Perturbative analysis of transverse effects of ((2)(chi)) cascading in resonators

The transverse effects caused by second-harmonic generation and cascading o f second-order nonlinearities on the self-consistent beams circulating in a resonator containing a nonlinear crystal are analyzed in a general and uni fied manner by use of a first-order perturbation theory. Various resonator configurations are considered, including those of practical relevance for g eneration of picosecond pulses by passive mode locking of solid-state laser s. The result is a closed form expression for self-induced loss modulation of the resonator. We compared the various resonators and modes of operation by numerically finding the maximum transmission modulation achievable and explicitly calculating for each of them the optimum phase mismatch and the optimum parameters of the Gaussian beam in the crystal. (C) 1998 Optical So ciety of America [S0740-3224(98)01612-9] OCIS codes: 190.2620, 140.3410.