Maxwell’s Equations in a Plane Waveguide with Nonhomogeneous Nonlinear Permittivity: Analytical and Numerical Approaches

The paper focuses on the problem on monochromatic electromagnetic waves propagation in a shielded planar dielectric waveguide. The waveguide is filled with nonhomogeneous nonlinear medium. The nonlinearity is expressed by nonnegative unbounded monotonically increasing function with power growth. Such nonlinearity is a generalization of the well-known Kerr nonlinear law. The existence of propagation constants and eigenwaves is proved. Besides, it is proved that the studied problem has nonlinearized solutions as well as linearized ones.