Propagation of symmetric hybrid electromagnetic waves in a planar inhomogeneous nonlinear waveguide: a numerical study

Background. The paper is devoted to a nonlinear eigenvalue problem arising in the theory of waveguides. The main goal is to numerically investigate the existence of a new type of symmetric hybrid waves propagating in an inhomogeneous nonlinear medium. Materials and methods. The original problem is reduced to a nonlinear eigenvalue problem for Maxwell's equations. The numerical method is based on the solution to the auxiliary Cauchy problem and makes it possible to determine the eigenvalues. Results. A numerical method for solving the problem of the propagation of symmetric hybrid waves in a plane inhomogeneous nonlinear waveguide is proposed. Numerical results are presented. Conclusions. Nonlinear symmetric hybrid waves are very interesting because they have no counterparts in the linear theory. It is a new class of nonlinear waves. Probably, this type of waves can be useful in radio engineering.