Modes in an anisotropic inhomogeneous medium with axial symmetry

The modes which can exist in anisotropic inhomogeneous dielectric waveguides with axial symmetry are derived. The structure and phase velocities of eigenmodes are derived for an arbitrary but reasonably smooth (in particular, quadratic) transverse variation of the permittivity tensor. The eigenmodes have a polarization which varies, depending on the distance from the waveguide axis. In the region of strong anisotropy, the polarization is nearly radial or nearly azimuthal. Estimates indicate that the anisotropy is strong over the whole cross section of a stressed laser rod, with the exception of a small region near the axis.