setup can be found in Figure S6. ■ASSOCIATED CONTENT * sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c01692. Figure S1 showing phase and amplitude profiles for the blazed metagratings; Figure S2 showing error of eq 1; Figure S3 showing simulation results for a metasurface blazed grating with 8 elements; Figure S4 showing plots of reflected field distribution for a blazed grating at several air gap values; Figure S5 showing details of the fabrication of the MEMS metasurface devices with relevant discussion; Figure S6 showing a schematic of optical measurement setup; Figure S7 showing characterization and discussion of air gap as a function of voltage (PDF) ■AUTHOR INFORMATION Corresponding Author Sergey I. Bozhevolnyi −Centre for Nano Optics, University of Southern Denmark, Odense DK-5230, Denmark; orcid.org/0000-0002-0393-4859; Email: seib@ mci.sdu.dk Authors Paul C. V. Thrane −Centre for Nano Optics, University of Southern Denmark, Odense DK-5230, Denmark; SINTEF Smart Sensors and Microsystems, 0737 Oslo, Norway; orcid.org/0000-0001-5296-2912 Chao Meng −Centre for Nano Optics, University of Southern Denmark, Odense DK-5230, Denmark; orcid.org/00000002-2126-6954 Fei Ding −Centre for Nano Optics, University of Southern Denmark, Odense DK-5230, Denmark; orcid.org/00000001-7362-519X Complete contact information is available at: https://pubs.acs.org/10.1021/acs.nanolett.2c01692 Author Contributions § P.C.V.T. and C.M. contributed equally to this work. Notes The authors declare the following competing financial interest(s): The paper authors along with J. Gjessing and C. Dirdal from SINTEF are inventors on a related patent application led by the University of Southern Denmark and SINTEF under United States Patent Application No. 17/ 467542. ■ACKNOWLEDGMENTS The authors thank C. Dirdal for useful discussions and feedback on the manuscript. This research is supported by the Research Council of Norway (Project 323322), the VKR Foundation (Award in Technical and Natural Sciences 2019 and Grant 37372), and the EU Horizon 2020 Research and Innovation Programme (Marie Skłodowska-Curie Grant Agreement 713694). ■REFERENCES (1) Qiu, C. W.; Zhang, T.; Hu, G.; Kivshar, Y. Quo Vadis, Metasurfaces? Nano Lett. 2021,21, 5461−5474. (2) Scheuer, J. Optical Metasurfaces Are Coming of Age: ShortAnd Long-Term Opportunities for Commercial Applications. ACS Photonics 2020,7, 1323−1354. (3) Chen, W. T.; Zhu, A. Y.; Capasso, F. Flat Optics with Dispersion-Engineered Metasurfaces. Nature Reviews Materials 2020, 5, 604−620. (4) Kamali, S. M.; Arbabi, E.; Arbabi, A.; Faraon, A. A Review of Dielectric Optical Metasurfaces for Wavefront Control. Nanophotonics 2018,7, 1041−1068. (5) Ding, F.; Pors, A.; Bozhevolnyi, S. I. Gradient metasurfaces: a review of fundamentals and applications. Rep. Prog. Phys. 2018,81, 026401. (6) Hail, C. U.; Michel, A. K. U.; Poulikakos, D.; Eghlidi, H. Optical Metasurfaces: Evolving from Passive to Adaptive. Advanced Optical Materials 2019,7, 1801786. (7) Shaltout, A. M.; Shalaev, V. M.; Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 2019, 364, eaat3100. (8) Yang, J.; Gurung, S.; Bej, S.; Ni, P.; Lee, H. W. H. Active Optical Metasurfaces: Comprehensive Review on Physics, Mechanisms, and Prospective Applications. Rep. Prog. Phys. 2022,85, 036101. (9) Du, K.; Barkaoui, H.; Zhang, X.; Jin, L.; Song, Q.; Xiao, S. Optical metasurfaces towards multifunctionality and tunability. Nanophotonics 2022,11, 1761−1781. (10) Ding, F.; Yang, Y.; Bozhevolnyi, S. I. Dynamic Metasurfaces Using Phase-Change Chalcogenides. Advanced Optical Materials 2019, 7, 1801709. Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.2c01692 Nano Lett. XXXX, XXX, XXX−XXX F Research Article Vol. 11, No. 11 / November 2024 / Optica 1560 02π φ(x,y,Ta1) 0 2π φ(x,y,Ta2) Va1 Va2 (b) x y TM TE Total m=0 m=−1 m=+1 m=+2m=−2 (f) Incident Beam +1 Order−1 Order VMEMS=Va1 VMEMS=Va2 BMS MEMS (a) x(TM) z y(TE) k MEMS-BMS BDG 1 ∠r |r| Supercell for MEMS-BMS BDG -400° -200° 0° 200° 400° (c) 0.9 0.8 0.7 0.6 0.5 Ta=150 nm+q2λ/2 Ta=350 nm+q1λ/2 23 4 567 8 910 11 12 12Λ Λ MS1 MS2 Λ x y Air Gap Ta (nm) 0.8 0.6 0.4 0.2 00 500 1000 1500 2000 2500 3000 3500 4000 Reflectance Ta = 350 nm Ex (V/m) 1 0 -1 Ta = 150 nm Reflec. Field (TM) (d) x z y Enorm (V/m) 0 1 2 3 4 5 6 Ta = 350 nm Ta= 150 nm Total Field (TM) (e) x z y Fig. 3. MEMS-BMS BDG with reconfigurable diffraction orders: design. (a) Schematic rendering of the MEMS-BMS BDG for active reflected beam switching between the +1 and −1 diffraction orders by electrically actuating the MEMS-BMS between two distinct air gaps with different voltages. (b) Reversible 1D linear phase gradients of the supercell at air gaps of Ta1=(350 +q1×λ/2)nm and Ta2=(150 +q2×λ/2)nm. (c) Calculated reflection amplitudes (black markers) and phases (red markers) of 12 selected unit cells for constructing the MEMS-BMS BDG supercell, with an incident wavelength of λ=800 nm. (d), (e) Simulated reflected (d) and total (e) electric fields of the MEMS-BMS BDG supercell under a TM excitation with λ=800 nm for Ta=150 and 350 nm, respectively. (f) Calculated diffraction efficiencies of different orders (|m| ≤ 2) as a function of the air gap sizes Ta for both TM and TE excitations with λ=800 nm. to 1750 and 1950 nm (i.e., q1=q2=4, Fig. S13), the efficiencies still remain at ∼65% (m= −1) and ∼70% (m= +1) but decrease slightly due to stronger intercell coupling for increased air gap sizes [31,58]. Overall, the MEMS-BMS BDG designed promises a high-contrast dynamic switching capability between ±1 diffraction orders within a large MEMS-BMS separation range [Fig. 3(f)]. Furthermore, its operation is robust with respect to the operation wavelength (Fig. S14), maintaining a high quality when diffracting into +1 order at Ta=q1×λ/2 over a broad wavelength range, although exhibiting somewhat stronger deterioration when diffracting into −1 order. The latter is related to the circumstance that the −1 order diffractioninvolves both MS layers and the intervening SU-8 layer, making it sensitive to the incident wavelength. In contrast, the +1 order diffraction is governed solely by the MS1 layer, featuring a broad bandwidth operation similar to the MEMS-tunable single-layer MS cases [20,31]. Finally, the MEMS-BMS BDG operation was also found robust with respect to the influence of increased loss of the gold meta-atoms (Fig. S15), moderate variations in SU-8 thickness (Fig. S16), and deviations in meta-atom sizes (Figs. S17). D. MEMS-BMS Blazed Diffraction Grating: Characterization The MEMS-BMS BDG designed above was assembled from a separately fabricated BMS on a glass substrate (14 mm× 14 mm ×400 µm), a fast-speed ultra-flat piezoelectric MEMS mirror (500 µm in diameter, Fig. S19), and a printed circuit board (see Appendix A and Supplement 1 S12). The fabricated BMS was inspected with optical and electron microscopy after each MS1, SU-8, and MS2 layer fabrication step to monitor metaatom geometries and sizes, SU-8 thickness, and alignment quality between the two MS layers [Fig. 4(a) and Figs. S21 to S23]. The MEMS gold mirrors were also checked with optical microscopy to avoid any contaminations on the mirror surface. After assembling, the MEMS-BMS separation was characterized by examining the reflection spectra of the MEMS-BMS using a broadband light source (Fig. S25). The initial air gap distance was ∼2.5 µm, determined mainly by the viscosity and amount of the glue we applied during assembly. By actuating the inner (or outer) MEMS electrodes, the MEMS mirror can be moved closer to (or away from) the BMS. The total air gap (Ta) tuning range, achieved by Research Article Vol. 11, No. 11 / November 2024 / Optica 1561 (a) 0.5 μm Glass SU8 MS1 MS2 BMS Glass MS1 MS1 0.1 0.2 0.3 0.4 Diffraction Efficiency Air Gap Ta (nm) 0 0.5 1 -0.5 0180020002200240026002800300032003400 -1 Diffraction Contrast 5 0 10 15 20 2 5 10 15 20 VMEMS (V) Inner Electrodes Outer Electrodes (d) TM TE m=-1 m=+1 Contrast q=4 q=5 q=6 q=7 (e) Time (μs) 𝜏rise=6 μs𝜏fall=5 μs 𝜏rise=5 μs 𝜏fall=6 μs Vm -400 -300 -200 -100 0 100 200 300 400 0 10 20 30 20 30 9 11 VMEMS (V) Intensity (mV) m=-1 m=+1 (b) kx (k0) Air Gap Ta (nm) 0.50.40.3 0.20.10 -0.5-0.4-0.3-0.2-0.1 1800 2000 2200 2400 2600 2800 3000 3200 3400 λ=850 nm 0 0.2 0.4 0.6 0.8 1 Ix(c) TM TE kx (k0) Intensity (arb. units) qDiffraction Orders at Fourier Plane 4 5 6 7 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 0.4 0.2 0 -0.5-0.4-0.3-0.2 0.50.40.3 0.20.1-0.1 0 Fig. 4. MEMS-BMS BDG with reconfigurable diffraction orders: experiment. (a) Scanning electron microscopy (SEM) images of MS1 and BMS on the glass substrate. (b) Measured diffraction intensities as a function of air gap sizes Taat the Fourier plane for the incident wavelength of λ=850 nm under TM excitation. (c) Extracted diffraction intensities for different Fabry–Perot orders of q=q1=q2=4, 5, 6, 7 at two specific air gaps that actively channel the reflected power between the +1 and −1 diffraction orders. (d) Measured diffraction efficiencies of the −1 (black) and +1 (red) orders at the wavelength of λ=850 nm as a function of Tafor both TM and TE excitations. Diffraction contrast between ±1 orders is also shown (green). (e) Response time of switching between ±1 diffraction orders (q=q1=q2=4), measured by actuating the inner electrodes of the MEMS mirror with a periodic rectangle signal between 9 and 12 V. applying voltages up to 23 V, was found to be from 1.7 to 3.5 µm, covering four adjacent Fabry–Perot orders (q1=q2=4, 5, 6, 7) at the design wavelength of λ=800 nm (Fig. S25). To characterize the MEMS-BMS BDG, we built an optical setup comprising a fiber-coupled supercontinuum laser with polarization optics (linear polarizer and half-wave plate) and a CMOS camera for capturing direct/Fourier images, or alternatively using a spectrograph for wavelength-resolved Fourier plane imaging (see Appendix A and Fig. S26). The MEMS mirror was electrically actuated to modulate the optical response of the MEMS-BMS BDG, observed visually at the Fourier plane with different diffraction orders well separated (|m| ≤ 2), as shown in Figs. 4(b) and 4(c). For both polarizations, it is clearly seen that the blazed direction can be switched between +1 and −1 diffraction orders in a periodic manner [Figs. 4(b) and 4(c)]. The experimental diffraction efficiencies of −1/+1 orders at 850 nm wavelength are ∼30%/25% (q1=q2=4), and the contrast between ±1 orders can reach ∼ + 0.80/−0.75, indicating pronounced switching between ±1 diffraction orders [Fig. 4(d)]. The high-contrast switchable diffraction orders, induced by actuating the inner electrodes of the MEMS mirror with 1-Hz alternating 9/11 V voltages, are also documented in a video captured by the CMOS camera (Visualization 3). Note that the optimum operation wavelength shifted from the designed wavelength of 800 nm to that of 850 nm with efficiencies notably lower than simulation predictions [Fig. 3(f)] due to increased loss and surface roughness of the polycrystalline gold meta-atoms [20,31] and the deviations in SU-8 thickness and meta-atom sizes in fabrication (Figs. S15 to S17, S27). It should also be noted that, starting from the maximum Research Article Vol. 11, No. 11 / November 2024 / Optica 1562 of +1 diffraction order, the major radiation power switches successively to 0 and −1 diffraction orders when increasing the air gap [Fig. 4(b)], scanning in steps over three distinct diffraction angles (Visualization 4). Combining this effect with the MS design for quasi-continuous beam steering between three (zeroth, first, and second) diffraction orders [20] may enable beam steering over five distinct diffraction angles covering practically any angular range within ±90◦, a functionality that might be useful for, e.g., LIDAR applications. The MEMS-BMS BDG performance at other incident wavelengths was also studied, showing the behavior expected from simulations (see the preceding section). For example, the +1 diffraction order exhibits better robustness to wavelength changes (Fig. S28), reaching efficiencies/contrasts of ∼25%/+0.8 and 22%/+0.8 for incident wavelengths of 800 and 900 nm, respectively, whereas the −1 order exhibits stronger wavelength dependence, with estimated efficiencies/contrast of ∼18%/−0.4 and 28%/–0.7. Additionally, the switching speed was also characterized by actuating the MEMS mirror with a periodic rectangle signal and detecting spatially separated ±1 orders, showing remarkably fast rise/fall times of ∼5µs [Fig. 4(e)], which is ∼2 orders of magnitude faster than our previous MEMS-tunable single-layer MSs [20,21,23,24]. E. MEMS-BMS Vortex Phase Plate The MEMS-BMS VPP for realizing dynamically controlled polarization-independent 2D vortex beam generation with reconfigurable topological charges of l= +1 and −1 [Fig. 5(a)] is designed by selecting four MEMS-BMS cells (Fig. 2and Supplement 1 S15), with desired reflection phase and high amplitudes|r| ≥ 0.8at two differentair gaps [Figs.5(b) and 5(c)]. Here, we remark that both MEMS-BMS VPP and BDG were fabricated on the same glass substrate using identical processes and assembled into a single MEMS-BMS component. SEM images were taken after MS1 and BMS fabrications [Fig. 5(d)], showing generally good quality, with meta-atom geometries mirroring the design and near-perfect alignment between the two MS layers, despite the presence of rounded corners in the cross-shaped meta-atoms. To characterize the MEMS-BMS VPP, we added a reference arm to our experimental setup, allowing direct investigation of the reflected phase profiles (Fig. S31). The reference Gaussian beam can be adjusted to perform both co-axis and off-axis interferometry with the beam reflected from MEMS-BMS VPP. For both polarizations, the generation of a vortex beam with switchable topological charges of l= ±1 is clearly observed in the interference patterns. With the MEMS mirror actuated at two different voltages of 14 and 17 V, near-field on-axis interferograms display spiral-shaped fringes with opposite winding, while far-field off-axis interferograms reveal fork-shaped fringes with opposite orientations [Fig. 5(e), Visualization 5 and Visualization 6]. The vortex beam characterized by a topological charge of l= −1 with Ta1=∼ q1×λ/2, exhibits better quality [Figs. 5(e) and S30] as only MS1 layer contributes to the overall MEMS-BMS response in this state. Due to the non-uniform reflection amplitudes of the MEMS-BMS unit cells [Fig. 5(c)] and four quadrant phase discretization, the intensity patterns display asymmetric profiles, which are also observed in simulations (Fig. S30). Given the possibilities of designing finer phase steps using low-loss dielectric meta-atoms [30], the efficiency of the MEMS-BMS VPP and the quality of the resulting vortex beam could be improved. 3. DISCUSSION AND CONCLUSION We have developed the electrically driven dynamic MEMS-BMS platform with fast response (∼5µs) by combining lightweight piezoelectric MEMS mirrors (see Appendix A) with plasmonic bilayer MSs. This platform accommodates tunable topological singularities in a 3D parameter space defined by the resonance properties of the meta-atoms in both MS layers and the MEMSBMS separation, enabling thereby complete reflection phase transformation and switching between two encoded functionalities by actuating the MEMS mirror. We have designed and experimentally demonstrated MEMS-BMS components operating in the near-infrared wavelength regime (∼800 nm) for reconfigurable BDG and VPP, both showing distinct optical responses at two operating states, specifically two MEMSBMS separations. The experimental diffraction efficiencies of ∼30%/25% were realized with the MEMS-BMS BDG for respective −1/+1 diffraction orders along with a high contrast of ∼ + 0.80/−0.75, confirming the opposite 1D phase gradients achieved as expected from the simulations. Note that, according to our simulations, the efficiencies of >60% and contrast of >±0.9 can be realized given more precise nanofabrication. For the MEMS-BMS VPP, the generation of the switchable vortex beam with reconfigurable topological charges of l= ±1 was evidenced by tracking the reflection intensity and 2D phase profiles. Since the dual-state operation is achieved using only two sets of voltages, the MEMS-BMS can be scaled up to larger aperture sizes while maintaining small pixel sizes for optimal optical responses, without increasing the control complexity. To further enhance the MEMS-BMS performance, expanding the meta-atom library with diverse materials, geometries, shapes, and orientations in each MS layer could provide more complete amplitude/phase transformations and additional multiplexing channels, leveraging the design’s inherent flexibility. Another intriguing direction would be to further exploit the tunable MEMS-MS platform for dedicated investigations of emergence, evolution, and annihilation of the topological phase singularities [24,60–63]. The substantial design freedom and fine-tuning capabilities of the developed platform enable studies of topological singularities in a highdimensional parameter space, paving the way for multifunctional and multiplexing tunable topological meta-optics. APPENDIX A: METHODS 1. Numerical Calculations The calculation of the complex reflection coefficient of the MEMS-BMS unit cell [Fig. 2(a)] is conducted in two distinct steps: first, a simulation model is constructed in COMSOL Multiphysics v5.6. This model consists of a gold meta-atom placed within a square unit cell with a side length of 3=300 nm. The upper/lower halves of the infinite space are occupied by glass/ SU-8 for the MS1 unit cell, or SU-8/air materials for the MS2 unit cell. Periodic boundary conditions were applied in both x and ydirections; thereby the simulation is related to a 2D infinite array composed of periodically arranged MS unit cells. With this model, we calculated the complex reflection and transmission coefficients of single-layer MS1 and MS2 unit cells with varying meta-atom geometries and dimensions, for normally incident light from either the upper or lower side. Note that each corner of the cross-shaped meta-atoms is rounded with a radius of 5 nm in the COMSOL simulations. Subsequently, we integrated the Research Article Vol. 11, No. 11 / November 2024 / Optica 1563 Incident Beam l=−1l=+1 (a) VMEMS=Va2 VMEMS=Va1 MEMS-BMS VPP (c)(b) ϕ(x,y,Ta2) 0 0.5ππ 1.5π ϕ(x,y,Ta1) 0 0.5π π 1.5π BMS MEMS x(TM) z y(TE) k Va1 Va2 x y x y (d) 0.5 µm Λ Λ MS1 MS2 1 ∠r -200° -100° 0° 100° 200° |r| Unitcells for MEMS-BMS VPP 0.9 0.8 0.7 0.6 0.5 Λ (e) TM 17 V (l=+1) Interferogram(DI)Interferogram (FI) TM TE TM TE 14 V (l=−1) Substrate (l=0) Vm MEMS-BMS VPP Pol. I1 0.8 0.6 0.4 0.2 0 Intensity (FI) 23 4 ∠r |r| 150+q2λ/2 Ta(nm) 350+q1λ/2 Glass MS1 MS1 Glass SU8 MS1 MS2 BMS I1 0.8 0.6 0.4 0.2 0 I1 0.8 0.6 0.4 0.2 0 Fig. 5. MEMS-BMS VPP for generating vortex beam with switchable topological charges. (a) Schematic rendering of the MEMS-BMS VPP for generating vortex beams with switchable topological charges of l= −1 and +1 when the MEMS-BMS is electrically reconfigured between two air gaps with different voltages. (b) Tunable spiral phase distributions for switchable vortex beams with l= −1 and +1 at respective air gaps of Ta=(350 +q1×λ/2)and (150 +q2×λ/2)nm. (c) Calculated reflection amplitudes (black markers) and phases (red markers) of four selected unit cells for constructing the MEMSBMS VPP. (d) SEM images of the MS1 and BMS on the glass substrate. (e) Measured on-axis interferograms at the direct image plane (scale bar, 20 µm), off-axis interferograms at the Fourier plane (scale bar, 0.1k0,k0=2π/λ), and the intensity profiles at the Fourier plane (scale bar, 0.1k0,k0=2π/λ) of the generated vortex beams at the wavelengths of λ=750 nm for both TM and TE excitations. The vortex beam’s topological charge switches from l= −1 to +1 by actuating the inner electrodes of the MEMS mirror from 14 to 17 V, respectively. The interferograms are produced by superposing the vortex beam with a reference Gaussian beam. MS1/MS2 unit cells with the MEMS gold mirror using the transfer matrix method and calculated the total complex reflection coefficients of the MEMS-BMS unit cell (Supplement 1 S2 and S3, Figs. S2 to S6). To avoid any unwanted near-field coupling effects between MS layers, the thickness of the SU-8 layer between MS1 and MS2 layers is increased from 136 nm (i.e., OLBMS =λeff/4) to 389 nm (i.e., OLBMS =3λeff/4), for a design wavelength of 800 nm (Supplement 1 S5 and S6). With the above-developed approach, we calculated the phase response maps for Ta=150 +q2×λ/2 and 350 +q1×λ/2 (q1and q2are non-negative integers) with MS1/MS2 unit cells comprising various meta-atom geometries and sizes (Fig. 2and Figs. S5, S6). To design the MEMS-BMS BDG with reconfigurable diffraction orders, we selected 12 MEMS-BMS unit cells, each featuring a reflection amplitude ≥0.7, from the phase maps, for approximating two contrasting linear phase profiles (i.e., ±2π/123) at two distinct air gaps. The entire MEMSBMS BDG arrangement consists of periodically arranged BDG supercells along both the xand ydirections, with periods of 123=3.6 µm along the xdirection and 3=0.3 µm along the ydirection. In simulation, we applied periodic boundary conditions along both xand ydirections, corresponding to a periodically arranged 2D infinite array. A normally incident plane wave was applied, and the reflected light directed to different diffraction orders was monitored, with different air gaps Research Article Vol. 11, No. 11 / November 2024 / Optica 1564 for estimating the dynamic diffraction efficiencies and contrast. Using this model, the MEMS-BMS BDG operation was investigated under different incident wavelengths [Fig. 3(f) and Fig. S14], increased loss of the gold meta-atoms (Fig. S15), variations in SU-8 thickness (Fig. S16), deviations in metaatom sizes (Fig S17), and the tolerance to the angle of incidence (Fig. S18). The MEMS-BMS VPP for vortex beam generation with switchable topological charges was designed in a similar fashion. In this design, we selected four MEMS-BMS unit cells, each featuring a high-reflection amplitude ≥0.8, to achieve a tunable 2D spiral phase switching between 2πand −2πat two different air gaps. The entire MEMS-BMS VPP structure was simulated with the 3D finite-difference time-domain (FDTD) method. Due to the high computational demands, we scaled down the overall size of the MEMS-VPPto a diameter of3µm and employeda Gaussianbeam with a 1.2-µm waist radius as the incident light in simulation. Reflected fields were monitored and subsequently projected to the far field, for visualizing the intensity and phase profile at the Fourier plane (Fig. S30). 2. Fabrication The BMSs for MEMS-BMS components were fabricated by repeating the standard electron-beam lithography (EBL), gold deposition, and lift-off processes twice. Additionally, an SU-8 spacer layer was added after the fabrication of the MS1 layer (Supplement 1 S12). For the fabrication of each MS layer, the process includes several steps: first, a 100-nm-thick poly(methyl methacrylate) (PMMA A2, MicroChem) layer and a 40-nm-thick conductive polymer layer (AR-PC 5090, Allresist) were successively spin-coated on a square glass substrate (14 mm ×14 mm ×400 µm). Then, the MS pattern was defined at the central area of the glass substrate using EBL (JEOL JSM-6500F field-emission SEM with a Raith Elphy Quantum lithography system). After development, the MS layer was formulated by depositing a 1-nm Ti adhesion layer and a 50-nm gold layer (Tornado 400, Cryofox) followed by lift-off in acetone. Note that the alignment markers were also fabricated concurrently with the MS1 layer. This is crucial as it facilitates the alignment process during the fabrication of the MS2 layer. After the fabrication of the MS1 layer, an SU-8 layer, aiming for a target thickness of 389 nm, was spin-coated over the entire glass substrate, followed by a soft bake, UV curing, and hard bake process to make it a permanent spacer layer. Finally, the MS2 layer was fabricated following the same steps as those used for the MS1 layer, with an additional alignment process included. Compared with our earlier work, this MEMS mirror utilizes the same fabrication process [20,21], but with a different electrode layout and smaller mirror diameter [Fig. 1(d) and Fig. S19]. The smaller mirror diameter of 500 µm reduces mirror mass, resulting in higher resonance frequency and faster actuation. The piezoelectric membrane responsible for moving the mirror consists of four cantilevers, instead of the annular membrane used earlier. The stiffness of these cantilevers is less than that of the annular membrane, but together with the smaller mass of the mirror, the total response is faster while still having a displacement range of ∼1µm for 23 V. This is adequate for operating our MEMS-BMS component between two configuration states, which requires ∼200 nm, as well as for investigating the MEMS-BMS behaviors across several adjacent Fabry–Perot orders that exhibit a period of λ/2=400 nm for incident light with λ=800 nm. Before assembling the MEMS-BMS component, the ultra-flat piezoelectric MEMS mirror was sputtered with a 100-nm-thick gold layer to block any transmission around the near-infrared wavelength of λ=800 nm. 3. Characterization The experimental setup for MEMS-BMS BDG is shown in Fig. S26. A collimated fiber-coupled supercontinuum laser (SuperK Extreme, NKT) was directed through a first half-wave plate (HWP1, AHWP10M-980, Thorlabs), an ND filter, a mirror, a linear polarizer (LP; LPNIR050-MP2, Thorlabs), a second half-wave plate (HWP2, AHWP10M-980, Thorlabs), a lens L1(f=200 mm), two beam splitters (BS1,2; CCM1-BS014, Thorlabs) successively, and then focused onto the MEMS-BMS BDG by an objective (Obj; M Plan Apo, ×50/0.55, Mitutoyo). The combination of LP and HWP2is used for adjusting the input linear polarization orientation while keeping a constant incident power. The reflected light was collected by the same objective and passed through BS2and a tube lens (TL; TTL200-S8, Thorlabs), generating the first direct image where an iris is placed for filtering out the reflected light within the interested area in the MEMSBMS component. The first direct image is then transformed by a relay lens (RL; AC254-200-B-ML, f=200 mm, Thorlabs) to the corresponding Fourier image and captured by a CMOS camera (CMOS; DCC1545M, Thorlabs), according to a 2 f configuration. A flip lens (FL; AC254-100-B-ML, f=100 mm, Thorlabs) is used for switching between the direct and Fourier images. Additionally, a flip mirror (M2) is used to switch between the CMOS camera and spectrograph (Model SR-303i-A-SIL, Andor), for direct/Fourier plane imaging or wavelength-resolved Fourier plane imaging, respectively. To characterize the MEMS-BMS components, a normally incident Gaussian beam was slightly focused into a spot with a diameter of ∼30 µm, which is comparable to the fabricated MEMS-BMS sizes of 28.8 µm×28.8 µm for the BDG and 30 µm×30 µm for the VPP. This beam spot size corresponds to a beam divergence of ∼0.7◦, estimated using θ=λ/(πnw0), where θis the beam divergence, λis the free-space wavelength (800 nm), nis the refractive index of the medium (1.466), and w0is the beam radius (15 µm). Note that an iris is used in the intermediate image plane to filter out the area of interest in the measurement, as shown in Fig. S26C and Fig. S31B. The experimentally obtained diffraction contrast is calculated by [I(m= +1)−I(m= −1)]/[I(m= +1)+I(m= −1)]. To estimate the switching speed of the MEMS-BMS BDG between ±1 diffraction orders, the setup described above is modified by replacing the supercontinuum laser and CMOS camera with a CW Ti: sapphire laser (Spectra-Physics 3900S, wavelength range: 700–1000 nm), and a photodetector (PD; PDA20CS-EC, Thorlabs), respectively. The signals from the PD are acquired with an oscilloscope (DSOX2024A, Keysight). In the measurement, the MEMS-BMS BDG is actuated with periodically alternating voltage signals from a function generator (TOE 7402, TOELLNER). For characterizing MEMS-BMS VPP, we added a reference arm to the above-described setup (Fig. S31). The modified setup resembles a Michelson interferometer in which the reference Research Article Vol. 11, No. 11 / November 2024 / Optica 1565 Gaussian beam can be adjusted to perform on-axis and off-axis interferometry with the beam reflected from the MEMS-BMS VPP. The reference arm introduced a reference Gaussian beam with a similar intensity and nearly equal optical path length to that of the reflected light from the MEMS-BMS. The interferogram profiles at the direct image and Fourier planes can be captured by a CMOS camera, for estimating the topological charges of the generated vortex beam. The intensity profiles at the direct and Fourier image planes can be recorded with the reference beam blocked. Funding. ATTRACT programme funded by the European Union’s Horizon 2020 Research and Innovation Programme (101004462); Villum Fonden (37372, 50343, award in Technical and Natural Sciences 2019); Danmarks Frie Forskningsfond (1134-00010B); Norges Forskningsråd (323322). Acknowledgment. We gratefully acknowledge Karolina Milenko and Zeljko Skokic at SINTEF for designing and fabricating the MEMS mirrors, Shailesh Kumar for help setting up the spectrograph, Torgom Yezekyan and Volodymyr Zenin for assistance with experiment setup, as well as Zhengli Han for fruitful discussions. C.M. and S.I.B. conceived the idea. C.M. performed the simulations, fabricated the BMS samples, built the setup, conducted the measurements, and analyzed the data. P.C.V.T. assembled MEMS-BMS devices. C.M. and F.D. provided the first draft of the manuscript. All authors contributed to the discussion of the results obtained and writing the manuscript. S.I.B. supervised the project. Disclosures. 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ARTICLES 5.5 Metasurface Polarimeter for Structural Imaging and Tissue Diagnostics Thrane P.C.V., Meng C., Bykov A., Sieryi O., Ding F., Meglinski I., Dirdal C.A. and Bozhevolnyi S.I. Metasurface Polarimeter for Structural Imaging and Tissue Diagnostics. Submitted, preprint at https://doi.org/10.48550/arXiv.2501.05864 (2025). Metasurface Polarimeter for Structural Imaging and Tissue Diagnostics Paul Thrane1,2*†, Chao Meng2*†, Alexander Bykov3, Oleksii Sieryi3, Fei Ding2, Igor Meglinski4, Christopher A. Dirdal1, Sergey I. Bozhevolnyi2* 1Smart Sensors and Microsystems, SINTEF Digital, Gaustadalleen 23C, 0373 Oslo, Norway. 2SDU Centre for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark. 3OPEM, ITEE, University of Oulu, 90014 Oulu, Finland. 4College of Engineering and Physical Sciences, Aston University, Birmingham B4 7ET, U.K. * P.T: [email protected]; C.M: [email protected].dk; S.I.B: [email protected] † These authors contributed equally Abstract Histopathology, the study and diagnosis of disease through analysis of tissue samples, is an indispensable part of modern medicine. However, the practice is time consuming and labor intensive, compelling efforts to improve the process and develop new approaches. One perspective technique involves mapping changes in the polarization state of light scattered by the tissue, but the conventional implementation requires bulky polarization optics and is slow. We report the design, fabrication and characterization of a compact metasurface polarimeter operating at 640 nm enabling simultaneous determination of Stokes parameters and degree of polarization with ±2% accuracy. To validate its use for histopathology we map polarization state changes in a tissue phantom mimicking a biopsy with a cancerous inclusion, comparing it to a commercial polarimeter. The results indicate a great potential and suggest several improvements with which we believe metasurface polarimeter based devices will be ready for practical histopathology application in clinical environment. Introduction Polarimetric mapping and characterization of biological tissues, including Mueller matrix and Stokes imaging, have shown significant potential for applications in histological tissue characterization1–3. Mueller matrix imaging4, for example, has been found effective for the detection of morphological and structural alterations associated with cancer5,6, which has led to the developments of systems such as Mueller matrix imaging endoscopes7,8. Similarly, polarization-holographic Mueller matrix methods9,10 can be applied to the assessment of the 3D morphology of biological tissues with applications in disease diagnosis11, while Stokes polarimetry has been demonstrated as an effective tool for screening the progression of Alzheimer's disease12. These label-free and non-destructive imaging techniques can facilitate the analysis of biological tissue by eliminating the need for conventional sectioning and staining procedures. One such promising technique involves structural imaging of tissue samples by mapping how the state of polarization (SOP) of light is altered by scattering processes in the tissue, and has been applied to the diagnosis and grading of colon cancer13. Probing the biological structures in this way not only removes the need to stain the samples and can be done without sectioning and mounting but is also suitable for automated measurement acquisition and analysis. Such a development would significantly speed up diagnosis and subsequent treatment, in addition to reducing intraand interobserver variability of diagnosis arising from the strong reliance on personal skills and qualifications for conventional methods. Crucial for such polarization-based measurements are polarimeters – devices that measure the light SOP. Polarimeters fall into one of two categories depending on their principle of operation. Division-of-time systems have a time varying component that measures different properties of the incoming light at different times, determining the full SOP after several measurements. One common way of doing this is by sending the light through a rotating quarter waveplate with a static linear polarizer and then measuring the transmitted intensity, the Fourier decomposition of this signal is then used to find the SOP14. Division-of-space systems, on the other hand, split the incoming light into several parts with varying intensities dependent on the SOP, which can then be measured simultaneously and used to calculate the initial SOP15,16. Both categories of polarimeters have seen major developments in later years, building on advances in integrated optics to enable compact systems that are faster, more accurate and enable new use cases17. Nanostructured surfaces for simultaneous polarimetry have, for example, been used to make Figure 4. Characterization of the MS polarimeter with fully polarized light. a Photo of the calibration setup, where a fiber coupled laser (λ = 640 nm) sends light through polarization optics and into the MS polarimeter. The integrated CMOS camera has been removed in the photo (see Figure 1 d, which makes it possible to check the beam alignment on the MS with a separate camera placed outside the polarimeter (top-right of the picture). b and c Beam alignment images. The difference between the two images is the width of the incident beam. d Diffraction pattern acquisition. After alignment the CMOS camera is inserted into the setup and acquires diffraction pattern images. e Acquisition process summary: The average noise value is subtracted from the image, the diffraction spot intensities are summed up and these are used to calculate the Stokes vectors by applying a calibration matrix. f Measurement results of different polarization states with DOP = 1. Circles with the same color and connected by a line correspond to the same measurement of a Stokes vector and corresponding DOP. The top row presents measurements done with a Thorlabs PAX1000, the MS polarimeter before and after calibration. The bottom row displays the variation between measurements. g Subset of the polarization state measurements plotted on a Poincare sphere. Circles are measured by the Thorlabs PAX1000, + signs are from the MS polarimeter before calibration and triangles are after calibration. Points corresponding to the same measured polarization state are shown in the same color, for most measurements the circles and triangles overlap – indicating good agreement after calibration. When the DOP is less than 1, there is some light intensity in all the diffraction spots, even for the polarization states that the gratings have been designed for, see example images in Figure 5 a-c. The plots in Figure 5 d-e are DOP measurements of partially polarized states close to the line between s2 = 1 and s2 = -1, where the polarimeter is expected to have the worst performance due to the uneven efficiencies of the SCab grating. As can be observed in Figure 5 e, for large DOP > 0.8 the difference between the reference polarimeter and the MS polarimeter after calibration stays below 2%, while for lower DOP(i.e., 0.8>DOP>0.2) the difference is below 5%. When the DOP drops below 0.2 the difference becomes much larger, as the intensity variations in the diffraction spots become smaller. For this reason, replacing the CMOS sensor with a counterpart that has better intensity resolution and less noise should improve the accuracy for low DOP measurements. Figure 5. Characterization of the MS polarimeter with partially polarized light. a-c Three example images of the diffraction spots when measuring partially polarized light. d DOP measurements for a series of measurements where the DOP is cycled between 0 and 1 over four repetitions. e Difference between two polarimeters as a function of DOP. f Polarization state measurements of partially polarized light in a Poincare sphere. The distance to the origin is proportional to the DOP. Red and green colors respectively indicate the measurements from the MS polarimeter before and after calibration, while blue points are measurements by the reference polarimeter. The calibration results in Figures 4 and 5 were done using carefully prepared polarization states and simultaneous measurements with both the MS and reference polarimeters. To validate the MS polarimeter in a realistic use case it was tested in a setup for digital histopathology35. The calibration matrices used are the same as those in Figure 4, and the results are presented in Figure 6 together with a separate reference measurement done using the commercial polarimeter. Figure 6 a is an image of a tissue phantom consisting of 2 materials made to replicate the geometrical and optical scattering properties of a histological tissue block with a cancerous inclusion38. Right-handed circularly polarized light with DOP = 1 is focused onto a spot on this tissue phantom and the scattered light is measured using the MS polarimeter. The spot is scanned across a region of the tissue phantom and Figures 6 b, c are maps showing how the DOP of the scattered light varies across the sample as measured by the two polarimeters. As observed in the DOP maps, both polarimeters give similar results with lower DOP values in regions mimicking the cancerous tissue, although the MS polarimeter exhibits comparatively more noise in these locations. To quantify the differences between the two polarimeters, three areas are selected and marked in blue, green and magenta, respectively corresponding to areas outside the inclusion, where the inclusion is thin and where it is thick – these regions possess different average DOP values in the measurements. A breakdown of all the pixel measurements within each of these areas is given in Figures 6 d-h. The main source of differences between the two polarimeters can be understood by looking at the intensity distributions measured by the PAX1000 polarimeter shown in Figure 6d. Light scattered from the inclusion areas have on average less intensity and a much higher intensity variation; in the magenta-colored area the intensity is evenly distributed across 7 dBm, while for the blue marked area outside the inclusion most measurements are within 2 dBm of each other. This, combined with the lower DOP and correspondingly lower contrast between diffraction spot intensities for the inclusion areas result in the noticeably larger variation in the measurements from the MS polarimeter for these areas – look for example at the difference in distribution of the magenta-colored measurements in Figures 6 e and 6 f. This difference is still visible when breaking down the polarization states on component basis in Figures 6 g and 6 h, where the MS polarimeter does well for the 𝑠𝑠1 component but is slightly off for 𝑠𝑠2 and 𝑠𝑠3 which have distributions close to zero. Notice also that the MS polarimeter gives a larger DOP than the reference polarimeter for the areas marked with magenta and green. This is attributed to the fact that the calibration matrices were constructed using fully polarized light, and thus are biased towards highly polarized light. Future implementations will mitigate this effect by including also the DOP in the calibration as demonstrated in Figure 5, but for several different polarization states spread evenly across the Poincare sphere rather than just along one line. In total, the MS polarimeter does a good job characterizing the polarization states and the different regions of the tissue phantom are easily distinguished. However, it was found that for real tissue samples, which have less uniformity than the tissue phantom and thus even greater variability in scattered intensity and DOP, the current implementation of the MS polarimeter is not good enough in terms of dynamic range. While this can be partly mitigated by dynamically adjusting exposure times, the accompanying increase in acquisition time when scanning the whole sample is detrimental for real use cases. A simple solution is to replace the CMOS sensor with a strip array or one photodiode for each diffraction order. This modification would increase the dynamic range and sensitivity, as well as remove the current bottleneck in scanning speed which is limited by a maximum sampling rate of 400 Hz, determined by the speed of the rotating wave plate in the commercial polarimeter. For reference the maximum frame rate of the MS polarimeter is around 600 Hz, limited by the CMOS sensor frame rate for the relevant subset of pixels. To conclude, we have designed, fabricated and characterized a dedicated MS polarimeter, benchmarking it against a commercial polarimeter for both fully and partially polarized light of wavelength 640 nm. We have found that both design and fabrication MS imperfections can be calibrated away using a simple procedure involving several calibration matrices. Furthermore, we have demonstrated its use for digital histopathology, where it is expected to enable systems for scanning tissue samples that are faster, more compact and cheaper than current laboratory prototypes. Areas of improvement include increase in the dynamic range and mitigation of low DOP measurements, both of which are expected to be straightforwardly implemented in future devices by switching to fewer but more sensitive pixels and improving the set of polarization states used for calibration. We believe that, with these improvements in place, the considered metasurface polarimeter based devices will be ready for practical histopathology applications in clinical environment. Figure 6. Benchmarking with tissue phantom. a Microscope image of a tissue phantom used for comparing the MS polarimeter against a reference polarimeter (Thorlabs PAX1000). Within the area marked with an orange square, the DOP is imaged pointwise using the reference polarimeter b and MS polarimeter c. The measurement points within the areas marked with blue, green and magenta in b and c are presented in more detail in the remaining plots d-h using the same colors. d Histogram of the reflected power as measured by the PAX1000. e and f Polarization states plotted on a Poincare sphere with the DOP represented as the radius, as measured by the PAX1000, e, and the MS polarimeter, f. g and h Histograms of the corresponding Stokes parameters and DOP plotted for the PAX1000, g, and the MS polarimeter, h. Colored triangles indicate the average values of the various distributions. Methods Metasurface design and fabrication The MS unit cells and super cell gratings were simulated and optimized using the finite element method (FEM) in COMSOL Multiphysics 5.6. The permittivity of Au was based on tabulated values39 but with a factor 3 increase in the imaginary part of the permittivity for Au material. This adjustment gives closer agreement between simulation and experiments likely due to surface roughness, grain boundary effects and increased damping from a titanium adhesion layer. The MS was fabricated with electron-beam lithography (EBL) and a lift-off process: Starting with a chip from a polished Si wafer, a 3 nm Ti adhesion layer, a 120 nm Au layer, 3 nm Ti adhesion layer and a 50 nm SiO2 layer were deposited (Tornado 400, Cryofox). This was followed by spin coating of 100 nm PMMA (PMMA A2, MicroChem). The MS pattern was then inscribed using EBL (JEOL JSM-6500F field-emission SEM with a Raith Elphy Quantum lithography system) and subsequent development. The pattern was converted to Au structures by lift-off in acetone after deposition of a 2 nm Ti adhesion layer and 50 nm Au layer (Tornado 400, Cryofox). Polarimeter fabrication and calibration A model of the MS polarimeter was made in Zemax to optimize the choice of components and their alignment. The polarimeter consists of the MS substrate glued to a non-polarizing beam splitter (Thorlabs BS010) with a plano-convex lens (9 mm focal length) glued on the opposite side as shown in Figure 1, both using UV curing glue (Norland Optical Adhesive 61). The beam splitter was placed on a 6-axis stage connected to a CMOS camera (Thorlabs CS165MU/M) using a custom bracket. Alignment and calibration were done with the setup shown in Figure 4. A 640 nm fiber coupled laser was connected to a combined collimator/beam expander and sent through polarization controlling optics. Perfect alignment of the beam on the MS was confirmed by imaging the MS surface and beam position through the beam splitter by temporarily removing the integrated CMOS camera. To test the calibration for partially polarized light, a laser was sent through two polarization maintaining fibers, adjusting the relative angle between these two fibers changed the DOP between 0% and 100%. Tissue phantom measurements A two-component phantom was designed to mimic a histological tissue block, combining adipose and tumorous tissues with complex geometries. A real histological sample of biotissue was used as a basis, with the outlines of the tumorous tissue extracted from a polarimetric scan and converted to a 3D displacement map. The phantom was subsequently 3D printed by stereolithography using UV-curable resins (Formlabs Elastic and Formlabs Clear) with added zinc oxide nanoparticles to model the scattering properties of the adipose tissue. Upon completion, the printed object was rinsed in a solvent bath to remove any remaining resin and then cured in a UV oven to ensure full solidification and structural reinforcement. Finally, the cancerous inclusion of the phantom was added using opaque resin (Photocentric Flexible White and Zortax White Ivory) and the surface was polished after curing in an ultraviolet chamber38. The measurements of the tissue phantom were performed in a setup for polarimetric histopathology35. A supercontinuum laser was filtered using an acousto-optic tunable filter (640 nm let through) before going through static polarization controlling optics and then being focused onto the sample at an incidence angle of 55°. 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This work was also partially supported by the Research Collaborations grant (1203766815), under the International Science Partnerships Fund funded by the UK Department for Science Innovation and Technology in partnership with the British Council. Author contributions P.T., C.M., C.A.D., S.I.B. and I.M. conceived the idea. MS design and simulation was done by C.M., while P.T. did the system integration design. C.M. fabricated the MS and both P.T. and C.M. did the polarimeter integration. O.S. and A.B. fabricated the tissue phantom. C.M. and O.S. performed the measurements. P.T. a nd C. M . did the calibration and analyzed the results, with input from S.I.B. and F.D. All authors contributed to the discussion of the results and writing the manuscript. P.T. provided the first draft of the manuscript. C.M., C.A.D. and S.I.B. supervised the work. Competing interests The authors declare no competing interests. 112 CHAPTER 5. ARTICLES REFERENCES 119 78. 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