Perturbation theory of nonlinear resonators with an application to Kerr-lens mode locking

The beam propagation in nonlinear optical systems and resonators is formulated by means of operators, and a perturbation method is used to solve, to the first order, the problem of calculation of the nonlinear losses caused by intracavity nonlinearities. Steady-state situations and weak nonlinearities are assumed, but no other restrictions concerning the type of nonlinearity and the resonator structure are imposed. The main result is a simple, closed-form expression of the resonator-loss perturbations that can be determined without the preliminary calculation of the nonlinear self-consistent cavity field, and it has a clear 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 valid for any type of resonator, is numerically illustrated in a few cases of practical relevance.