Existence and properties of solutions to the spectral problem of the dielectric waveguide theory (Q5954759)

The authors present a theoretical analysis of the dispersion curves for inhomogeneous waveguides of arbitrary cross section. The existence of a spectrum is proved for the eigenmodes of weakly guiding dielectric waveguides. The method of analysis is based on a reduction of the problem on the unbounded domain to a parametric eigenvalue problem posed on a circle with a nonlocal boundary condition nonlinear in the spectral parameter.