PERTURBATION-THEORY OF NONLINEAR RESONATORS WITH AN APPLICATION TO KERR-LENS MODE-LOCKING

The beam propagation in nonlinear optical systems and resonators is fo rmulated by means of operators, and a perturbation method is used to s alve, to the first order, the problem of calculation of the nonlinear losses caused by intracavity nonlinearities. Steady-state situations a nd weak nonlinearities are assumed, but no other restrictions concerni ng the type of nonlinearity and the resonator structure are imposed. T he main result is a simple, closed-form expression of the resonator-lo ss perturbations that can be determined without the preliminary calcul ation of the nonlinear self-consistent cavity field, and it has a clea r physical interpretation. As an example of an application, a formula for the nonlinear losses of resonators used for Kerr-lens mode locking is derived in the context of Gaussian modes. The result, which is val id for any type of resonator, is numerically illustrated in a fea case s of practical relevance. (C) 1996 Optical Society of America.