Splitting of cones of optical axes in gyrotropic crystals in the presence of dichroism

Features of the appearance of conical singularities in the presence of linear dichroism and natural optical activity at the point of intersection of dispersion curves of the principal refractive indices of a crystal have been considered. It has been shown that even insignificant dichroism results in the splitting of cones of optical axes into cones of singular optical axes (in a partial case, cones are degenerate into planes) between which a “gap” with identical velocities of proper waves appears. The splitting angle for the AgGaS$_2$ crystal is estimated at about 5$^\circ$.