Abstract

We recently presented [1] the following “master equation” [2] applicable to any nonlinear cavity with linear properties describable by an ABCD matrix and with one nonlinear interaction per round trip: The intra-cavity field E is a function of fast (t) and slow (T) times, as well as ${\overrightarrow{r}}_{\perp }$, the transverse position vector. ∇_⊥ is the transverse gradient operator, and cosψ = S. Here S = (A + D)/2. We have included typical operators for gain and dispersion [2], and so the round-trip time T_R is that based on the group velocity. To describe KLM, we specialize the nonlinear function N(E) to the Kerr form N(E) = iη|E|²E, which requires that the ABCD elements be calculated at the Kerr lens.

© 1996 Optical Society of America