Two-dimensional wave propagation in layered periodic media

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. Whereas 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. This dispersive effect is confirmed by homogenization and direct numerical simulations.