Dispersion in layered periodic media

From Two-dimensional wave propagation in layered periodic media

by Manuel Quezada de Luna and David I. Ketcheson

What happens when waves pass through a composite made of alternating horizontal layers of two materials? The four possible kinds of behaviour are shown here. Each quadrant shows an initially symmetric perturbation near (x,y)=(0,0) expanding in a medium with different properties. The inset shows the layered structure of the materials. The coloured plots and solid red lines are the result of numerical simulation. The dashed lines are theoretical predictions.

The top left shows a wave in a homogeneous medium for reference. If the two materials are different, the behaviour depends on their relative impedances and sound speeds.

If the impedances differ (bottom left), then waves propagating normal to the layers are dispersed (by reflections) -- note the trailing ripples in the red and black trace plot (along x=0) to the left. Meanwhile, waves traveling along the layers exhibit no such dispersion.

On the other hand, if the sound speeds differ (top right), waves propagating along the layers are dispersed (by diffraction) while waves moving normal to the layers are not. This effective dispersion is a new discovery and the main subject of the manuscript.

If both the sound speed and the impedance differ (bottom right), then waves in both directions are dispersed.
See http://arxiv.org/abs/1309.6666.