Design of efficient high-order immersed metagratings using an evolutionary algorithm

TL;DR

This work tackles the challenge of achieving high-efficiency, polarization-insensitive diffraction in immersed gratings for compact spectrometers. It replaces conventional blazed gratings with a subwavelength metagrating in silicon, optimized by a covariance matrix adaptation evolution strategy (CMA-ES) to maximize average efficiency across the SWIR-3 band while minimizing polarization sensitivity. The approach yields average efficiency around 78% across the band with polarization sensitivity below 5%, outperforming the Sentinel-5 immersed blazed grating by about 15% and reducing chromatic variation. A manufacturing-tolerance analysis shows robustness to dimensional errors on the order of tens of nanometers, suggesting feasibility with current lithographic processes and potential extension to shorter wavelengths with suitable fabrication strategies. Overall, the results demonstrate that evolutionary-optimized metasurface-based immersed gratings can significantly enhance the performance of compact infrared spectrometers.

Abstract

Immersed reflection gratings improve spectral resolving power by enabling diffraction within a high refractive index medium. This principle has been widely adopted to make grating spectrometers more compact. Conventional immersed gratings have blazed profiles which typically show the highest efficiency for one main design wavelength. In addition, the blazed profiles tend to cause significant polarization sensitivity. In this work, we propose an alternative approach for designing an immersed grating composed of sub-wavelength structures, designed to increase diffraction efficiency and reduce polarization dependence. For a theoretical demonstration, a reflective metagrating immersed in silicon is optimized over the short-wave infrared band-3 (SWIR-3, here $2.304~μ$m-$2.405~μ$m), targeting the same diffraction angles as the immersion grating used in the Sentinel-5 Earth observation mission. The structure is optimized using a modified Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The optimized immersed metagrating achieves an average efficiency of (over the SWIR-3 band) $\sim 78\%$, compared to $\sim 62\%$ for the conventional immersed blazed grating, and reduces polarization sensitivity from roughly $\sim 15\%$ to $\sim 5\%$. A manufacturing tolerance analysis is also conducted to evaluate the design's performance under systematic manufacturing errors, which revealed a degradation of $\sim 10\%$ efficiency at feature size errors of $\pm 25{nm}$ and almost negligible effect on the efficiency at $-10{nm}$ and of $\sim 5\%$ at $+10{nm}$.

Figures (9)

• Figure 1: Illustration of an immersed grating with sawtooth (or triangular) blaze profile in (a) and an immersed metagrating based on subwavelength pillars in (c). A polychromatic incident ray (black) is diffracted into the blue and red rays representing the shorter and longer wavelengths of the light, respectively.A detailed schematic of the profiles with two unit cells each of a sawtooth and metagrating is shown in (b) and (d), respectively. The unit cells have Period $P$ and the light with incidence angle $\theta_i$ gets diffracted at angle $\theta_d$. The sawtooth profile is defined with 3 degrees of freedom, namely height, etching angle $\eta$ and blaze angle $\theta_b$. The metagrating profile has multiple subwavelength structures in one period P with a lattice constant $\Lambda$. This is highlighted by the red box in plot (d). Each lattice then had structures with varying fill factor ($b_i$). This fill factor can vary in both the XY plane and XZ plane. The metasurfaces have the height $h$ in the y dimension.
• Figure 2: A cartoon of the immersed metagrating unit cell of period PxP is shown on the left with the xyz planes labelled. On the right, the XZ plane of the design problem is shown. It is 5x5 lattice grid with lattice constant $\Lambda = 0.414\mu\mathrm{m}$ within a grating period of $P=2.070\mu\mathrm{m}$. The center of each lattice and its pillar coincide. The pillars have the same height and varying fill factors ($F_{x_i}$ and $F_{z_i}$) in the x and z dimensions. The fill factor of the pillars changes in the x dimension, but is constant in the z dimension.
• Figure 3: Results from the CMA-ES optimization of the width ($x_i$) and length $(z_i)$ of each of the 5 pillars and the height $H$, hence 11 degrees of freedom (DOF). The evolution of the DOF over each iteration of the optimization is given in (a), where the colorbar represents the value of each DOF in microns. The evolution of the FOM (averaged 5th order efficiency across the wavelengths) over the iteration is shown in (b).
• Figure 4: Complex refractive index of the metagrating for XZ plane in (a) and (b). The two color bars represent the real refractive index ($n$) and the imaginary extinction coefficient ($\kappa$). The graph visualizes the optimal width and length of the metasurfaces.
• Figure 5: Grating efficiency as a function of wavelength range for the metagrating (in solid lines) and sawtooth (in dashed lines). for S-polarized light (red), P-polarized light (blue) and Diagonal polarized light (black). The wavelength at which the efficiency is simulated are shown in crosses. The efficiencies are at grating order (m=) $-5$ corresponding to a diffraction angle of $\sim 49.8^\circ\, - \, 53.2^\circ$ (depending on the wavelength). The incidence angle of the source used is $62.6^\circ$