On the problem of propagation of nonlinear coupled TE-TM waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

Nonlinear coupled electromagnetic TE-TM wave propagation in a cylindrical double-layer nonlinear inhomogeneous dielectric waveguide with circular cross section is considered. Inner layer of waveguide is filled with linear medium. Nonlinearity inside the outer layer of waveguide is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed.