Intensity Fluctuations in a Two-mode Ring Laser

Intensity fluctuations in a two-mode ring laser with zero detuning are derived using a noise amplification rate-equation model. Both approximate and exact forms of the gain saturation are treated. Steady-state distributions of the intensity are derived analytically permitting calculation of the mean and normalized variance. Numerical solutions yield the time-dependent evolution of these quantities from initial input noise. Recently derived mode competition effects, such as a steady state value of } for the normalized variance (rather than zero as in a conventional laser) and negative correlations between the intensity fluctuations of the two modes, appear more simply here and their statistical origin is explained.