Competition between longitudinal modes in a ring laser with an anisotropic resonator

A theoretical investigation is made of a ring laser subjected to a longitudinal magnetic field in the case when the anisotropy of the resonator is purely circular in nature. Four-wave emission is considered. Two separate cases are discussed: 1) two pairs of identically polarized circular waves traveling in opposite directions; 2) two orthogonal pairs of circular waves. A nonlinear interaction between the traveling waves and the stability of both cases are considered.