Radial birefringence in optical resonators

Paraxial fields polarized in the transverse plane and represented in the polar coordinate system are expanded in an azimuthal Fourier series. For series terms with spiraling phases, the radial and azimuthal components are shown to mix during propagation. For simple rod lasers with thermally induced birefringence, this property may cause the dominant mode to be of mixed polarization rather than purely radial polarization. An explanation is given in terms of the properties of scalar field propagators and the way in which they combine to propagate the vector field components. Comparisons to other recent predictions show that the theory is correct, and the method provides a basis for understanding the complex results.