A semianalytical solution for the propagation of electromagnetic waves in 3‐D lossy orthotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1141-1148 ◽  
Author(s):  
José M. Carcione ◽  
Fabio Cavallini
Keyword(s):  
Magnetic Field ◽  
Plane Wave ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Computer Experiment ◽  
Transverse Magnetic ◽  
Wave Analysis ◽  
Helmholtz Equations ◽  
Magnetic Surfaces ◽  
Time Histories

We derive an analytical solution for electromagnetic waves propagating in a 3‐D lossy orthotropic medium for which the electric permittivity tensor is proportional to the magnetic permeability tensor. The solution is obtained through a change of coordinates that transforms the spatial differential operator into a pure Laplace operator and the differential equations for the electric and magnetic field components into pure Helmholtz equations. A plane‐wave analysis gives the expression of the slowness and attenuation surfaces as a function of frequency and propagation direction. The transverse electric and transverse magnetic surfaces degenerate to one repeated sheet so that, in any direction, the two differently polarized plane waves have the same slowness. A computer experiment with realistic geophysical parameters has shown that the anisotropic propagation and dissipation properties emerging from plane‐wave analysis agree with the different time histories of the magnetic field computed at a number of representative receiver locations.

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.

Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

2021 ◽  
Author(s):  
Leonid I. Goray
Keyword(s):  
Plane Wave ◽  
Wave Diffraction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Transverse Magnetic ◽  
Incident Field ◽  
Boundary Integral ◽  
Cylindrical Waves ◽  
Plane Wave Diffraction

Abstract The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

Propagation of electromagnetic waves in a warm plasma-filled cylindrical waveguide in the presence of an external magnetic field

1983 ◽  
Vol 29 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Sanjay Kumar Ghosh ◽  
S. P. Pal
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Electromagnetic Waves ◽  
Transverse Magnetic ◽  
Cylindrical Waveguide ◽  
Small Magnetic Field ◽  
Warm Plasma ◽  
Plasma Theory ◽  
The Waves ◽  
Constant External Magnetic Field

The propagation of electromagnetic waves in a plasma-filled cylindrical waveguide in the presence of a constant external magnetic field is investigated using warm plasma theory. It is found that the waves cannot be separated into transverse magnetic and transverse electric modes; only hybrid modes are propagated. Dispersion relations are derived for zero, finite and infinite magnetic fields. Frequency shifts for the wave propagation in the case of a small magnetic field are calculated.

The Acoustical Impedance at the Junction of Non-Coaxial Cylindrical Ducts

1992 ◽  
Vol 11 (4) ◽  
pp. 114-123 ◽  
Author(s):  
Keith S. Peat
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Plane Waves ◽  
Low Frequency ◽  
Evanescent Waves ◽  
Wave Analysis ◽  
Cross Sectional ◽  
Low Frequencies ◽  
Duct Systems

At low frequencies, only plane waves can continuously propagate along uniform ducts, but evanescent, non-planar waves arise from discontinuities in the duct cross-section. The effect of these evanescent waves can be considered as an acoustical impedance to the propagation of plane waves. It is then possible to increase the accuracy of low frequency plane-wave analysis of duct systems with cross-sectional discontinuities, by inclusion of these impedance corrections. This paper considers the derivation of the acoustical impedance at the junction of non-coaxial circular ducts, a common feature within silencer systems.

THE SCATTERING OF ELECTROMAGNETIC WAVES BY A CORRUGATED SHEET

1959 ◽  
Vol 37 (7) ◽  
pp. 787-797 ◽  
Author(s):  
T. B. A. Senior
Keyword(s):  
Plane Wave ◽  
Current Distribution ◽  
Scattered Field ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Physical Optics ◽  
Integral Expression ◽  
Conducting Sheet

The physical optics method is used to determine the scattering of a plane wave by a perfectly conducting sheet having sinusoidal corrugations. The only approximation concerns the current distribution on the sheet and the scattered field then appears as a spectrum of plane waves whose amplitudes are given by a simple integral expression.

THE MAGNETIC FIELD AT THE SURFACE OF A STRATIFIED FLAT CONDUCTOR IN THE FIELD OF PLANE WAVES WITH APPLICATION TO GEOPHYSICS

1962 ◽  
Vol 40 (11) ◽  
pp. 1583-1592 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Magnetic Field ◽  
Surface Layer ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Geomagnetic Variations ◽  
Wide Range ◽  
The Magnetic Field

The problem of plane electromagnetic waves incident on a stratified flat conductor is considered. Expressions for the amplitude and phase of the components of the resultant magnetic field at the surface of the conductor are obtained and evaluated for a wide range of frequencies, conductivities, surface layer depths, and angles of incidence. The frequencies f = 10−3 to 103 cycles/sec and the conductivities σ = 10−11 to 10−16 emu considered are of interest in studying geomagnetic variations.

BIREFRINGENCE IN CRYSTALS AND IN THE IONOSPHERE

1954 ◽  
Vol 32 (1) ◽  
pp. 16-34 ◽  
Author(s):  
C. H. M. Turner
Keyword(s):  
Magnetic Field ◽  
Dielectric Constant ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Diagonal Matrix ◽  
Effective Dielectric Constant ◽  
Normal Velocity ◽  
Electron Collisions ◽  
Velocity Of Propagation ◽  
The Magnetic Field

Propagation of plane electromagnetic waves in a homogeneous ionized gas in a uniform magnetic field is compared with the propagation of light in an optically inactive birefringent crystal. It is well known that propagation in a crystal may be described by using a system of real orthogonal axes for which the dielectric constant is given by a diagonal matrix. This paper shows that propagation of plane waves in the ionosphere may be described in a similar manner, the medium having an effective dielectric constant given by a diagonal matrix, provided that a system of "complex" orthogonal axes is used for the description of the components of the field vectors. This set of component axes (which is quite different from and not to be confused with coordinate axes) is equivalent to resolving the field vectors into components parallel to the magnetic field and two contrarotating circular components in a plane perpendicular to the magnetic field. An expression giving the velocity of each of the two modes of propagation in a given direction and expressions for the amplitude of each component of the field vectors are obtained (equations 43 and 44). Provided that one accepts the concept of a complex velocity of propagation, the results hold when electron collisions are included. When electron collisions are neglected, it is possible to form a double-sheeted surface, called the normal velocity surface, which is of some assistance in visualizing the manner in which the velocity of propagation of the plane waves in each mode changes with direction.

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