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Studying the surface wave spectrum of an open inhomogeneous rectangular dielectric waveguide. (English. Russian original) Zbl 1478.78046

Differ. Equ. 57, No. 9, 1150-1164 (2021); translation from Differ. Uravn. 57, No. 9, 1177-1190 (2021).
Summary: We consider the problem of surface waves in a regular open inhomogeneous waveguide structure of rectangular cross-section. This problem is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. A variational statement of the problem is used to find the solution. Theorems on the discreteness of the spectrum and on the distribution of the characteristic numbers of an operator function on the complex plane are proved. The characteristic numbers of the problem correspond to the waveguide propagation constants.

MSC:

78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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