Coupled Electromagnetic Wave Propagation in A Waveguide With Nonlinear Permittivity: Nonlinear Perturbation Approach And Existence of Nonlinearizable Solutions

We study propagation of a sum of two electromagnetic waves of the same frequency in a plane shielded waveguide with anisotropic nonlinear permittivity. Since the permittivity is nonlinear, then the sum of waves forms a coupled nonlinear wave. The main problem is to prove that the waveguide supports coupled nonlinear guided waves. The problem is formulated for Maxwell's equations and then is reduced to a specific type of nonlinear eigenvalue problems. Existence of the guided waves is proved using a nonlinear perturbation approach. Using this approach it is proved existence of solutions without linear counterparts. We also present numerical results that, on the one hand, illustrate the theoretical findings and, on the other hand, show that there are solutions that cannot be found using the developed approach.