Effect of the cross-relaxation rate on the transverse radiation dynamics of a wide-aperture laser

The effect of a finite polarisation relaxation time on the transverse structure of the optical field of a wide-aperture laser is considered. The conditions are found for the emergence of periodic autowaves for positive and negative frequency detuning. These conditions are shown to depend strongly on the cross-relaxation rate. It is established that the dynamics of finite-aperture lasers at high cross-relaxation rates is satisfactorily described by simplified models in which the polarisation is adiabatically eliminated.