EFFECTS OF NOISE ON TRANSIENTS OF INJECTION-LOCKED SEMICONDUCTOR-LASERS

An analysis of transients of semiconductor laser injection locking is presented. The analysis is based on the semiconductor rate equations and includes the effects of noise, amplitude phase coupling, carrier dynamics, and gain saturation. By adiabatically eliminating the carrier dynamics, a single nonlinear stochastic differential equation is obtained for the relative phase between the master and slave lasers. The validity of the adiabatic approximation is verified by numerically integrating the rate equations. The corresponding Fokker-Planck equation is used to study the steady-state locked condition 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, equivalent to a particle escaping over a potential barrier. The results of an experimental measurement of the locking time is presented. As predicted by the analysis, the locking time is reduced by either increasing the locking bandwidth or reducing the free running frequency difference.