Open AccessФотонные кристаллы на основе сред с произвольной анизотропией диэлектрической и магнитной проницаемостей
Author(s) -
Г.Ф. Глинский
Publication year - 2019
Publication title -
žurnal tehničeskoj fiziki
Language(s) - English
Resource type - Journals
eISSN - 1726-748X
pISSN - 0044-4642
DOI - 10.21883/jtf.2019.03.47163.273-18
Subject(s) - physics , eigenvalues and eigenvectors , angular momentum operator , photon polarization , angular momentum , photon , anisotropy , maxwell's equations , polarization (electrochemistry) , operator (biology) , hilbert space , quantum mechanics , classical mechanics , angular momentum coupling , total angular momentum quantum number , biochemistry , chemistry , repressor , transcription factor , gene
A general approach to analyzing eigenmodes in anisotropic and gyrotropic 3D photonic crystals based on dielectric and magnetic media is proposed. This approach is based on the representation of stationary macroscopic Maxwell equations in the operator form corresponding to the quantum-mechanical equation for a photon with spin s = 1. In these equations, the strengths of electric and magnetic fields are put into correspondence with state vectors in the complex Hilbert space. The permittivity and permeability serve as operators acting on these vectors. It is shown that the problem of determining the eigenmodes of a photonic crystal is reduced to searching for eigenvectors and eigenvalues of the Hermitian operator characterizing the spin–orbit interaction of a photon in the periodic anisotropic medium under study. It is proposed to use photon states with a certain wave vector (certain momentum) and a certain linear or circular spin polarization as a basis for the representation operator equations. One-dimensional photonic crystals are considered as an example. The influence of anisotropy and gyrotropy on the dispersion of eigenmodes in these crystals is investigated. The group velocity of the eigenmodes, momentum transferred by them, and spin angular momentum are analyzed for the case of gyrotropic media.