Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Yury Kravtsov ◽  
Bohdan Bieg
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Waves ◽  
Normal Modes ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Stokes Vector ◽  
Coupled Equations ◽  
Isotropic Approximation ◽  
Total Phase ◽  
Electromagnetic Beams

AbstractThe main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized.

scholarly journals Electromagnetic wave polarization state evolution in weakly anisotropic and nonuniform media with dissipation

2017 ◽  
Vol 9 (3) ◽  
pp. 94
Author(s):  
Bohdan Bieg ◽  
Janusz Chrzanowski
Keyword(s):  
Polarization State ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Plasma Phys ◽  
Magnetized Plasma ◽  
Tokamak Plasma ◽  
Dielectric Tensor ◽  
Stokes Vector ◽  
Poloidal Magnetic Field ◽  
Isotropic Approximation

The change of the polarization state of electromagnetic beam propagating in weakly anisotropic and smoothly inhomogeneous media with dissipation is analysed. On the basis of a quasi-isotropic approximation, which provides the consequent asymptotic solution of Maxwell's equation, the differential equation for the evolution of four component Stokes vector is derived. Obtained equation generalizes previous results for the nonadsorbing media and is written in terms of the dielectric tensor of birefringent media with dissipation. The formalism is illustrated by an example of magnetised plasma with dissipation due to the electron collisions. Full Text: PDF ReferencesK.G.Budden, Radio Waves in the Ionosphere (Cambridge U. Press 1961).V.I.Ginzburg, Propagation of Electromagnetic Waves in Plasma (Gordon & Breach 1970).Yu.A.Kravtsov, ""Quasiisotropic" Approximation to Geometrical Optics", Sov. Phys. Dokl. 13, 1125 (1969).A.A. Fuki, Yu.A. Kravtsov, and O.N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Lond., N.Y. 1997).Yu.A. Kravtsov and Yu.I. Orlov, Geometrical optics of inhomogeneous media (Springer Verlag, Berlin, Heidelberg 1990). CrossRef Yu.A. Kravtsov et al., "Waves in weakly anisotropic 3D inhomogeneous media: quasi-isotropic approximation of geometrical optics", Physics-Uspekhi 39, 129(1996). CrossRef F.De Marco, S.E.Segre, "The polarization of an e.m. wave propagating in a plasma with magnetic shear. The measurement of poloidal magnetic field in a Tokamak", Plasma Phys. 14, 245 (1972). DirectLink S.E.Segre, "A review of plasma polarimetry - theory and methods", Plasma Phys. Control. Fusion 41, R57 (1999). CrossRef M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford 1980). CrossRef B.Bieg et al., "Quasi-Isotropic Approximation of Geometrical Optics Method as Adequate Electrodynamical Basis for Tokamak Plasma Polarimetry", Physics Procedia 62, 102 (2015). CrossRef B.Bieg et al., "Two approaches to plasma polarimetry: Angular variables technique and Stokes vector formalism", Nucl. Instr. Meth. Phys. Res. Sect. A 720, 157 (2013). CrossRef S.E.Segre, "New formalism for the analysis of polarization evolution for radiation in a weakly nonuniform, fully anisotropic medium: a magnetized plasma", J. Opt. Soc. Am. A 18, 2601 (2001). CrossRef

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Normal modes of a waveguide as eigenvectors of a self-adjoint operator pencil

2021 ◽  
Vol 29 (1) ◽  
pp. 14-21
Author(s):  
Mikhail D. Malykh
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Wave Equations ◽  
Adjoint Operator ◽  
Normal Modes ◽  
Operator Pencil ◽  
Homogeneous Case ◽  
Permittivity And Permeability ◽  
Simply Connected ◽  
Magnetic Potentials

A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.

TWO-WAY COUPLED-MODE SOLUTIONS IN THE COMPLEX HORIZONTAL WAVENUMBER PLANE

2008 ◽  
Vol 16 (02) ◽  
pp. 225-256 ◽  
Author(s):  
STEVEN A. STOTTS
Keyword(s):  
Normal Modes ◽  
Lanczos Method ◽  
Numerical Implementation ◽  
Coupling Coefficients ◽  
Equation Solution ◽  
The Real ◽  
Coupled Equations ◽  
Coupled Mode ◽  
Layer Mode ◽  
Mode Solution

A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am.111 (2002) 1623–1643], referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am.96 (1994) 1741–1747]. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

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