Mode competition in a homogeneously broadened ring laser

The equations previously derived for the intensity fluctuations of a two-mode ring laser are applied to a homogeneously broadened laser. It is shown that the mean light intensity of the more lossy mode passes through a maximum and then tends to zero as the excitation is increased. The probability distribution of the intensity of each mode may exhibit two peaks, and spontaneous switching between the intensities associated with the peaks may occur. This is manifest in relative intensity fluctuations of the more lossy mode that can be much greater than unity. Estimates are given for the characteristic switching time.