Theoretical Studies of Active, Synchronous, and Hybrid Mode-Locking
- 124 Downloads
In previous work, we have shown how self-consistent solutions for both active mode-locking (AML) 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 the bandwidth controlled by a Fabry-Perot etalon, we demonstrated in the case of MLSP that for positive values of the cavity mismatch ... (= pump 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 ... > 0, the mismatch (like the filter) introduces delay, and both processes therefore transfer information across the pulse profile from front to back. For ... < 0 however, the information flows are opposed; the profile is then governed by a second-order difference equation and recourse to numerical methods is unavoidable. The set of steady-state solutions presented in Fig. 1 indicates that as ... is decreased, the profiles are forced into the region ahead of threshold, until a point is reached where they broaden abruptly; this effect has frequently been observed experimentally (e.g. ).
KeywordsSpontaneous Emission Saturable Absorber Pulse Profile Stochastic Source Cavity Period
Unable to display preview. Download preview PDF.