Nonlinear interaction between elliptically polarized waves in a ring gas laser in a magnetic field

A system of ten real first-order differential equations is derived to describe the temporal evolution of the emission of elliptically polarized opposite waves in a ring gas laser with a magnetic field applied to the active medium. The equations determine the emission frequencies and intensities of the opposite waves, and also their polarization states. Conditions for stable unidirectional emission of an elliptically polarized traveling wave are derived for a pure-isotope ring gas laser in the presence of a magnetic field. It is found that the width of the region of strong competition between linearly polarized opposite waves decreases to zero as the magnetic field increases and this is confirmed experimentally.