Abstract

In previous work, we have shown how self-consistent solutions for both active mode-locking and mode-locking by synchronous pumping (MLSP) may be derived from simple difference equations [1-2]. Using a rate-equation model for the gain and a unidirectional ring cavity with bandwidth control provided by a Fabry-Perot etalon, we demonstrated in the case of MLSP that for positive values of the cavity mismatch t_m (= pump repetition period - cavity period), steady-state profiles can be generated from a first-order difference equation (the "stepping" algorithm). The simplicity of this solution arises from the fact that, for t_m > 0, the mismatch and the filter memory both transfer information over the pulse profile in the same direction (from front to back). For t_m <0, however, the information flows are in opposition; the profile is then governed by a second-order difference equation and recourse to numerical methods is often unavoidable. The set of steady-state solutions presented in fig. 1 indicates that as t_m is decreased the profiles are forced into the region ahead of threshold, until a point is reached where they broaden abruptly; this effect has been widely observed in experimental systems (e.g. [3]).

© 1984 Optical Society of America