Inverse Design of Few-Layer Metasurfaces Empowered by the Matrix Theory of Multilayer Optics

Zhancheng Li, Wenwei Liu, Dina Ma, Shiwang Yu, Hua Cheng, Duk-Yong Choi, Jianguo Tian, and Shuqi Chen

Phys. Rev. Applied 17, 024008 – Published 2 February 2022

Abstract

Few-layer metasurfaces, which are planar artificial arrays composed of more than one functional layer, have been showing unprecedented capabilities for the implementation of integrated and miniaturized optical devices with high efficiency and broad working bandwidth. However, the rich design freedoms of few-layer metasurfaces severely challenge their design and optimization. A universal strategy for the design of few-layer metasurfaces with different desired optical functionalities and an arbitrary number of layers, which can lower the design complexity and the time cost for structural optimization, is still eagerly anticipated by the scientific community. Here, we demonstrate an inverse design strategy based on deep-learning technology for the design of few-layer metasurfaces. By combining the matrix theory of multilayer optics, the proposed algorithm can predict the entire scattering matrix of a few-layer metasurface in tens of seconds with an acceptable accuracy and realize the inverse design of few-layer metasurfaces with different desired functionalities. Thus, the proposed inverse design strategy provides an efficient solution for the reduction of the design complexity of few-layer metasurfaces and significantly lowers the time cost for the structural optimization when compared with the numerical simulation methods based on an iterative process of trial and error, which will be of benefit to and expand the related research.

Received 12 September 2021
Revised 7 November 2021
Accepted 11 January 2022

DOI:https://doi.org/10.1103/PhysRevApplied.17.024008

Physics Subject Headings (PhySH)

Classical optics Light-matter interaction Metasurfaces Nanophotonics

Artificial neural networks Multilayer thin films

Deep learning

Atomic, Molecular & Optical

Authors & Affiliations

Zhancheng Li ¹, Wenwei Liu¹, Dina Ma¹, Shiwang Yu¹, Hua Cheng^1,*, Duk-Yong Choi ², Jianguo Tian¹, and Shuqi Chen^1,3,4,†

¹The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, Renewable Energy Conversion and Storage Center, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China
²Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra ACT 2601, Australia
³The Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
⁴Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China

^*Corresponding author. hcheng@nankai.edu.cn
^†Corresponding author. schen@nankai.edu.cn

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Vol. 17, Iss. 2 — February 2022

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Images

Figure 1
Schematic diagram of the proposed “EV-CNN-MT” deep-learning algorithm built on the evolution algorithm, the convolutional neural network, and the matrix theory of multilayer optics, for the inverse design of few-layer metasurfaces with desired optical functionalities. The input is the target distributions of several coefficients of the scattering matrix, which represent the desired optical functionality. The output is the design detail of the few-layer metasurface whose optical response is equal or close to the desired one, including the structural configurations of each layer and the distance between the adjacent layers. The algorithm consists of three main components: the convolutional neural network simulator for the prediction of the scattering matrix of the monolayer periodic metasurface, the numerical model based on the matrix theory of multilayer optics for the calculation of the scattering matrix of the few-layer metasurface based on the predicted scattering matrices of the monolayer periodic ones, and the evolution algorithm for finding the few-layer metasurface whose optical response is equal or close to the desired one.
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Figure 2
Quantitative analysis on the performance of the well-trained CNN simulator. (a) The value L of the loss function for the individuals in the test data. (b) The proportion of the test data for which the value L of the loss function is in a different range. (c) A typical example of the unit cell of a monolayer periodic metasurface. (d) The predicted (dot plot) and simulated (line plot) results of the real and imaginary parts of the eight coefficients of the scattering matrix of the monolayer periodic metasurface in (c), and the corresponding calculated results of the prediction errors (area plot).
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Figure 3
Inverse design of bilayer metasurfaces with different optical functionalities based on the proposed deep-learning algorithm. Inverse design of a bilayer metasurface as a bandpass optical filter for x-polarized waves: (a) the target amplitude distribution of $t_{x x}^{f}$ corresponding to the desired functionality; (b) the structural configuration of the inverse-designed bilayer metasurface; (c) the simulated and the predicted results; and (d) the prediction error (difference between the predicted and the simulated results) of the amplitude distribution of $t_{x x}^{f}$ for the designed bilayer metasurface. Inverse design of a bilayer metasurface as a broadband polarization convertor for x-polarized waves: (e) the target amplitude distribution of $t_{x x}^{f}$ and $t_{y x}^{f}$ corresponding to the desired functionality; (f) the structural configuration of the inverse-designed bilayer metasurface; (g) the simulated and the predicted results; and (h) the prediction error of the amplitude distribution of $t_{x x}^{f}$ and $t_{y x}^{f}$ for the designed bilayer metasurface, and the corresponding calculated results of the PCR. Inverse design of a bilayer metasurface to realize the diodelike asymmetric transmission of the x-polarized waves: (i) the target amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , and $t_{y x}^{f}$ corresponding to the desired functionality; (j) the structural configuration of the inverse-designed bilayer metasurface; (k) the simulated and the predicted results; and (l) the prediction error of the amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , and $t_{y x}^{f}$ for the designed bilayer metasurface, and the corresponding calculated results of the transmission difference $δ T$ . Inverse design of a bilayer metasurface as a broadband linear-polarizer: (m) the target amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , $t_{y x}^{f}$ , and $t_{y y}^{f}$ corresponding to the desired functionality; (n) the structural configuration of the inverse-designed bilayer metasurface; (o) the simulated and the predicted results; and (p) the prediction error of the amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , $t_{y x}^{f}$ , and $t_{y y}^{f}$ for the designed bilayer metasurface.
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Figure 4
Inverse design of the few-layer metasurfaces with the same optical functionalities and different numbers of layers based on the proposed deep-learning algorithm. The few-layer metasurfaces are inversely designed to realize the diodelike asymmetric transmission of x-polarized optical waves with the operation frequency from 150 to 300 THz, that is, the amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , and $t_{y x}^{f}$ are $| t_{x x}^{f} | = 0$ , $| t_{x y}^{f} | = 0$ , and $| t_{y x}^{f} | = 0.9$ from 150 to 300 THz. (a) The structural configuration of the inverse-designed few-layer metasurface with different numbers of layers. (b)–(e) The simulated and the predicted results and (f)–(i) the prediction error of the amplitude distribution of $t_{x x}^{f}$ , $t_{x y}^{f}$ , and $t_{y x}^{f}$ for the designed few-layer metasurface.
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Figure 5
Experimental validation of the optical responses of the two inverse-designed few-layer metasurfaces that can be treated as broadband linear polarizers. (a) The structural configuration of one inverse-designed few-layer metasurface and its (b) SEM image of the upper layer, and the (c) simulated results, predicted results, and (d) experimental results of the transmission spectra ( $T_{i j} = | t_{i j} |^{2}$ ) for the designed few-layer metasurface. (e) The structural configuration of the other inverse-designed few-layer metasurface and its (f) SEM image of the lower layer, and the (g) simulated results, predicted results, and (d) experimental results of the transmission spectra for the designed few-layer metasurface.
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