Theory analysis of cross-injection locking of two diode lasers

A complicated nonlinear dynamical system——cross-injection locking diode lasers system is proposed. Equations are derived for the simplest system which is composed of two lasers only, and the locked steady-state analytical solutions are obtained for the simplest case in which the two lasers have the same free-running frequency without locking. The results show that with an equal coupling，locking bandwidth of cross-injection is approximately twice than that of master-slave injection and even in such special system a frequency shift may happen after the constituent lasers are locked.