Lock-Time Analysis of Injection-Locked Lasers

Transient characteristics of optical injection-locked (OIL) solid-state lasers are analyzed using rate equations, with a focus on how the lock-time, which is defined as the time required for the slave laser to lock onto the master laser’s frequency, is affected by the injection strength, detuning frequency, and cavity field’s initial phase. In particular, mean lock-time, the lock-time averaged over a random initial phase difference between the two laser signals, is systematically investigated. The study, aided by asymptotic stability and phase-space trajectory analyses, shows that the dynamics of OIL lasers is quite complex as well as diverse in its behavior. Findings involving the mean lock-time indicate that it is fairly insensitive to frequency detuning except near the locking edge, wherein extremely large variations can occur, ranging from a very small to a very large value in a narrow interval. It is also found that there is a trend reversal of the mean lock-time with respect to the injection strength; after initially undergoing a decrease with increasing injection level, the lock-time starts to increase once again beyond a certain injection strength. There are also some interesting features predicted, such as instantaneous locking and pseudo-stable behavior. The transient process following switching off of the injected light is also briefly investigated and compared to the injection-locking process. The results of this research should provide useful insight when exploring the feasibility, limitations, and design guidelines of various potential OIL applications in which the response speed is of importance.