Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

The problem of propagation of monochromatic electromagnetic TE waves in a double-layer cylindrical dielectric waveguide filled with nonlinear inhomogeneous medium is considered. The physical problem is reduced to solving a nonlinear transmission eigenvalue problem for ordinary differential equation. Eigenvalues of the problem are the propagation constants of the waveguide. The paper proposes a method to determine approximate eigenvalues of the nonlinear problem. This method is based on solving an auxiliary Cauchy problem (the shooting method). Existence of the eigenvalues, which correspond to a new propagation regime, is predicted. A comparison with the linear case is given.