Acoustics and optics of absorptive crystals: a universal formalism for topological effects
Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii prosp. 59, Moscow, 119333, Russian Federaion
A universal form for equations determining the 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 the polarization fields and wave surfaces of elastic and electromagnetic waves close to the 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 that connect pairs of split axes; and that in the polarization fields new singular points with the Poincaré indices n = ±1/4 arise. 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 continual phenomenon occurring throughout this entire region. For each wave normal direction here there is a universal refraction cone, the same as for zero damping. The ray velocity vectors have their ends moving along the universal section of this cone. This section is elliptic in acoustics and circular in optics. Kinematics of this precession depends in an essential way on the direction of the wave normal.