Abstract

When the effects of spontaneous emission are negligible, the third-order equations of motion for the bidirectional ring laser with backscattering can be solved exactly. The solution can be expressed in terms of elementary functions except in the case of unequal pump parameters or unequal cross- and self-saturation terms, in which cases the solution involves elliptic integrals. The solution reveals an instability in the relative phase between the two counterpropagating modes which gives rise to phase jumps of xrad. The onset of this instability is marked by intensity and phase oscillations. Additionally, the analytic solution may be utilized to determine the backscattering properties and operating point of the laser via intensity measurement. The results are compared with related solutions of the Fokker-Planck equation associated with the Langevin equations for the laser, with numerical solutions of the Langevin equations, and with experiments.

© 1989 Optical Society of America