Flat emission grating couplers design enabling optical antennas for high performance LIDAR systems

Flat emission grating couplers design enabling optical antennas for high performance LIDAR systems Thenia Prousalidi*a, Giannis Poulopoulosa, Evrydiki Kyriazia, Georgios Syriopoulosa, Peter Maatb, Roel Botterb, Charalampos Zervosa, Dimitrios Apostolopoulosa, Hercules Avramopoulosa aPhotonics Communications Research Laboratory, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou, 15773 Athens, Greece; bLionix BV International, Hengelosestraat 500, 7521 AN Enschede, Netherlands ABSTRACT We propose a novel design of grating couplers to be used as the building blocks of the optical antennas of Lidar systems, designed in the well-established Si3N4-TriPleX platform, that offers low-loss waveguides and allows the integration of the dispersive grating elements with ultra-low-loss and low-energy photonic beamformer circuits. The grating couplers are based on standard asymmetric double-stripe waveguide geometry and are designed with 100nm spectral range around 1550nm. More specifically, we design non-uniform geometry grating couplers, varying the waveguide width and filling factor, targeting constant effective refractive index across the propagation direction, and thus constant emission angle, while optimizing for a uniform emission profile. The designs allow to achieve low theta angle divergence as well as maximum wavelength steering. The reported design showcases theta angle 3dB divergence of 1o, phi angle 3dB divergence of 20o and wavelength steering of 10o/100nm. The proposed components show low fabrication complexity and are compatible with standard fabrication processes. A comparison between uniform and non-uniform grating designs is also presented, investigating also their performance in an OPA configuration. The described methodology is based on mode solving simulations (Lumerical FDE) and propagation simulations (Lumerical FDTD), while the OPA profile extraction is performed with Matlab Sensor Array Analyzer Toolbox. Keywords: LIDAR, Grating coupler, Silicon Nitride, optical antenna, flat emission 1. INTRODUCTION In recent years, the integration of Lidar systems in applications such as autonomous vehicles necessitates the miniaturization of the components and the development of efficient and cost-effective solutions. Photonics based Lidar implementations have been identified as key enabling technologies for next generation sensing systems, due to their cost, size and energy advantages, as well as their increased frequency operational bandwidth, which translate into high range resolution. A key component of integrated photonics-based Lidar are the optical radiators used for emission and detection of the light (optical antennas). These optical antennas are typically implemented as multi-bean radiators that consist of an array of single radiator elements (building blocks) deployed in a specific configuration. For this application grating couplers (GCs) are used as the building blocks (BB) of the radiators, and the multiple BB are arranged in optical phased arrays (OPAs), a linear array configuration where the BBs are placed one next to the other. Such an OPA configuration is shown in Figure 1. Two very important parameters of the optical radiator are the theta (θ) and phi (φ) angles, shown in the figure. The design process of the optical radiators is split in the following two phases: first, the single radiator element (BB) design is performed via simulations in photonic simulation tools (Finite-Difference Eigenmode (FDE) and Finite-Difference Time-Domain (FDTD)), and then the design is verified with 3D FDTD simulations to extract the BB parameters. As a second step, the complete optical phased array configuration is optimized using MATLAB’s antenna array and global optimization toolboxes. Layerstack and antenna design considerations The platform for the development of the optical radiators is the Lionix Si3N4 TriPleX Platform. We have chosen to work with the asymmetric double stripe (ADS) waveguide geometry. A detailed cross-section of the ADS layerstack is shown in Figure 2. The bottom Si3N4 layer thickness is 75 nm, the top Si3N4 layer thickness is 175 nm, the distance between the two layers is 100 nm and the nominal waveguide width is 1.1 μm. *[email protected] The multiple layers of Si3N4 and SiO2 allow to make low index contrast waveguides which is beneficial for reduced sensitivity of the waveguided modes effective refractive index (neff) to the waveguide geometry variation. This is desired to achieve long gratings with uniform emission profiles where not all the power exits the grating at the very beginning. The spectral range of interest for the design process is 1500 nm – 1600 nm. Figure 1: Schematic of a lidar system in OPA configuration based on grating couplers as single antenna elements. The theta (θ) and phi (φ) angles are noted. Source: [1]. Figure 2: Schematic cross-section of the standard TriPleX ADS. Source: [2]. Design targets The designed grating coupler BBs aim to meet the following multiple requirements concerning their performance: 1. Maximize the θ steering angle wavelength sensitivity. This is a very important characteristic of LIDAR systems, and it defines how much the θ angle can be stirred by varying the laser wavelength in the available range. Maximizing the steering angle ensures a wide field of view. This can be achieved by having a uniform emission profile of the BB, across long grating elements. 2. Another requirement is achieving low divergence of the θ and φ angles. This ensures enhanced object recognition and high angular resolution which is beneficial for accurately mapping the surroundings and capturing fine details in the environment. Narrower beam divergence also helps in maintaining better focus over longer distances. This is important for LIDAR applications that require long-range detection, such as in autonomous vehicles. In general, θ angle divergence depends on the design of the individual grating elements, while the φ angle divergence depends on the aperture of the OPA, meaning the number of grating elements in the OPA, and the distance between the elements. 3. At the same time, the designed gratings target flat emission profile across the grating length. This is necessary both for maximizing the wavelength sensitivity, and also for achieving gratings with long effective areas. The uniform emission profile can be engineered by designing non uniform gratings, with varying geometry characteristics along the propagation direction of the light. 4. Last, we target long length gratings. Apart from the aforementioned advantages this has to offer, it is also very crucial for the optical radiators that will act as receivers. Having gratings with long length facilitates to collect and couple into the PIC more light spatially in the receiver side. 2. DESIGN OF SINGLE RADIATOR ELEMENT As a first step, the design of the single radiator element was performed to optimize the performance of the OPA’s BB. This was done with Lumerical’s FDE and FDTD solvers. Several grating coupler configurations. First, nominal uniform pitch and width configurations were simulated, that are the simplest gratings to fabricate. However, these components have exponential emission profiles and cannot meet all the specified requirements. Therefore, non-uniform gratings were designed as well, targeting uniform emission profiles and gratings with longer lengths. The geometrical parameters that were varied to realize non-uniform designs are the filling factor (FF) and grating waveguide width, across the propagation length. Varying these two parameters simultaneously, it is possible to keep the effective refractive index (neff) of the supported mode constant, and therefore the emission angle θ also constant for a specific wavelength. In the next paragraphs the design process and extracted parameters of the uniform and non-uniform grating designs are analyzed. Uniform design The effective index of a grating period that consists of an unetched part (also referred to as tooth) with effective index of the supported mode n1 and an etched part with effective index of the supported mode n0, with filling factor FF, is given by equation (1) The FF of the uniform grating couplers is considered constant and equal to 0.5. The pitch is also kept constant and can be freely chosen given the desired emission angle θ, according to equation (2), (2) where θ is the emission angle, neff is the effective refractive index of the grating, λ is the operational wavelength, Λ is the pitch (grating period) and nc the effective index of the wave incident on the grating. To design the uniform gratings and optimize their geometrical parameters 3D-FDTD simulations were performed. A topview of the uniform grating BB is shown in Figure 3. Figure 3: Topview of the uniform GC, showing the constant pitch, FF and width across the propagation direction. Considering a constant FF of 0.5, the grating pitch (Λ), width and length were optimized according to the designed targets. The values that lead to minimum θ and φ anlge divergence are width = 2 μm and length = 100 μm. The simulated emission profile of this uniform GC design is shown in Figure 4. This illustrates the non-uniform emission profile that the uniform grating designs showcase. It is evident that the uniform gratings cannot achieve the targeted uniform emission profiles and long grating lengths. Therefore, non-uniform designs have also been investigated, as presented in the next paragraph. Figure 4: Left: topview of the emission profile of the uniform grating for width of 2 μm and length of 100 μm. Right: 1D plot of the emission profile along the dashed line of the left figure. Non-uniform design Given that the uniform grating designs have performance limitations, non-uniform configurations were also investigated to meet the design goals. The non-uniformity concerns the geometrical characteristics of the design and suggests that along the grating length there are variations of the FF and the grating waveguide width. This variation is done to engineer the emission profile of the grating. To make it more uniform, the power needs to exit in a controlled manner from the grating, across many periods. Therefore, by properly adjusting the FF and waveguide width a more uniform emission condition can be achieved where equal amounts of power are emitted from each grating period. We have carried out an extensive study that aims to optimize the geometry and make the emission profile more uniform compared to the uniform grating design. While the variation of the grating’s geometry changes the emission profile, it will also inevitably change the neff of the grating periods, according to equation (1). From this equation it can be derived how the FF affects the grating neff. At the same time, changing the cross section of the waveguide (width) will affect the effective index of the supported mode, therefore changing n0 or n1 in equation (1). This means that the geometry variation needs to be designed carefully so that the emission angle for a given wavelength remains constant along the grating length. According to equation (2), this can be ensured be keeping the grating neff constant, therefore both the width and FF of each period need to be varied accordingly [3]. A topview and sideview of the non-uniform investigated design with varying width and FF are shown in Figure 5. Figure 5: (Left) topview and (Right) sideview of the investigated non-uniform grating design with varying width and FF. The design process has started with FDE simulations in Lumerical’s software. As a first step the neff of a waveguide cross-section was calculated, varying its width, given the ADS TriPleX layerstack. The results are shown in Figure 6. This neff corresponds to the neff of the grating tooth that is unetched and is represented as n1 in equation (1). In the ADS TriPleX platform, to create the grating teeth it is possible to fully etch the Si3N4, therefore removing both layers of the Si3N4 layerstack. Then, the etched part of the grating geometry consists of SiO2. Therefore, as n0 the refractive index of the SiO2 is considered, which is approximately nSiO2 = 1.44537 at 1550 nm. Figure 6: neff of the TE0 mode varying the waveguide width. Using equation (1) and the calculated n0 and n1 values, it is then possible to compute the neff of a grating period, for the different width and filling factor (FF) combinations. This is shown in Figure 7 (Left). From the results shown in Figure 7 it can be observed that for specific pairs of waveguide width and FF the neff remain constant (dashed pink line). The calculated contour lines along which neff is constant are shown in Figure 7 (Right). These contour lines are the desired regions from which the width-FF pairs can be extracted. By designing a non-uniform grating with varying width and FF from such a contour line, it is ensured that the neff remains constant through the grating, therefore the angle θ is also constant, while also targeting a uniform emission profile. Overall, from this plot, and given a width variation between 1 μm and 2 μm, we can extract the width-FF pairs form the chosen contour line, and define the non-uniform grating structure. Figure 7: (Left) neff as calculated via FDE simulations, varying the waveguide width and FF and (Right) calculated neff contour lines varying width and FF. Having defined the width-FF pairs, the next phase of the design follows, which is the 3D-FDTD simulations in Lumerical’s software. With these simulations the design process that has been performed is verified and the farfield data can be simulated and extracted, allowing to calculate the θ and φ angles divergence, the wavelength sensitivity of the θ angle as well as the efficiency of the gratings. It is also possible to visualize the farfield and emitted power data, a useful tool to verify the grating’s performance. The 3D-FDTD simulations require apart from the width-FF pairs the pitch and the grating length. The pitch can be freely chosen according to the desired emission angle, given equation (2). The length depends on the chosen number of periods N, that is also used to extrapolate the width-FF pairs from the contour plots. For our design we have chosen to design gratings with length of around 50 μm. Having defined the width-FF pairs, pitch and number of periods (N), then the design can be simulated in the 3D-FDTD simulator tool. The simulation results for a specific configuration with pitch of 1.15 μm and total length of 46 μm (40 periods) are shown in Figure 8. These includes a 2D sideview and topview of the emission profile, as well as a 1D view of the emission profile across the white dotted line of the topview. From these plots it can be seen that the emission profile is more uniform compared to the uniform designs, and it takes longer for the power to exit the grating. From this simulation, it is also possible to extract the farfield from which the θ and φ angles divergence can be derived. The reported design showcases θ angle 3dB divergence of 1o, φ angle 3dB divergence of 20o. Figure 8: Simulated emission profile results at 1550 nm for the designed non-uniform grating with length of 46 μm. From the farfield data, another very important plot that can be extracted is the emission angle θ varying the wavelength in the range 1.5 – 1.6 nm, also called wavelength steering angle. The results are shown in Figure 9, for pitch around 750 nm. It can be observed that the steering angle for this grating configuration is around 10o/100 nm. 3. DESIGN OF THE COMPLETE OPA STRUCTURE After the simulation and design of the single radiator element, the next step is the design of the complete OPA structure. This was performed with the help of the Sensor Array Analyzer toolbox provided by Matlab. This is a powerful toolbox that allows to create and simulate OPA structures and antennas. One can define the number of the single radiator elements (N), their topology (e.g. linear array), their distance d (defined as the center-to-center distance between two adjacent elements) and also import the farfield data of the single element that will eventually define the radiation pattern of the complete antenna. Once the antenna structure is defined, is then possible to simulate and visualize the radiation pattern of the antenna (3D directivity plots) and extract the θ and φ angle divergence. Figure 9: Calculated emission angle θ of the farfield profile for the non-uniform grating design with 750 nm pitch, varying the wavelength in the range 1.5 - 1.6 μm. The two importing design parameters of the OPA structure are the number of elements N and the distance d between two adjacent elements. The distance is illustrated in Figure 10. Using the toolbox these two parameters can be varied and the resulting radiation plots are then compared, to define the effect of N and d on the OPA performance, and optimize the OPA design. The parameters that are used to assess the operational efficiency of this antenna are the 3 dB divergence of the theta (θ) and phi (φ) angles (in spherical coordinates). The OPA radiation pattern has been simulated for different number of elements between 2 and 8, as well as different distances d between 1 and 2 λ, where λ is the center wavelength and equals 1.55 μm. The results are presented in Figure 11. From these plots some useful conclusions can be extracted. First of all, the θ angle divergence can be measured. This can be achieved by examining the elevation cut of the directivity plots, for azimuthal angle equal to 0O. Such an elevation cut is shown in Figure 12. For all the different antenna configurations of Figure 11, the 3 dB divergence of the theta angle is 1O. This is illustrated in Figure 12 where the 3 dB region around the peak directivity value is marked with the red horizontal lines, and the corresponding divergence of the theta angle is marked with the vertical dashed lines and equals 1O. This agrees with the results from the 3D-FDTD simulations and it confirms that θ is not affected by Ν, d, but rather depends on the design of the individual grating elements. By optimizing the designs there is still some room for improvement and θ divergence of 0.9oC can be achieved. Figure 10: Topology of the complete OPA structure, showing the θ and φ angles as well as the distance d. On the other hand, the divergence of the φ angle is affected both by the number of elements and by their distance. Increasing the number of elements is the antenna reduces the φ divergence. Also, increasing the distance between adjacent elements reduces the φ divergence. Figure 11: 3D directivity plots (in dBi) produced with Sensor Array Analyzer app, varying the number (N) of grating elements and the distance (d) between them. 4. CONCLUSIONS This work focused on the simulation and design of optical radiators for LIDAR systems in the well-established Si3N4TriPleX platform, that offers low-loss waveguides and allows the integration of the dispersive grating elements with ultra-low-loss and low-energy photonic beamformer circuits. The radiators are implemented as OPAs that employ grating couplers as single radiator elements. The design process was split into two phases: the design of the single grating element (building block) and the optimization of the complete OPA structure. The first phase included simulations using Lumerical’s software that targeted the design of both uniform and non-uniform grating couplers based on standard asymmetric double-stripe waveguide geometry and designed with 100nm spectral range around 1550nm. The design process aimed to optimize multiple performance metrics and investigated the effect of the important design parameters on the device and system performance. Non-uniform geometry grating couplers were designed, varying the waveguide width and filling factor, targeting constant effective refractive index across the propagation direction, and thus constant emission angle, while optimizing for a uniform emission profile. The designs allow to achieve low theta angle divergence as well as maximum wavelength steering. The reported design showcases theta angle 3dB divergence of 1o, phi angle 3dB divergence of 20o and wavelength steering of 10o/100nm. The proposed components show low fabrication complexity and are compatible with standard fabrication processes. The second phase targeted the optimization of the complete OPA structure, using the Sensor Array Analyzer toolbox by Matlab. During this phase, we investigated the effect of the OPA design parameters, namely the number of antenna elements and their spacing, on the OPA performance. The results showcase how these parameters affect the θ and φ angle divergence and help to choose the best topology according to the application needs. Figure 12: Elevation cut for azimuth angle = 0o, for the directivity plots presented in Figure 11. ACKNOWLEDGEMENTS This work has received funding from the European Union’s Horizon 2020 innovation program under grant agreement No. XXXX (PARALIA). . REFERENCES [1] M. Hu, Y. Pang, and L. Gao, “Advances in Silicon-Based Integrated Lidar,” Sensors, vol. 23, no. 13, p. 5920, Jun. 2023, doi: 10.3390/s23135920.