A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions

TL;DR

The paper introduces a fast, accurate, and robust boundary integral equation-based solver for plane wave scattering from layered periodic structures with many inclusions, overcoming Wood's anomalies and enabling high-precision simulations.

Contribution

It develops a novel periodic integral equation method that remains stable at Wood's anomalies and efficiently solves large-scale scattering problems with many inclusions.

Findings

Achieves 9-digit accuracy for 1000-inclusion gratings

Solves large problems in under 5 minutes on a laptop

Uses a new approach to handle periodicity without Green's function failures

Abstract

We present a solver for plane wave scattering from a periodic dielectric grating with a large number $M$ of inclusions lying in each period of its middle layer.Such composite material geometries have a growing role in modern photonic devices and solar cells. The high-order scheme is based on boundary integral equations, and achieves many digits of accuracy with ease. The usual way to periodize the integral equation---via the quasi-periodic Green's function---fails at Wood's anomalies. We instead use the free-space Green's kernel for the near field, add auxiliary basis functions for the far field, and enforce periodicity in an expanded linear system; this is robust for all parameters. Inverting the periodic and layer unknowns, we are left with a square linear system involving only the inclusion scattering coefficients. Preconditioning by the single-inclusion scattering matrix, this is solved iteratively in $O(M)$ time using a fast matrix-vector product. Numerical experiments show that a diffraction grating containing $M=1000$ inclusions per period can be solved to 9-digit accuracy in under 5 minutes on a laptop.