Analitical theory Flouqet-Bloch waves for gyrotropic magnetophotonic krystals

doi:10.26565/2311-0872-2019-31-01

А. А. Shmat’ko V. N. Karazin Kharkiv National University http://orcid.org/0000-0002-3714-1638
V. N. Mizernik Scientific Physical-Technologic Center of MES and NAS of Ukraine
Е. N. Odarenko Kharkiv National University of Radio Electronics http://orcid.org/0000-0001-7656-0440

DOI: https://doi.org/10.26565/2311-0872-2019-31-01

Keywords: magnetophotonic crystals, gyromagnetic media, Floquet-Bloch theory, Hill equation, third boundary value problem, transmission and locking zones, bulk and surface waves

Abstract

The relevance of the problem considered in the work is determined by the widespread use of magnetophotonic crystals in various devices of the terahertz microwave and optical ranges. The key is the analytical solution of the third boundary value problem for the Hill equation with mixed Cauchy boundary conditions. This approach made it possible to explicitly find new solutions for electromagnetic fields in the crystal layers and dispersion characteristics for TE and TM waves, which is important for the development of new multifunction devices in the terahertz range..

The purpose of the work is to develop an analytical theory of Floquet-Bloch waves for gyrotropic magnetophotonic crystals with a transverse magnetic field.

Materials and methods. Magnetophotonic crystals consist of gyrotropic (gyroelectric or gyromagnetic materials) two-layer structures over a period, the parameters of which vary from the magnitude of the applied magnetic field. Analytical methods for solving the Hill equation through fundamental solutions of the third boundary value problem.

Results. The fundamental solutions of the Hill equation are determined in an analytical form. Analytical expressions for the dispersion characteristics of TE and TM Floquet-Bloch waves are found. The existence of bulk and surface waves in the transmission zones of a magnetophotonic crystal is established. The existence of an extraordinary surface wave with an atypical field distribution in the crystal layers for positive effective electric or magnetic permeability is shown.

Conclusions. The proposed new approach for determining the solutions of the Hill equation based on the fundamental solutions of the third boundary-value problem made it possible to obtain in an analytical form the dispersion characteristics and fields of controlled gyromagnetic magnetophotonic crystals for TE and TM Floquet-Bloch waves. This will make it relatively easy to calculate various devices based on controlled Bragg structures.

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Author Biographies

А. А. Shmat’ko, V. N. Karazin Kharkiv National University

4, Svobody Square, Kharkiv, 61022, Ukraine

V. N. Mizernik, Scientific Physical-Technologic Center of MES and NAS of Ukraine

2, Svobody Square, Kharkiv, 61022

Е. N. Odarenko, Kharkiv National University of Radio Electronics

pr. Nauki, 14, Kharkiv, Ukraine

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