Nonlinear polarisation of the medium in a two-mode laser with an arbitrary intracavity phase anisotropy

A simple procedure is proposed for calculating the polarisation of the active medium of a laser. It is based on the third-order expansion in terms of the field of two longitudinal modes with arbitrary polarisation and spatial configurations. This procedure reduces to the representation of a resonant interaction of the corresponding standing waves by elementary processes involving an equivalent set of travelling waves. Universal expressions are derived for the polarisation of an isotropic medium. The validity of these expressions is demonstrated by considering the example of the competition between orthogonal modes with elliptic polarisations.