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Yu ZJ, Li MX, Xing ZY et al. Genetic algorithm assisted meta-atom design for high-performance metasurface optics. Opto-Electron Sci 3, 240016 (2024). doi: 10.29026/oes.2024.240016
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Genetic algorithm assisted meta-atom design for high-performance metasurface optics
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Abstract
Metasurfaces, composed of planar arrays of intricately designed meta-atom structures, possess remarkable capabilities in controlling electromagnetic waves in various ways. A critical aspect of metasurface design involves selecting suitable meta-atoms to achieve target functionalities such as phase retardation, amplitude modulation, and polarization conversion. Conventional design processes often involve extensive parameter sweeping, a laborious and computationally intensive task heavily reliant on designer expertise and judgement. Here, we present an efficient genetic algorithm assisted meta-atom optimization method for high-performance metasurface optics, which is compatible to both single- and multi-objective device design tasks. We first employ the method for a single-objective design task and implement a high-efficiency Pancharatnam-Berry phase based metalens with an average focusing efficiency exceeding 80% in the visible spectrum. We then employ the method for a dual-objective metasurface design task and construct an efficient spin-multiplexed structural beam generator. The device is capable of generating zeroth-order and first-order Bessel beams respectively under right-handed and left-handed circular polarized illumination, with associated generation efficiencies surpassing 88%. Finally, we implement a wavelength and spin co-multiplexed four-channel metahologram capable of projecting two spin-multiplexed holographic images under each operational wavelength, with efficiencies over 50%. Our work offers a streamlined and easy-to-implement approach to meta-atom design and optimization, empowering designers to create diverse high-performance and multifunctional metasurface optics.-
Keywords:
- metasurface /
- metalens /
- Bessel beam /
- metahologram /
- genetic algorithm
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References
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Yu ZJ, Li MX, Xing ZY et al. Genetic algorithm assisted meta-atom design for high-performance metasurface optics. Opto-Electron Sci 3, 240016 (2024). doi: 10.29026/oes.2024.240016
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Figure 1.
Flowchart illustrating the genetic algorithm-based meta-atom design process. The algorithm commences with the random initialization of a population, where each individual is defined by parameters such as material (m), period (p), height (h), and lateral sizes (w1, w2, …, wn, l1, l2, ..., ln) that characterize meta-atom structures. Electromagnetic responses are simulated for each individual, and their performance is assessed via associated fitness functions. In single-objective tasks, lower fitness function values denote superior performance, while in multi-objective tasks, non-dominated sorting is employed. Blue and yellow dots represent individuals evaluated in iterations for a dual-objective task, with their coordinates representing the associated fitness function values. The blue dots constitute the non-dominated front (rank 1), wherein improving one objective necessitates compromising others. Ignoring the blue dots yields a new non-dominated front (rank 2) represented by the yellow dots. Such ranking aids in assessing individual performance considering all associated fitness functions, with crowding distances further differentiating performance within the same ranking. For instance, the blue point within the dashed box exhibits a lower crowding distance, indicating poorer performance compared to other blue dots of the same rank. Tournament selection identifies parents for generating the next generation through crossover and mutation. During crossover, two parents exchange parts of their chromosomes to produce two children, while in the mutation step, genes in each child’s chromosome are randomly altered. For simplicity, the chromosome is represented using binary notation. Iterations persist until termination conditions are met, resulting in an optimized meta-atom library.
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Figure 2.
High-efficiency broadband PB phase metalens in the visible. (a) Schematic representation of the focusing metalens with a diameter D and focal length f. Inset: Schematic representation of a nanofin-shaped meta-atom structure with a constituent material m, period p, height h, as well as cross-sectional length l and width w. The meta-atom is set to have an in-plane rotation angle of θ, and will impart a phase modulation of 2θ over a circularly-polarized incident light based on the Pancharatnam–Berry (PB) phase modulation mechanism. (b) Convergence plot of the optimization process. Four different evaluation metrics, which are the polarization conversion efficiency (PCEopt) and fitness function value (Fopt) of the optimal individual in each iteration, and the averaged polarization conversion efficiency (PCEavg) and averaged fitness function value (Favg) over the whole population in each iteration, all get flatten after approximately 75 iterations. (c) PCE of the inverse designed meta-atom (blue curve) and simulated focusing efficiency (η) of the metalens (orange curve) as a function of free-space illumination wavelength. (d) Intensity distribution at the focal plane along the x-axis (orange dots) for the constructed PB phase metalens, simulated at free-space illumination of λ0 = 532 nm. Theoretical prediction (orange solid line) is shown for comparison. Inset: 2D intensity distribution at the focal plane.
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Figure 3.
Spin-multiplexed metasurface dual beam generator. (a) Schematic depiction of the spin-multiplexed metasurface dual-beam generator with a diameter D, positioned in the z = 0 μm plane with its center at the coordinate origin. The device generates a zeroth-order Bessel beam under right-handed circular polarized (RCP) illumination and a first-order Bessel beam under left-handed circular polarized (LCP) illumination. (b) Hypervolume plotted against iteration number. The hypervolume curve tends to plateau after approximately 250 iterations, indicating convergence of the genetic algorithm (GA). (c) Non-dominated front plot of the population in the final iteration of the algorithm. (d) Schematic illustration of the 8 meta-atom structures obtained through the GA optimization. Their electromagnetic (EM) performance at λ0 = 532 nm is represented by red dots in a polar coordinate system, where the azimuthal angle denotes the phase shift modulation value (in radians) and the distance from the origin signifies the polarization conversion efficiency (PCE).
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Figure 4.
Bessel beams generated by the optimized spin-multiplexed metasurface. (a, b) The normalized intensity profile of the zeroth-order Bessel beam (NA1 = 0.7) in the y-z plane at free-space RCP illumination of λ0 = 532 nm (a) and its corresponding horizontal cut at z = 7 μm (b). (c, d) The normalized intensity profile of the first-order Bessel beam (NA2 = 0.3) in the y-z plane at free-space LCP illumination of λ0 = 532 nm (c) and its corresponding horizontal cut at z = 20 μm (d).
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Figure 5.
Wavelength and spin co-multiplexed four-channel metahologram. (a) Schematic depiction of the wavelength and spin co-multiplexed four-channel metahologram with a side length L, positioned in the z = 0 μm plane with its corner at the coordinate origin. The letters “H” and “S” are reconstructed at the z = 150 μm plane, under the RCP and LCP illumination at free-space wavelength of λ0= 532 nm. The letters “U” and “T” are reconstructed at the same plane, under the RCP and LCP illumination at free-space wavelength of λ1= 633 nm. (b) Phase shift modulation plot of the 16 meta-atom structures obtained through the final iteration of the GA optimization. The meta-atoms are represented as blue points, with their coordinates representing the phase shift modulation values for x-polarized incident light under wavelengths of 532 nm and 633 nm. di represents the distance from the i-th point to its nearest point in the coordinate system. For the clarity of display, we draw a red dashed circle centered at the i-th point with a radius of di, where the nearest point lies on the circle. (c) Hypervolume plotted against iteration number. The hypervolume curve tends to plateau after approximately
1700 iterations, indicating convergence of the GA. (d) Non-dominated front plot of the population in the final iteration of the algorithm. -
Figure 6.
Simulated holographic imaging results of the four-channel metahologram. Four images (capital letters “H”, “U”, “S” and “T”) are selectively projected into the target plane, depending on the combination of free-space wavelength (532 nm or 633 nm) and spin state (RCP or LCP) of the illumination light. The image plane is located 150 μm above the metahologram device.
