[Paper Review] Multiplexed Supercell Metasurface Design and Optimization with Tandem Residual Networks

Christopher Yeung, Ju-Ming Tsai+6 more|arXiv (Cornell University)|Aug 2, 2020

Metamaterials and Metasurfaces Applications63 references92 citations

TL;DR

This paper proposes a tandem residual deep learning framework for inverse design of multiplexed supercell metasurfaces with over 100 subunit elements, enabling high-accuracy generation of complex broadband, narrowband, and multi-resonant absorbers in the mid- and long-wave infrared. Using only 3,600 full-wave electromagnetic simulations across a design space exceeding three trillion configurations, the model achieves precise spectral targeting while accounting for strong mode coupling and spatial arrangement effects.

ABSTRACT

Complex nanophotonic structures hold the potential to deliver exquisitely tailored optical responses for a range of applications. Metal-insulator-metal (MIM) metasurfaces arranged in supercells, for instance, can be tailored by geometry and material choice to exhibit a variety of absorption properties and resonant wavelengths. With this flexibility, however, comes a vast space of design possibilities that classical design paradigms struggle to effectively navigate. To overcome this challenge, here we demonstrate a tandem residual network approach to efficiently generate multiplexed supercells through inverse design. By using a training dataset with several thousand full-wave electromagnetic simulations in a design space of over three trillion possible designs, the deep learning model can accurately generate a wide range of complex supercell designs given a spectral target. Beyond inverse design, the presented approach can also be used to explore the structure-property relationships of broadband absorption and emission in such supercell configurations. Thus, this study demonstrates the feasibility of high-dimensional supercell inverse design with deep neural networks that is applicable to complex nanophotonic structures composed of multiple subunit elements that may exhibit coupling.

Motivation & Objective

• To address the challenge of navigating the exponentially large design space of multiplexed supercell metasurfaces with strong inter-element coupling.
• To overcome the nonuniqueness and vanishing gradient problems in deep learning-based inverse design of complex nanophotonic structures.
• To enable high-accuracy, data-efficient inverse design of supercell metasurfaces with over 100 distinct resonator elements.
• To discover structure-property relationships—such as absorption, emissivity, and bandwidth trade-offs—directly from the trained neural network.
• To demonstrate that a single deep learning model can simultaneously generate geometric parameters and optimal spatial arrangements for complex supercell configurations.

Proposed method

• A tandem residual network architecture is employed, combining an inverse-modeling network with a forward-modeling network to resolve nonuniqueness in supercell design.
• The network uses 1D convolutional layers and residual blocks to handle high-dimensional design spaces and mitigate vanishing gradients.
• The inverse network takes a target absorption spectrum as input and outputs geometric parameters (widths, lengths) and spatial arrangements of resonators.
• The forward network validates predictions by simulating full-wave electromagnetic responses, enabling feedback and refinement.
• The training dataset consists of 3,600 full-wave simulations across a design space of over three trillion possible configurations, with fixed cross widths (500 nm) and variable cross lengths (1.4–3 µm).
• Structure-property relationships are probed by querying the forward network to compute metrics like thermal emittance and maximum absorption as functions of target bandwidth and temperature.

Experimental results

Research questions

• RQ1 Can a deep learning model effectively navigate a high-dimensional design space of over three trillion possible supercell configurations for MIM metasurfaces?
• RQ2 Can a tandem residual network architecture overcome the nonuniqueness and vanishing gradient problems in inverse design of multiplexed supercells with strong coupling?
• RQ3 To what extent can a single trained model generate accurate, complex supercell designs with multiple unique resonator elements and optimized spatial arrangements?
• RQ4 Can the trained model be used to rapidly uncover structure-property relationships, such as emissivity and bandwidth trade-offs, without additional simulations?
• RQ5 How does the performance of a residual-based architecture compare to traditional fully connected tandem networks in inverse metasurface design?

Key findings

• The tandem residual network successfully designs supercell metasurfaces with narrowband, multi-resonant, and broadband absorption responses using only 3,600 training simulations.
• The model achieves high accuracy in predicting geometric parameters and spatial arrangements, with predicted absorption spectra closely matching full-wave simulation results (ground truth).
• The network identifies that as target bandwidth increases (FWHM), the maximum absorption decreases and the mean squared error (MSE) between target and predicted response increases.
• The integrated normal-incidence emissivity increases with larger target bandwidths, compensating for reduced peak absorption, and the relationship is temperature-dependent due to blackbody spectral radiance variation.
• The forward network enables rapid parameter sweeps—completing emittance and absorption trend analysis in under one minute—demonstrating the model’s utility as a fast surrogate for full-wave EM simulation.
• The framework enables efficient exploration of complex design spaces and reveals non-trivial dependencies between spectral response, geometric parameters, and thermal emission properties within the trained parameter range.