Waves with linear, quadratic and cubic coordinate dependence of amplitude in crystals

There exist inhomogeneous electromagnetic and elastic waves with linear, quadratic and cubic coordinate dependence of amplitude, in addition to the usual plane harmonic waves in crystals. This article is concerned with conditions for initiation of such waves and mathematical techniques for their description. New types of electromagnetic waves with quadratic and cubic coordinate dependence of amplitude on the transverse coordinate in a transparent biaxially anisotropic plate are found. Any transparent biaxial crystal is demonstrated to have an infinite set of cuts, each suitable for initiation of one or more such waves.