研究目的

The paper focuses on the problem of coupled electromagnetic wave propagation in a GL filled with a nonlinear inhomogeneous medium. The waveguide is located in the cylindrical coordinates Oρ?z, where the waveguide symmetry axis coincides with z axis. The nonlinearity is expressed by the Kerr law. The permittivity inside the waveguide depends on the field and on the radial coordinate. The coupled wave in the waveguide is a sum of two polarised monochromatic waves (surface TE and leaky TM); each of these polarisation depends harmonically on z-variable. The main problem is to determine coupled propagation constants and coupled eigenmodes and show their properties.

研究成果

The existence of coupled surface TE and leaky TM waves in a GL with a nonlinear inhomogeneous dielectric cover was proved. The method developed allows us to prove the existence of coupled eigenvalues of the nonlinear problem that are close to the eigenvalues of the corresponding linear problem and are actually perturbations of the latter.

研究不足

The study is limited to the analysis of coupled surface TE and leaky TM waves in a specific type of waveguide (Goubau line) filled with a nonlinear inhomogeneous medium. The analysis assumes classical solutions and does not consider other types of waves or more complex waveguide structures.