Effects of noise on transients of injection locked semiconductor lasers

Semiconductor laser injection locking transients are analyzed. By adiabatically eliminating the carrier dynamics, a single nonlinear stochastic differential equation is obtained for the relative phase between the master and slave lasors. The corresponding Fokker-Planck equation is used to study the steady-state locked conditions as well as phase transients of the locking process. Noise causes the steady-state relative phase between the master and the slave lasers to be a random variable with a standard deviation of approximately a few degrees for typical injection levels. The standard deviation can be reduced by using a phase detector with a limited bandwidth. The mean locking time in the presence of noise is slightly less than the deterministic prediction. Noise also causes the locked lasers to have a finite probability to momentarily unlock