Temporal dynamic of the non-linear mirror: an analytical description

This paper describes an improvement on the theory of the non-linear mirror proposed by Stankov. This improvement isachieved by applying an analytical perturbative method that the authors previously developed, and which we have appliedhere to the Stankov mirror. In particular with our technique, we can separately consider the depletion of the fundamentalwave (Fw) due to the generation of the second harmonic (SH) and the distortion of the reflectivity of the non-linear mirror.Our analytical method facilitates immediate description and quantification of each physical step in these processes. Withrespect to the distortion of the reflectivity of the non-linear mirror due to the group velocity mismatch (GVM) between theFW and the SH, our approach allows us to obtain an analytical expression for the FW output even in a non-stationarycondition. Furthermore we compare the pulse lengthening rate (PLR) due to the finite gain bandwidth, with the pulseshortening rate (PSR) of the non-linear device, reporting the solution for achieving a stable mode-locking regime as afunction of the steady state parameter. Finally we report on a successful comparison between the proposed method and theresults of a previously reported experimental demonstration. 0 1997 Elsevier Science B.V.