Equivalent circuits in Fourier space for the study of nonlinear waves guided by thin films

By applying Fourier transformations to Maxwell's equations, the authors derive transmission-line equations representing the transverse electric (TE) and transverse magnetic (TM) modes of dielectric planar layers. The propagation constant of any mode can be found from the resonance conditions of the T-circuit representation of the transmission line. The method developed for the linear case is extended to include the nonlinear waves guided by such structures. The following realistic material systems are treated: a cladding medium with either a self-focusing or a self-defocusing nonlinearity and bounding media with all combinations of self-focusing and self-defocusing nonlinearities. Dielectric films with arbitrary refractive index profiles bounded by nonlinear media are examined. Useful results concerning the field distribution and the guided power versus propagation constant are derived.<>