A NOTE ON HYBRID WAVES IN PLANE LAYERED WAVEGUIDING STRUCTURES 

Biteleva Elena Olegovna, Student, Penza State University (40 Krasnaya street, Penza, Russia), len.biteleva@yandex.ru
Valovik Dmitriy Viktorovich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street,Penza, Russia), dvalovik@mail.ru

517.927, 517.968, 519.6

10.21685/2072-3040-2017-3-1

Background. The paper focuses on the problem of propagation of a hybrid electromagnetic wave in a plane layer filled with anisotropic dielectric. Such kind of problems attracts attention due to the mathematical aspects of the theory as well asthe importance in microelectronics and photonics.
Materials and methods. Classical methods of ordinary differential equations.
Results. A linear two-parameter eigenvalue problem arising in the theory ofguided electromagnetic waves is considered. The field configuration is adjustedwith the symmetry of a plane layered waveguide. The guided wave is characterised by a pair of coupled propagation constants. The dispersion equation, which determinesthe coupled propagation constants, is derived. The equivalency between theoriginal waveguiding problem and the dispersion equation is proved.
Conclusions. The paper suggests a novel concept of a hybrid electromagneticwave in a plane layered structure. The hybrid wave is the most general field configuration,which can exist in a plane waveguide. This concept generalises well knowntypes of polarised guided waves (TE and TM waves).

hybrid electromagnetic wave, plane waveguide, two-parameter eigenvalue problem, Maxwell equations

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