Rigorous formulation of oblique incidence scattering from dispersive media

TL;DR

This paper develops a finite-difference time-domain method for simulating electromagnetic scattering in layered dispersive media, accurately modeling complex wave interactions at oblique incidence.

Contribution

It introduces a novel FDTD formulation based on an equivalent wave equation for dispersive media with Debye, Drude, and Lorentz models, enabling precise simulation of oblique scattering.

Findings

Demonstrates good convergence with analytical solutions

Validates approach with scattering from a slab

Shows applicability to surface wave analysis

Abstract

We formulate a finite-difference time-domain (FDTD) approach to simulate electromagnetic wave scattering from scatterers embedded in layered dielectric or dispersive media. At the heart of our approach is a derivation of an equivalent one-dimensional wave propagation equation for dispersive media characterized by a linear sum of Debye-, Drude- and Lorentz-type poles. The derivation is followed by a detailed discussion of the simulation setup and numerical issues. The developed methodology is tested by comparison with analytical reflection and transmission coefficients for scattering from a slab, illustrating good convergence behavior. The case of scattering from a sub-wavelength slit in a dispersive thin film is explored to demonstrate the applicability of our formulation to time- and incident angle-dependent analysis of surface waves generated by an obliquely incident plane wave.