Data-driven Deep Learning
for the design of
color filter metasurfaces

Optical color filter denotes a specialized structure or material designed to discriminate and manipulate distinct light wavelengths through the selective transmission or reflection of particular colors while simultaneously absorbing or attenuating undesired colors. Typical color filters rely on the manipulation of chemical composition to achieve the desired optical properties, which can lead to issues such as absorption losses, thermal effects, and alterations in chemical28 characteristics. An alternative approach involves the utilization of structural color filters, which offer distinct advantages and applications in diverse fields such as photorealistic color printing, color holography, anti-counterfeiting measures, and more. Metasurfaces have emerged as promising platforms for realizing structural color filter. he design of metasurfaces, particularly for color filtering purposes, presents significant physical challenges since achieving a narrow resonance that selectively filters a single color requires precise control over the geometry and arrangement of the resonators. Moreover, it is challenging to confine the resonant response to a single wavelength without any spectral tails or unwanted broadband effects. Also, one-shot optimization of such devices using Artificial Neural Network (ANN) is not straightforward given that several designs with extremely similar optical response while regular ANN having only a single output. Therefore, resorting to inverse design techniques is crucial in order to achieve optimal performance. In this context, we study a novel data-driven approach for efficiently designing fabrication-constrained color filter metasurfaces. Our methodology combines the powerful capabilities of Multi-Valued Artificial Neural Networks (MVANNs) and back-propagation optimization, effectively overcoming the limitations inherent in relying solely on the latter, which can lead to undesired local minima, or exclusively on MVANNs, which may result in poor performance due to extrapolation.

Schematic representation of the simulated structure. The light is injected from top with normal incidence with electric field polarized in the x-direction. The inset refers to a single unit-cell surrounded by periodic boundary conditions along x-directions. The geometrical parameters are indicated in the inset as well.

Optimization diagram (with an example of optimization for λ = 550 nm). Firstly, we generate a target reflection spectrum. In this case, we used Lorentzian functions as their shape are a generalization of Fano resonance peaks, and therefore, eases the process of finding the solution. Then we pass the target through the MVANN to obtain 20 designs, and validate those designs using a surrogate model (also part of the methodology). We then choose the solution that presented the least MSE compared to the target. The next step is performing Back-Propagation (BP) optimization on that design. We also search the dataset for the best design and run BP optimization. We then simulate the designs and use the best result based on the simulation.

Detailed examination of 6 different optimizations, displaying their dimensions (in nm) of each geometrical parameter and the corresponding sRGB color representation of the simulated spectrum.