Gradient-based optimization of scatterer arrangements based on the T-matrix method

Abstract

The demand for inverse design is increasing as the ability to fabricate sub-10 nm features expands the design space by orders of magnitude. Efficient inverse design benefits from differentiable models of light-structure interaction. While traditional full-wave solvers based on finite differences, finite elements, or Fourier modal methods have already been presented for that purpose, a dedicated tool adapted for performing multiple scattering simulations is still lacking. To overcome this limitation, we provide a multiple-scattering framework compatible to automatic differentiation, suitable for treating periodic and non-periodic arrangements of scatterers. It yields exact gradients regarding geometric and positional parameters in finite clusters and infinite metasurfaces. In this work, we use spheres as the elementary building blocks to demonstrate the framework's capabilities as a standalone tool. However, the framework is adaptable to arbitrarily shaped scatterers, provided the individual T-matrices are calculated using differentiable full-wave Maxwell solvers. Since the gradients are obtained simultaneously in a single backward pass, the framework is well-suited for moderately dimensional problems. It is also possible to combine multiple performance goals into a single objective function. The versatility of our method is illustrated in proof-of-concept examples that focus on various aspects of Kerker-type physics. In the first example, a finite cluster of scatterers is optimized in order to reach a high forward-to-backward scattering ratio, and we show experimental feasibility of the designs. In the second example, a metasurface made from multiple scatterers in each unit cell is designed to maximize the reflectance contrast between orthogonal linear polarizations of the incident light. We make the framework publicly available at https://github.com/tfp-photonics/dreams.