Acoustics and optics of absorptive crystals: a universal formalism for topological effects

A universal form of the equations for acoustical and optical wave fields in absorptive crystals is obtained. On this basis, a unified formalism is constructed and used to describe the effect of absorption on the topology of polarization fields and wave surfaces of elastic and electromagnetic waves close to conical acoustic and optical axes. Unless forbidden by symmetry, both types of axes are split by absorption, with the consequences that the wave surfaces acquire self-intersection lines connecting pairs of split axes and that new singular points with the Poincaré indices $n = \pm1/4$ arise in the polarization fields. Near the split points, the waves of degenerate branches show an abrupt increase in ellipticity, which transforms the internal conical refraction from a local property along the degeneracy direction into a continuum phenomenon occurring throughout this entire region. For each direction of the wave normal, there is a universal refraction cone, the same as for zero absorption. The ends of ray velocity vectors move along the universal section of this cone. This section is elliptic in acoustics and circular in optics. The kinematics of this precession depend in an essential way on the direction of the wave normal.