Nonparaxial wave beams in a uniaxial birefringent crystal

The solutions are obtained to vector wave equation for nonparaxial beams propagating along the optic axis in a uniaxial birefringent crystal. We have revealed that circularly polarised nonparaxial beams may be presented as a set of transverse electric and transverse magnetic waves keeping their structure up to a scale factor when propagating. A beam with arbitrary field distribution may be written as a composition of such the wave fields. We have shown that a circularly symmetric vortex beam with the initial circular polarisation preserves its structure inside the crystal. A circular symmetry of nonparaxial vortex beam with the initial linear polarisation gets lost as the beam transmits through the crystal. The circular symmetry is not recovered in the paraxial case, being an inherent property of the linearly polarised beams.