Diffraction Catastrophes in the Optics and Acoustics of Crystals

In this paper, different types of singular points of the wave vector surface are considered. It is demonstrated that the light and acoustic beam propagation along the directions related to these points is identified with the simplest diffraction catastrophes. The possibility of transformation of one type of catastrophes to another in the presence of small disturbance is established. To illustrate this, we show an example of removing the degeneracy of phase velocities along the optical (acoustic) axis in a gyrotropic crystal and transforming a diffraction catastrophe, consisting in the correspondence of one wave normal to the whole cone of rays, into a diffraction catastrophe of the fold. The latter is characterized by the formation of sharp edges and the allocation of an additional sub-surface on the ray surface. Owing to this, not two but four (in acoustics – quasi transversal) waves with different group velocities may propagate in a definite direction near the (acoustic) axis.