Two-dimensional wave propagation in layered periodic media
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.
Keywords
Cite
@article{arxiv.1309.6666,
title = {Two-dimensional wave propagation in layered periodic media},
author = {Manuel Quezada de Luna and David I. Ketcheson},
journal= {arXiv preprint arXiv:1309.6666},
year = {2014}
}