Topological wave features near degeneracies in acoustics and optics of absorptive crystals

The unified formalism for description of acoustic and optic properties is developed for directions close to degeneracies in absorbing crystals. The absorption splits a conical degeneracy which causes topological transformations in polarization and geometrical features of degenerate branches. Polarization ellipses distributions gain singularities at the degeneracy points characterized by the Poincaré indices n = ±1/4. The slowness surfaces acquire lines of self-intersection connecting the split degeneracy points where the wedge of intersection has infinitely sharp tips. Geometrical and polarization singularities due to absorption create non-trivial features in conical refraction. For any direction of propagation in the vicinity of the split axes the ray velocity precesses along the universal cone of refraction. Kinematics of this precession appreciably depends on the propagation direction. Conditions for experimental observation of the predicted effects are discussed.