Canonical perturbative approach to nonlinear systems with application to optical waves in layered Kerr media

We investigate electromagnetic wave reflection and propagation in layered K err structures by introducing a method based on the application of canonica l perturbation theory to fields in nonlinear media. Via the Hamilton-Jacobi formalism of classical mechanics, the waves in linear layers are expressed with constant canonical variables. The nonlinearity is treated as a small perturbation that modifies the constant invariants. We explicitly evaluate the nonlinear fields correct to first order by perturbation and compare the results to a rigorous nonlinear thin-layer model. Both polarizations, TE a nd TM, are considered separately. An exact quadrature solution of the nonli near field in TM polarization is derived. We show that with weak nonlineari ties the perturbative technique yields simple and accurate analytical expre ssions for the nonlinear fields. The results give physical insight into the use of nonlinear media for controlling the scattered fields in layered str uctures.