Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)1836610.22363/2312-9735-2018-26-2-119-128Research ArticleEigen Waves of a Plane Symmetric Anisotropic WaveguideBikeevO N<p>Head of Laboratory of Institute of Physical Researches and Technologies of Peoples’ Friendship University of Russia (RUDN university)</p>bickejev@gmail.comLovetskiyK P<p>Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)</p>lovetskiy_kp@rudn.universitySevastianovA L<p>Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University)</p>sevastianov_al@rudn.universityPeoples’ Friendship University of Russia (RUDN university)1512201826211912821042018Copyright © 2018, Bikeev O.N., Lovetskiy K.P., Sevastianov A.L.2018<p>Precise dispersion equations for a plane symmetric dielectric anisotropic waveguide are obtained, in which the waveguide layer is isotropic, and the framing media are assumed to be anisotropic uniaxial media. The tensors of the dielectric permittivity of the framing media are not assumed to be diagonal, namely, in one of them this tensor is formed by rotating the diagonal tensor by some angle between the optical axis of the anisotropic medium and the direction of propagation of the electromagnetic wave. The tensor of dielectric permittivity of another anisotropic medium is rotated by the same angle, but in the opposite direction, with the optical axes of both framing media lying in a plane parallel to the boundaries of the waveguiding structure. Thus, in framing media, the existence of six-component electromagnetic waves is maintained. In the dispersion properties of such a waveguide, certain features are observed in comparison with the case when the framing media are assumed to be isotropic. It is found that the first symmetric mode of such a waveguide has a finite deceleration with zero thickness of the isotropic layer, which indicates the possibility of the appearance of surface electromagnetic waves (the so-called Dyakonov waves) at the boundaries of this isotropic layer. It is noted that the transition of the antisymmetric mode to the Dyakonov wave occurs with a finite thickness of the waveguiding layer. Dependencies of the deceleration of the elementary (symmetric) mode on the angle of rotation of the optical axis of anisotropic media relative to the direction of propagation of the guided wave of the waveguide structure are given.</p>surface electromagnetic waveanisotropic mediumpermittivity tensorwaveguide modestransverse amplitude distributionguided wavesповерхностная электромагнитная волнаанизотропная средатензор диэлектрической проницаемостиволноводные модыпоперечное распределение амплитуднаправляемые волны[O. Takayma, L.-C. Crasovan, S. Johansen, D. Mihalache, D. Artigas, L. Torner, Dyakonov Surface Waves: A Review, Electromagnetics 28 (2008) 126–145.][J. A. Polo Jr., L. A., A Surface Electromagnetic Waves: a Review, Laser & Photonics Reviews 5 (2011) 234–246.][O. Takayama, L. Crasovan, D. Artigas, L. Torner, Observation of Dyakonov Surface Waves, Physical Review Letters 102 (2009) 043903.][L. Torner, C. Santos, J. P. Torres, D. Mihalache, New Waveguide Modes in Anisotropic Structures, Fiber and Integrated Optics 13 (1993) 271–280.][M. A. Boroujeni, M. Shahabadi, Modal Analysis of Multilayer Planar Lossy Anisotropic Optical Waveguides, Journal of Optics A: Pure and Applied Optics 8 (2006) 856–863.][G. Kweon, S. Hwang-bo, C. Kim, Eigenmode of Anisotropic Planar Waveguide, Journal of the Optical Society of Korea 8 (3) (2004) 137–146.][J. Lekner, Reflection and Refraction by Uniaxial Crystals, Journal of Physics: Condensed Matter 3 (1991) 6121–6133.][O. N. Bikeev, L. A. Sevastianov, Surface Electromagnetic Waves at the Interface of Two Anisotropic Media, RUDN Journal of Mathematics, Informational Sciences and Physics 25 (2) (2017) 141–148, in Russian. doi:10.22363/2312-9735-2017-25-2-141-148.][S. R. Nelatury, J. A. Polo, A. Lakhtakia Jr., Surface Waves with Simple Exponential Transverse Decay at a Biaxial Bicrystalline Interface: Errata, Journal of the Optical Society of America A 24 (2007) 2102–2102.][D. B. Walker, E. N. Glytsis, T. K. Gaylord, Surface Mode at Isotropic-Uniaxial and Isotropic-Biaxial Interfaces, Journal of the Optical Society of America A 15 (1) (1998) 248–260.][N. S. Averkiev, M. I. Dyakonov, Electromagnetic Waves Localized at the Boundary of Transparent Anisotropic Media, Optics and Spectroscopy 68 (5) (1990) 1118–1121.]