We derive a local nonlinear thin-layer theory for electromagnetic fields that propagate in layered structures of isotropic, dispersive, and spatially local Kerr media. By use of an ansatz of plane waves together with a thin-layer approximation, the two-dimensional Kerr–Maxwell equation is rigorously solved within a very thin slab, and the characteristic matrix of the nonlinear medium is determined. The theory makes use of periodicity and allows a direct calculation of the nonlinear field throughout the structure on the basis of the transmitted field. The method is applied in the two polarizations, TE and TM, and is illustrated with a numerical example. The nonlinear thin-layer technique provides a simple and accurate analytical theory that includes multiple plane-wave incident fields and takes rigorously into account all nonlinear interactions of these waves.
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