Numerical formulation of three-dimensional scattering problems for optical structures

TL;DR

This paper presents a high-precision numerical method for 3D optical scattering problems using Yee's scheme, achieving extremely accurate S-matrix calculations compatible with FDTD.

Contribution

It introduces a frequency domain formulation that ensures unitarity of the S-matrix with minimal numerical error, enhancing accuracy in 3D optical simulations.

Findings

Achieves S-matrix accuracy within 10^{-8} in double precision.

Compatible with FDTD for efficient wave propagation analysis.

Ensures unitarity condition for power conservation.

Abstract

This paper describes a numerical formulation for calculating wave propagation with high precision in a three-dimensional system. Yee's discretization scheme is used to formulate a frequency domain method that is compatible with the finite-difference time-domain (FDTD) procedure. When the S-matrix satisfies a unitarity (power flow conservation) condition, the method enables arbitrary S-matrix elements to be obtained within a numerical error of less than $10^{-8}$ ($2 \times 10^{-13}$) for double precision format.