Acoustic wave degeneracies in two-dimensional phononic crystals

The paper studies numerically the degeneracy of the acoustic wave spectrum in 2D phononic crystals (PC) and PC slabs. A PC structure constituted of parallel steel rods immersed into water and forming the square lattice is considered. Given the projection k(z) of the wave vector on the direction parallel to the rods, the bulk wave spectrum of the infinite PC represents a set of frequency surfaces f(i)(k(x), k(y)), i = 1, 2,.... where k(x,y) are the components of the wave vector in the plane perpendicular to the rods. The shape of frequency surfaces in the vicinity of points where these surfaces come into contact is investigated. Three types of surface shapes and, correspondingly, contacts are identified. According to the terminology adopted in crystal acoustics, they can be called conical, tangential, and wedge types of contact or degeneracy. The evolution of the degeneracy with changing rod radius and cross-section shape is examined. Degeneracy in the spectrum of leaky modes propagating along a single waveguide and two parallel Coupled waveguides in a PC slab is also investigated. (C) 2008 Elsevier B.V. All rights reserved.