Abstract

Linear stability analysis of the bidirectional ring laser model of Khanin gives an analytic expression for instabilities. We describe the derivation of the model and indicate several oversights which have led to errors in models recently discussed in the literature. We find that there is a critical value of detuning necessary for instabilities that is of the order of the relaxation oscillation frequency and that there is a limited range of excitation values over which the instability occurs. The instabilities may be observed asymptotically close to the laser threshold for large detuning, when the field decay rates are large compared with the population inversion decay rates and when there is some difference in the decay rates for the fields in the two directions. Asymptotic limits for the boundaries of the instability region are presented. Bistability as well as instabilities appear depending on the degree of difference in the two field decay rates. Causes of such asymmetries in decay rates in real ring lasers are discussed. Time-dependent solutions show several different kinds of pulsation depending on the degree of detuning and excitation. For small detunings the laser periodically switches direction of operation with nearly complete suppression of the counterpropagating beam for relatively long periods of time. For larger detunings the solutions are more periodic and correspond to anticorrelated modulations of lasing in both directions simultaneously.

© 1986 Optical Society of America