Radiative energy band gap of nanostructures coupled with quantum emitters around the epsilon-near-zero frequency

1 Radiative energy bandgap of nanostructures coupled with quantum emitters 1 around the epsilon-near-zero (ENZ) frequency 2 Tao Gong,1,2 Inigo Liberal,3 Miguel Camacho,4 Benjamin Spreng,1 Nader Engheta,5,* and Jeremy N. 3 Munday1,* 4 1Department of Electrical and Computer Engineering, University of California, Davis, CA, USA 5 2Department of Materials Science and Engineering, University of California, Davis, CA, USA 6 3Institute of Smart Cities, Public University of Navarre, Pamplona, Spain 7 4Department of Electronics and Electromagnetism, University of Seville, Seville, Spain 8 5Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, 9 USA 10 11 Abstract 12 Epsilon-near-zero (ENZ) materials have been demonstrated to exhibit unique electromagnetic properties. Here 13 we propose the concept of radiative energy bandgap for an ENZ nanoparticle coupled with a quantum emitter 14 (QE). The radiative emission of the coupled QE-nanoparticle can be significantly suppressed around the ENZ 15 frequency and substantially enhanced otherwise, yielding an effective energy bandgap for radiation. This 16 suppression is effectively invariant with respect to the particle size and is therefore an intrinsic property of the 17 ENZ material. Our concept also heralds an alternative pathway to quench the emission from a QE, which may 18 find potential application in quantum information storage. 19 20 The optical properties of a homogeneous non-magnetic material are fundamentally determined by its 21 frequency-dependent permittivity (𝜀 = 𝜀𝑟+ 𝑖𝜀𝑖). For most materials in a broad frequency range 𝜀𝑟 is either 22 positive or negative, yielding a dielectric or metal-like property, respectively. Nonetheless, there can be narrow 23 frequency bands where 𝜀𝑟 approaches near-zero values (referred to as epsilon-near-zero, or ENZ), as they are 24 inherent in the material’s dispersion. For metals, the ENZ frequencies usually reside in the UV region [1-4]. 25 Other photonic materials, such as transition-metal nitrides and doped semiconducting oxides, have ENZ 26 frequencies in the visible and near-infrared (NIR) regimes, enabling more amenable experimental 27 characterization and potential applications [5-9]. Besides, structured materials (metamaterials, waveguides, or 28 composites), exhibiting effective ENZ-like behaviors, can enable tuning of the ENZ frequency due to 29 resonances or structural mode dispersion through careful design of their geometry and size, however, at the 30 cost of sophisticated fabrication processes and spatial dispersion [10-12]. 31 At the ENZ frequency, the electromagnetic field can be described spatially in a quasi-static limit (while 32 temporally dynamic) with negligible phase advances and strong spatial coherence, resulting in a wealth of 33 fascinating phenomena such as electromagnetic field supercoupling [13,14], resonance pinning [15], perfect 34 optical absorption [16], and ultrafast optical switching [17,18]. In particular, profound modulation of the 35 spontaneous emission from a quantum emitter (QE) has been investigated when coupled with ENZ structures. 36 2 For instance, the emission is dramatically quenched when a QE is placed inside of an enclosed cavity bound 1 by ENZ walls [19,20]. Contrastingly, strong emission enhancement occurs if the QE is positioned in a nano- 2 channel or waveguide at the cut-off frequency where the ENZ condition holds [21-23], also leading to 3 nonperturbative decay dynamics [24]. However, these emission modulations require the emitter to be placed 4 inside of a closed or semi-closed ENZ structure, bringing about inevitable experimental challenges and 5 limitations. 6 In this work, we theoretically investigate the radiation properties of a perpendicularly oriented QE coupled 7 with an ENZ nanoparticle with realistic material dispersion. We propose and demonstrate numerically the 8 concept of a radiative energy bandgap for a coupled QE-ENZ nanoparticle system. Specifically, the system 9 always exhibits suppressed radiation around the ENZ frequency of the nanoparticle, forming a radiation 10 “stopband”, while strong resonance-induced emission enhancement occurs outside the band. Additionally, we 11 find that the bandgap is almost invariant with respect to the structural size. As such, the radiation suppression 12 is mostly determined by the optical properties of the ENZ material (i.e., the ENZ frequency and the dispersion 13 around it) rather than the shape or size of the nanoparticle, in contrast to that induced by photonic or plasmonic 14 resonances. Our results also suggest an alternative route to quench the spontaneous emission from a QE for 15 potential application in quantum information storage. 16 For a nanoparticle with a given geometry, size, and material, the allowed electromagnetic modes are 17 defined with resonance frequencies and corresponding field distributions. The resonant modes at frequencies 18 with positive 𝜀 correspond to dielectric resonances originating from the displacement currents due to the 19 oscillations of bound electrons, while those at frequencies with negative 𝜀 relate to plasmonic resonances 20 resulting from the oscillation of free electrons at the surface of the particle [25]. Considering the permittivity 21 of a natural material with the conventional Drude-like dispersion, plasmonic resonances are usually located at 22 lower frequencies than the dielectric resonances. Yet, around the ENZ frequency, no resonant modes would 23 exist as the wavelength approaches infinity with quasi-static field spatial distribution across the particle. 24 Consequently, a nanoparticle inherently features discrete mode energy states separated by a primary gap 25 centered around the ENZ frequency, as shown by the schematic in Fig. 1(a). 26 A direct manifestation of the resonant modes of a nanoparticle is Mie scattering [26]. Figure 1(b) shows 27 the scattering intensity of an ITO nanosphere in the far zone illuminated by a broadband plane wave. The ITO 28 material considered here is purchased from Sigma Aldrich® in the form of an ITO-coated glass with a 29 measured film thickness of about 20 nm and a measured surface resistivity of 85.3 Ω/sq (PubChem SID: 30 329762435). It features an ENZ frequency of ~1.06 eV, corresponding to a free-space wavelength of ~1.172 31 μm. We measured its permittivity using spectroscopic ellipsometry over a broad wavelength range (Fig. S1 in 32 the Supplemental Material [27]). This material is chosen for analysis because: (1) The material’s dispersion 33 nicely spans from positive to negative values in the UV-NIR wavelength regime; (2) the nontrivial loss of the 34 material makes the analysis more practically insightful (Figure S1 in the Supplemental Material [27] lists the 35 loss (the imaginary part of relative 𝜀, i.e., 𝜀𝑖) at several frequency points of interest: 0.385 at the ENZ 36 frequency, 0.27 at 𝜀𝑟= 1 and 0.52 at 𝜀𝑟= −1); (3) the material is commercially available, ensuring consistent 37 and repeatable material properties. The intensity distribution of the scattered field reveals that the wavelength 38 associated with the primary dielectric resonance scales approximately with the sphere diameter 𝐷 as 39 3 𝜆~𝑛(𝜆)𝐷, where 𝑛(𝜆)=√𝜀(𝜆) denotes the wavelength-dependent refractive index of the material [28]. We 1 note that the plasmonic resonance converges to the wavelength (~1.4 μm) that renders 𝜀~ − 2 in the small 2 sphere size limit. This wavelength corresponds to the localized surface plasmon resonance (LSPR). As the 3 size increases, resonance redshifts due to retardation effects [29,30]. Effectively, a wavelength (energy) gap 4 of the scattered photons arises around the ENZ frequency for a given nanosphere. 5 6 7 FIG. 1. (a) Schematic of the nanoparticle resonant mode energy states and the effective energy bandgap. Around 8 the epsilon-near-zero (ENZ) frequency, no resonant modes can exist, thus an energy “bandgap” arises. (b) 9 Calculated scattering intensity from a nanosphere made of ITO upon the illumination from a broadband plane 10 wave. Strong scattering occurs when plasmonic or dielectric resonant modes are excited, yet scattering is much 11 weaker around the ENZ frequency. A scattered photon wavelength (energy) bandgap therefore is induced. 12 13 An alternative manifestation of the bandgap effect is through the coupling with a QE (e.g. an excited 14 fluorescent molecule or a quantum dot). When a QE is placed in proximity to a nanoparticle, a coupled system 15 is created: the presence of the nanoparticle modifies the local density of electromagnetic states at the position 16 of the QE, altering its spontaneous emission rate. In parallel, the presence of the QE may excite resonant modes 17 of the nanoparticle and the nanoparticle will re-radiate (scatter) the photons which may interfere with the QE 18 emission as well. Therefore, as a system, the radiative emission is significantly modified in terms of the 19 spectral profile when compared to an otherwise standalone QE [31-34]. Note that the alteration of the radiative 20 emission depends strongly on the orientation of the QE, the size and shape of the nanoparticle, and the 21 permittivity of the material composing the particle in a nontrivial manner [35-37]. In the past, research on the 22 emission properties of such coupled systems have prevalently been centered on using plasmonic 23 nanoparticles/nanoantennae to enhance or quench the fluorescence and tailor the radiation pattern of molecules 24 whose emission wavelengths are close to the corresponding plasmon resonances of the nanoparticles or 25 nanoantennae [31,32,36,38-42]. Our study here instead focuses on the radiative emission properties of the 26 coupled system in a broader range crossing the ENZ frequency. 27 4 Let us examine in brevity how the spontaneous emission from the QE is modified when coupled with a 1 nanoparticle. The inset of Fig. 2(a) shows a perpendicularly oriented QE (modeled as an oscillating dipole) 2 placed at a fixed distance (20 nm) above an ITO nano-platelet of a square shape with a thickness of 50 nm and 3 varying lateral size (side of the square). Here we perform the finite-difference-time-domain (FDTD) 4 simulation using the Lumerical® software. In the simulation, the QE is set as a dipole source with a broad 5 emission bandwidth. A box power monitor is placed to enclose either the dipole alone (for the emission 6 calculation from just the QE) or both the dipole and the nanoplatelet (for the emission calculation from the 7 coupled system) to collect the radiation power. The spontaneous emission from the QE when coupled to the 8 ITO platelet is substantially enhanced (by a factor of ~1300), with the maximum enhancement occurring at a 9 wavelength of ~1.29 μm. This maximum translates to the resonance frequency of the propagating surface 10 plasmon polariton (SPP) where 𝜀~ − 1, particularly when the lateral size of the plate is sufficiently large (Fig. 11 2(a)). This enhancement can be attributed to the resonant energy transfer from the QE to the SPP mode of the 12 nanoplatelet [38]. We also note that the enhancement saturates when the lateral size goes beyond 200 nm. This 13 behavior is due to the non-negligible loss in the material which limits the propagation of the SPP within ~200 14 nm laterally; a further increase in the lateral size does not increase the coupling strength from the QE to the 15 polariton. 16 The radiative emission from the coupled QE-nanoplatelet system undergoes either an enhancement or 17 suppression, depending on the wavelength of interest. Intriguingly, the radiation is notably suppressed around 18 the ENZ frequency irrespective of the lateral size of the platelet, although the optimal suppression and the 19 corresponding wavelength varies slightly (Fig. 2(b)). The suppression of radiation can be understood as a result 20 of the destructive interference of the QE and the induced dipole in the platelet. In an ideal scenario, the 21 boundary condition at the interface between a bulk ENZ material and vacuum is equivalent to that between 22 vacuum and a perfect magnetic conductor (PMC), where an image dipole is induced inside the material with 23 a 180 degree out-of-phase oscillation along the perpendicular direction. By contrast, a laterally oriented QE 24 cannot induce such an image dipole hence no evident radiation inhibition would result. However, the non- 25 monotonic variation of the suppression as well as its corresponding wavelength is indicative of the deviation 26 from the perfect image charge model because of the convoluted interplay between the material’s loss, finite 27 thickness and finite lateral size of the platelet, and the finite distance between the QE and the platelet. As a 28 comparison, an ideal ENZ platelet with negligible loss features a smooth convergence of the wavelength of 29 optimal suppression to the ENZ frequency (Fig. S2(a) in the Supplemental Material [27]). Figure 2(c) shows 30 that although the radiation from the coupled system is suppressed at the ENZ frequency, the total emission 31 (radiative plus nonradiative) from the QE is increased by more than 200 times. This behavior indicates that 32 most of the energy transferred from the QE is dissipated nonradiatively at the ENZ frequency due to 33 considerable loss inside the material even if no resonant mode is excited. The inset shows the electric field 34 distribution in the platelet with a lateral size of 100 nm at two different wavelengths. At the SPP resonance 35 wavelength (~1.3 μm), the field is mostly concentrated at the top ITO-air interface because the SPP propagates 36 near the surface; however, the field is distributed throughout the slab at the ENZ frequency (~1.172 μm). We 37 note here at the ENZ frequency the attenuation of the field in the vertical direction is attributed to the loss of 38 the material, not due to surface wave effect as for the SPP resonance. For comparison, the field distribution in 39 5 an ideal ENZ platelet is relatively uniform vertically across the slab, as shown in Fig. S2(a) in the Supplemental 1 Material [27]. 2 The full spectra of the radiated power from the coupled QE-platelet with varying lateral size is shown in 3 Fig. 2(d). We observe a narrowband of radiation suppression located around the ENZ frequency, with a 4 maximum of nearly 50% suppression. This behavior signifies a radiation energy “bandgap” where much fewer 5 photons can be radiated out. Note that loss relaxes the extreme boundary conditions characterizing ideal ENZ 6 media and therefore weakens the radiation suppression compared with low-loss cases. In fact, if the ITO 7 material is replaced with an ideal ENZ material, complete suppression is attainable (Fig. S2(b) in the 8 Supplemental Material [27]). We further note that the maximum radiation enhancement takes place around 9 the SPP resonance (~1.3 μm), but the corresponding wavelength progressively blueshifts as the size increases. 10 This behavior indicates that the maximum energy transfer from the QE to the nanoplate at the SPP resonance 11 does not necessarily convert into optimal radiation, as the radiation is due to the outcoupling of the surface 12 plasmon mode into radiation. At the SPP resonance the outcoupling is not the most efficient since most of the 13 energy is dissipated nonradiatively. For shorter wavelengths (𝜀 > 0), the radiation enhancement is attributed 14 to the primary dielectric resonant mode, and higher-order resonances cannot be excited with such a thin slab. 15 In small size limit, the enhancement is consistently small across all wavelengths, in agreement with the scaling 16 law of the radiative rate with the nanoparticle size. 17 18 19 FIG. 2. Radiative emission enhancement of a perpendicularly oriented QE coupled with an ITO nanoplatelet of 20 varying lateral size. The QE is placed 20 nm above the 50 nm-thick plate. (a) Optimal enhancement of the 21 spontaneous emission from the QE (red, right axis) and its corresponding wavelength (blue, left axis) as a function 22 of the platelet lateral size L. Inset: schematic of the structure. (b) Optimal suppression (minimum enhancement) of 23 the radiation from the coupled QE-platelet (red, right axis) and its corresponding wavelength (blue, left axis) as a 24 function of L. (c) Enhancement factor of the spontaneous emission from the QE as a function of L at two specific 25 wavelengths: 1.172 μm (ENZ frequency, blue curve) and 1.3 μm (SPP resonance, red curve). Inset: the electric 26 field intensity distribution inside the platelet. (d) Enhancement spectra of the radiative emission from the coupled 27 6 QE-platelet for varying L. A marked radiation suppression is observed within a wavelength band around the ENZ 1 frequency (the white dashed line). The white solid line denotes the wavelengths corresponding to the optimal 2 radiation suppression for different L. 3 4 The outcoupling of the excited mode into radiation also hinges on the plate thickness. Here we fix the 5 lateral size of the plate to be 100 nm (Fig. 3(a,c)) and 500 nm (Fig. 3(b,d)), respectively, and vary the plate 6 thickness. In a similar vein, we observe a radiation suppression band near the ENZ frequency, with an optimal 7 suppression above 50% (maximum at 80%). Moreover, the wavelength at which optimal suppression occurs 8 approaches the ENZ frequency as the plate thickens (Fig. 3(c) and 3(d)). This effect can be understood as the 9 better accuracy of the image dipole model for thicker ENZ plate as discussed above. In addition, the bandgap 10 is almost invariant with respect to the thickness of the platelet (Fig. 3(a,b)). At short wavelengths, the dielectric 11 resonances enhance the radiation more notably with larger and thicker plates, and more resonant modes of 12 higher orders are induced (Fig. 3(b)). For the maximum radiation enhancement around the plasmon resonance 13 frequency, we note that in both cases the wavelength of optimal enhancement converges to ~1.32 μm, slightly 14 redshifted from the SPP resonance (Fig. S3 in the Supplemental Material [27]). This behavior indicates that 15 the most efficient outcoupling of the plasmon mode into radiation is relatively agnostic to the thickness, 16 especially when the lateral size is large. This effect can be understood as the induced dipole and the 17 propagating field being confined close to the top surface. For the plate with a smaller lateral size, larger field 18 can be found down the side walls, rendering the radiation more dependent on the thickness than from the one 19 with a larger lateral size. 20 21 22 FIG. 3. Radiative emission enhancement of a perpendicularly oriented QE coupled with an ITO nanoplatelet of 23 varying thickness. The QE is placed 20 nm above the plate. The lateral size of the plate is (a,c) 100 nm and (b,d) 24 500 nm. (a) and (b): Enhancement spectra of the radiative emission from the coupled QE-platelet for varying 25 platelet thickness. A marked radiation suppression is observed within a wavelength band around the ENZ 26 frequency (the white dashed line) for both lateral sizes, with the maximum suppression for greater than 80%. The 27 7 white solid line denotes the wavelengths corresponding to the optimal radiation suppression for different 1 thicknesses. (c) and (d): Optimal suppression (minimum enhancement) of the radiation from the coupled QE- 2 platelet and its corresponding wavelength as a function of the platelet thickness. The wavelength of optimal 3 suppression converges to the ENZ frequency as the plate is thickened. 4 5 Let us simplify the geometry to a sphere, with only one parameter to be considered: sphere radius. We first 6 examine the emission modulation of the QE. Figure 4(a) shows that the enhancement from the QE can reach 7 ~1600 when coupled to the plasmon resonance of the ITO sphere. The enhancement peak occurs at a 8 wavelength that shifts gradually from the LSPR at ~1.41 μm to the SPP resonance at ~1.3 μm as sphere radius 9 increases. This effect can also be visualized in Fig. 4(b) where a strong emission enhancement band is observed 10 in the neighborhood of the plasmonic resonances. Concurrently, the radiation from the coupled QE-nanosphere 11 is also modified when compared to an isolated emitter. Figure 4(c) shows the non-monotonic change of the 12 corresponding wavelength for the maximum radiation suppression. As expected, the larger the sphere, the 13 closer the wavelength is to the ENZ frequency for the optimal suppression. Remarkably, the suppression can 14 reach nearly 90% when sphere radius goes up to ~300 nm. Analytically, the radiation suppression from the 15 coupled QE-nanosphere around the ENZ frequency can be approximated. To first-order, the radiation 16 enhancement factor in the near-field coupling regime follows [43]: 17 𝛾𝑟𝑎𝑑 𝛾0~1 + 4 𝑅3𝑅𝑒(𝛼1)+4 𝑅6|𝛼1|2 18 where 𝛾𝑟𝑎𝑑 is the radiation rate of the coupled system, 𝛾0 is the spontaneous emission rate of a standalone 19 QE, 𝑅 is the radius of the nanosphere, and 𝛼1~𝜀𝑆−1 𝜀𝑆+2 𝑅3 is the polarizability of the nanosphere assuming a 20 dipolar response because the dipolar mode represents the highest scattering cross-section. For an ideal ENZ 21 material, 𝜀𝑆~0, 𝛼1~ − 1/2𝑅3, and therefore 𝛾𝑟𝑎𝑑 𝛾0~0. As discussed in the preceding section, the non-ideal 22 radiation suppression with the ITO nanosphere arises from the considerable loss around the ENZ frequency. 23 To quantify the influence of losses, we model the relative permittivity of the ENZ material using a Drude term 24 as 𝜀(𝜔)= 1 − 𝜔𝑝 2 𝜔(𝜔+𝑖𝜔𝛾𝑝), where the plasma frequency 𝜔𝑝= 1.1 𝑒𝑉 and the damping frequency 𝛾𝑝 is 25 related to the loss as 𝜀𝑖=𝜔𝑝 2𝛾𝑝 𝜔(𝜔2+𝛾𝑝 2). We set the radius of the sphere to be 200 nm. Figure S5 in the Supplemental 26 Material [27] confirms that the smaller the loss, the greater the radiation suppression is. The suppression is 27 about 85% with 𝜀𝑖~0.385, which also agrees well with the value for the ITO nanosphere with the same size. 28 Further, the edge of the radiation suppression band is plotted to exemplify the invariance of the bandgap with 29 respect to the size of the sphere (Fig. 4(d), two green dashed lines). Note as a conceptual example here we 30 define the radiation suppression band to be such that the enhancement factor is smaller than 1. 31 Outside the suppression band, we make three observations: Firstly, the radiation map resembles the Mie 32 scattering map in Fig. 1(b). Secondly, compared with Fig. 4(b), the maximum enhancement of the radiation 33 from the coupled QE-sphere due to plasmonic resonances occurs at a wavelength redshifted from the exact 34 LSPR (around ~1.41 μm) due to the dipole-dipole interaction and retardation effects [43]. Thirdly, the 35 8 dielectric resonances induce much smaller enhancement factors for the spontaneous emission from the 1 individual QE when compared to the plasmonic resonances. This effect is caused by the much weaker coupling 2 of the QE emission into the nonradiative decay in the sphere when it is excited through the dielectric resonant 3 modes. Instead, most of the enhancement of the QE emission is transferred to the enhanced overall radiation 4 of the coupled system. This behavior is the exact opposite to what happens at the plasmonic resonances, where 5 nonradiative dissipation in the nanosphere dominates due to the Ohmic loss. A direct comparison between the 6 enhancement of the spontaneous emission of the QE and of the coupled system can be seen in Fig. S4 in the 7 Supplemental Material [27]. 8 9 FIG. 4. Radiative emission enhancement of a perpendicularly oriented QE coupled with an ITO nanosphere of 10 varying radius. The QE is placed 20 nm above the sphere. (a) Optimal enhancement of the spontaneous emission 11 from the QE and its corresponding wavelength as a function of the sphere radius. (b) Enhancement spectra of the 12 emission from the QE for varying radius of sphere. Optimal coupling from the QE to the sphere is located within a 13 wavelength band in the neighborhood the plasmon resonances, progressively transitioning from LSPR with small 14 sphere size to SPP resonance with large sphere size (the two white dashed lines denote the wavelengths of the two 15 resonances). The white solid line denotes the wavelengths corresponding to the optimal radiation enhancement for 16 different radius. (c) Optimal radiation suppression (minimum enhancement) from the coupled QE-sphere and its 17 corresponding wavelength as a function of the sphere radius. The wavelength for the optimal suppression 18 converges to the ENZ frequency with increasing sphere size. (d) Enhancement spectra of the radiation from the 19 coupled QE-sphere for varying sphere radius. A marked suppression band is observed around the ENZ frequency 20 (the white dashed line). The white solid line denotes the wavelengths corresponding to the optimal radiation 21 suppression for different radius. The two green dashed lines denote the “band edge” of the radiation suppression 22 band. 23 24 As above demonstrated, the marked radiation suppression of a coupled QE-nanostructure around the ENZ 25 frequency is determined by the material’s ENZ property and independent of the geometry and size of the 26 nanostructure, unlike the plasmonic or dielectric resonance-induced radiation enhancement [44,45]. For 27 9 further validation, we find that nanodisks also exhibit the same effect, as shown in Fig. S6 in the Supplemental 1 Material [27]. As such, radiation suppression can be readily achieved by matching the frequency of the 2 spontaneous emission of the QE with the ENZ frequency of the material constituting the nanostructure. 3 Practically, the ENZ frequencies for many materials, in particular transition-metal nitrides and doped 4 semiconducting oxides (e.g., TiN, ITO, etc.), are manifestly tunable via electrical biasing, doping and 5 appropriate control of fabrication conditions. Therefore the coupled QE-nanostructure system can serve as a 6 “radiation switch” by modulating the ENZ frequency. Such switches can be potentially deployed in an array 7 or ensemble of emitters where the neighboring emitters can be controlled to mitigate the interference with one 8 another [46,47]. 9 10 In conclusion, we have put forward the concept of a radiative energy bandgap for a coupled QE-ENZ 11 nanoparticle system. A radiation energy gap is always found close to the ENZ frequency, beyond which strong 12 radiation enhancement arise from plasmonic or dielectric resonant mode excitation. Our work also indicates 13 that in order to suppress the radiation, the optical properties of the material are more important than the 14 geometry or size of the nanoparticle. Therefore, our proposed concept suggests an alternative route to quench 15 spontaneous emission, which may open new opportunities in the field of molecular fluorescence modulation 16 and quantum information technology. 17 18 The authors wish to acknowledge financial support from the Defense Advanced Research Program 19 Agency (DARPA) QUEST program No. HR00112090084. 20 21 References 22 [1] W. S. M. Werner, K. Glantschnig, and C. Ambrosch-Draxl, J. Phys. Chem. Ref. Data 38, 1013 (2009). 23 [2] R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, Phys. Rev. B 24 86 (2012). 25 [3] J. M. McMahon, G. C. Schatz, and S. K. Gray, Phys. Chem. Chem. Phys. 15, 5415 (2013). 26 [4] S. Bagheri, N. Strohfeldt, M. Ubl, A. Berrier, M. Merker, G. Richter, M. Siegel, and H. Giessen, ACS Photonics 5, 27 3298 (2018). 28 [5] H. Reddy, U. Guler, Z. Kudyshev, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, ACS Photonics 4, 1413 29 (2017). 30 [6] J. A. Briggs, G. V. Naik, Y. Zhao, T. A. Petach, K. Sahasrabuddhe, D. Goldhaber-Gordon, N. A. Melosh, and J. A. 31 Dionne, Appl. Phys. Lett. 110, 101901 (2017). 32 [7] E. L. Runnerstrom, K. P. Kelley, E. Sachet, C. T. Shelton, and J.-P. Maria, ACS Photonics 4, 1885 (2017). 33 [8] G. V. Naik, J. Kim, and A. Boltasseva, Opt. Mater. Express 1, 1090 (2011). 34 [9] M. A. Noginov, L. Gu, J. Livenere, G. Zhu, A. K. Pradhan, R. Mundle, M. Bahoura, Y. A. Barnakov, and V. A. 35 Podolskiy, Appl. Phys. Lett. 99, 021101 (2011). 36 [10] E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, Phys. Rev. Lett. 110, 013902 (2013). 37 [11] Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, Nat. Photonics 9, 738 (2015). 38 [12] O. Reshef, P. Camayd-Muñoz, D. I. Vulis, Y. Li, M. Lonc ar, and E. Mazur, ACS Photonics 4, 2385 (2017). 39 [13] M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006). 40 [14] B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008). 41