Generalised theory of polarisation modes for resonators containing birefringence and anisotropic gain

Polarisation eigenmode theory is well established for laser cavities in which the principal axes for gain and polarisation elements are parallel. Here we generalise the theory to include the case for gain axes at arbitrary angle to the birefringence, which is the case for Raman lasers based on cubic-class gain crystals that contain stress-induced birefringence. The theory describes regimes dominated by gain, linear or circular birefringence, and the intermediate regime in which elliptically polarised output modes are obtained. Previously reported behaviour for diamond Raman lasers are found to be in accord with the findings. Design criteria are obtained to enable prediction of polarisation behaviour as functions of birefringence and resonator design.