# BSU bulletin. Mathematics, Informatics

Bibliographic description:
Itigilov G. B.
,
Shirapov D. S.
,
Olzoeva S. I.
HELMHOLTZ EQUATIONS OF ELECTROMAGNETIC WAVES IN GYROTROPIC ELLIPTICAL WAVEGUIDES // BSU bulletin. Mathematics, Informatics. - 2018. №3. . - С. 85-93.
Title:
HELMHOLTZ EQUATIONS OF ELECTROMAGNETIC WAVES IN GYROTROPIC ELLIPTICAL WAVEGUIDES
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-3-85-93UDK: 519.87
Annotation:
In the propagation of electromagnetic waves in waveguides, the formulation of boundary value problems is of great importance, the solution of which leads to the derivation of dispersion equations of great practical importance. Analysis of disper- sion equations makes it possible to reveal the patterns of propagation of electro- magnetic waves in waveguides and on their basis to develop various instruments of the microwave range. The problem of research is considerably complicated if the waveguide is filled with a gyrotropic medium. There is currently no complete mathematical model of the propagation of electromagnetic waves in gyrotropic el- liptical waveguides, which includes the Helmholtz equations, the expression for the transverse components and boundary conditions.
In this paper, on the basis of general expressions for arbitrarily magnetized regular gyrotropic waveguides with a generalized orthogonal curvilinear cross-sectional shape obtained by solving a system of Maxwell differential equations, the Helmholtz equations for elliptical waveguides filled with longitudinally and transversely magnetized ferrite are obtained. The obtained equations supplement the theoretical basis for the electrodynamic analysis of gyrotropic elliptical waveguides.
Keywords:
electromagnetic wave; hybrid wave; gyrotropic elliptical waveguide; magnetic permeability tensor; longitudinal magnetization; elliptical magnetization; hyperbolic magnetization; Maxwell equation; Lame coefficients; Helmholtz equa- tion.
List of references:
Laks B., Batton K. Sverhvysokochastotnye ferrity i ferrimagnetiki [Microwave Ferrites and Ferrimagnetics]. Transl. from English. Moscow: Mir Publ., 1965. 676 p.

Sul G., Uoker L. Voprosy volnovodnogo rasprostraneniya elektromagnitnykh voln v girotropnykh sredakh [Issues of the Waveguide Propagation of Electromagnetic Waves in Gyrotropic Media]. Moscow: Inostr. Lit. Publ., 1955. 189 p.

Gurevich A. G. , Melkov G.A. Magnitnye kolebaniya i volny [Magnetic Fluc- tuations and Waves]. Moscow: Fizmatlit Publ., 1994. 464 p.

Tuz V. R., Shulga V. M., Han W., Sun H.-B., Fesenko V. I., Fedorin I. V. Dis- persion peculiarities of hybrid modes in a circular waveguide filled by a composite gyroelectromagnetic medium. Journal of Electromagnetic Waves and Applications. 2017. V. 31, No. 3. Pp. 350–362. DOI: 10.1080/09205071.2017.1285726.

Efimov I. E., Shermina G. A. Volnovodnye linii peredachi [The Waveguide Transmission Lines]. Moscow: Svyaz' Publ., 1979. 232 p.

Neganov V. A., Nefedov E. I., Yarovoj G. P. Sovremennye metody proektiro- vaniya linij peredach i rezonatorov sverh- i krajnevysokih chastot [The Modern Design Methods of Projecting the Lines of Transfers and Resonators of Super- and Extremely High Frequencies]. Moscow: Pedagogika-Press Publ., 1998. 328 p.: il.

Shirapov D. Sh., Itigilov G. B. Obobshchennye uravneniya Gel'mgol'tsa giro- tropnykh volnovodov proizvol'noi formy poperechnogo secheniya [Generalized Helm- holtz Equations for Gyrotropic Waveguides of Arbitrary Cross-Sectional Shape]. Sovremennye problemy distantsionnogo zondirovaniya, radiolokatsii, rasprostraneniya i difraktsii voln: Materialy II Vserossiiskoi nauchnoi konferentsii. Modern problems of remote sensing, radar, wave propagation and diffraction: Proceedings of the II all- Russian scientific conference. Murom, 2018. Pp. 209–219.

Itigilov G. B. Matematicheskoe modelirovanie rasprostraneniya elektromagnit- nykh voln v ogranichennykh girotropnykh oblastyakh proizvol'noi formy Dis. … kand. Techn. nauk [Mathematical Modeling of Propagation of Electromagnetic Waves in Bounded Gyrotropic Regions of Arbitrary Shape. Cand. techn. sci. diss.] Ulan-Ude, 2014. 146 p.