Geodesic
Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 460-468

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Problems on the propagation of surface TE and TM waves in an inhomogeneous anisotropic two-layered planar or cylindrical magneto-dielectric waveguide are considered. The problem is reduced to the analysis of a Sturm–Liouville problem of a special kind with boundary conditions of the third kind, nonlinearly depending on the spectral parameter. The conditions under which TE and TM waves can propagate are obtained, and the regions of localization of the corresponding propagation constants are determined. 
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     author = {Yu. G. Smirnov},
     title = {Eigenvalue transmission problems describing the propagation of {TE} and {TM} waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {460--468},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/}
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Yu. G. Smirnov. Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 460-468. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a9/