1. The origins of band gaps
A 2D phononic crystal can be made by creating an array of air-filled cylinders in a solid material (insert) so that the speed of sound varies periodically. The dispersion relations - plots of frequency, ω, versus wave vector, k − for different phonons in this structure (blue lines) reveal that wave propagation is not supported for certain range of frequencies (yellow region): this is a phononic band gap. In a homogeneous material, ωnbsp;= c • k, where c is the velocity of sound, and the dispersion relation would appear as a straight line on this graph. The directions with the highest symmetry in this structure are Γ−X and Γ−M (see insert).