Complex ray in anisotropic solids: Extended Fermat's principle

Abstract

In contrast to homogeneous plane waves, solutions of the Chris-toffel equation for anisotropic media, for which a determined number of can be observed in a fixed direction of observation, inhomogeneous plane waves provide a continuum of rays that propagate in this direction. From this continuum, some complex plane waves can be extracted for verifying a definition of quasi-arrivals, based on the condition that the time of flight would vary the less in extension to the Fermat's principle that stipulates a stationary time of flight for wave arrivals. The dynamic response in some angular zones contain prominent, although not singular, features whose arrivals cannot be described by the classical ray theory. These wave packet's arrivals can be described by quasi-fronts associated to specific inhomogeneous plane waves. The extent of the phenomena depends on the degree of anisotropy. For weak anisotropy, such quasi-fronts can be observed. For strong anisotropy, the use of inhomogeneous plane waves, due to their complex slowness vector, permits a simple description of quasi-arrivals that refer to the internal diffraction phenomenon. Some examples are given for different wave surfaces, showing how the wave fronts can be extended beyond the cuspidal edges for forming closed wave surfaces.