Two-dimensional wave propagation in layered periodic media

TL;DR

This paper investigates two-dimensional wave propagation in layered periodic media, deriving an anisotropic dispersive effective medium approximation that captures microscopic diffraction effects, with results validated by numerical simulations.

Contribution

It introduces a high-order homogenization method for 2D layered media, revealing new effective dispersion phenomena even in constant impedance materials.

Findings

Dispersive effects arise from microscopic diffraction in 2D.

Effective medium approximation accurately predicts wave behavior.

Numerical simulations confirm theoretical predictions.

Abstract

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using high-order homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coefficient equations.