We present a method, based on the coherent potential approximation, for the treatment of disorder in photonic crystals. We apply the method to the study of light absorption by a three-dimensional array of plasma spheres distributed randomly in a host dielectric medium. We find that the effect of disorder on the absorbance of a thick slab of the material consisting of many layers of spheres is much less pronounced than in the corresponding case of a single layer of spheres.

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of nonoverlapping elastic spheres, characterized by Lamé coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lamé coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two-dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.

We study the effect of planar defects in phononic crystals of spherical scatterers. It is shown that a plane of impurity spheres introduces modes of vibration of the elastic field localized on this plane at frequencies within a frequency gap of a pure phononic crystal; these show up as sharp resonances in the transmittance of elastic waves incident on a slab of the crystal. A periodic arrangement of impurity planes along a given direction creates narrow impurity bands with a width which depends on the position of these bands within the frequency gap of the pure crystal and on the separation between the impurity planes. We show how a slight deviation from periodicity (one impurity plane is different from the rest) reduces dramatically the transmittance of elastic waves incident on a slab of the crystal.

We present a new version of a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of non-overlapping spherical particles of given periodicity parallel to the surface. The homogeneous media to the left and right of the slab may be different (have different real and positive dielectric functions and magnetic permeabilities).