Spherical axially symmetric electromagnetic waves in isotropic medium

2003 ◽  
Author(s):  
M.V. Pavlova ◽  
Y.A. Zyuryukin
Keyword(s):  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Axially Symmetric

scholarly journals Oblique propagation of electromagnetic waves in a slowly-varying non-isotropic medium

1936 ◽  
Vol 155 (885) ◽  
pp. 235-257 ◽  
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Electron Density ◽  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Mathematical Theory ◽  
Stratified Medium ◽  
Oblique Propagation ◽  
Isotropic Media ◽  
Mathematical Justification

The influence of the earth’s magnetic field on the propagation of wireless waves in the ionosphere has stimulated interest in the problem of the propagation of electromagnetic waves through a non-isotropic medium which is stratified in planes. Although the differential equations of such a medium have been elegantly deduced by Hartree,f it appears that no solution of them has yet been published for a medium which is both non-isotropic and non-homogeneous. Thus the work of Gans and Hartree dealt only with a stratified isotropic medium, while in the mathematical theory of crystal-optics the non-isotropic medium is always assumed to be homogeneous. In the same way Appleton’s magneto-ionic theory of propagation in an ionized medium under the influence of a magnetic field is confined to consideration of the “ characteristic ”waves which can be propagated through a homogeneous medium without change of form. In applying to stratified non-isotropic media these investigations concerning homogeneous non-isotropic media difficulty arises from the fact that the polarizations of the characteristic waves in general vary with the constitution of the medium, and it is not at all obvious that there exist waves which are propagated independently through the stratified medium and which are approximately characteristic at each stratum. The existence of such waves has usually been taken for granted, although for the ionosphere doubt has been cast upon this assumption by Appleton and Naismith, who suggest that we might “ expect the components ( i. e ., characteristic waves) to be continually splitting and resplitting”, even if the increase of electron density “ takes place slowly with increase of height”. It is clear that, until the existence of independently propagated approximately characteristic waves has been established, at any rate for a slowly-varying non-isotropic medium, no mathematical justification exists for applying Appleton's magnetoionic theory to the ionosphere. It is with the provision of this justification that we are primarily concerned in the present paper. This problem has been previously considered by Försterling and Lassen,f but we feel that their work does not carry conviction because they did not base their calculations on the differential equations for a non-homo-geneous medium, and were apparently unable to deal with the general case in which the characteristic polarizations vary with the constitution of the medium.

WAVE PROPAGATION IN A CYLINDRICAL WAVE GUIDE CONTAINING INHOMOGENEOUS PLASMA INVOLVING A TURNING POINT

1963 ◽  
Vol 41 (1) ◽  
pp. 113-131 ◽  
Author(s):  
S. N. Samaddar
Keyword(s):  
Electric Fields ◽  
Electromagnetic Waves ◽  
Turning Point ◽  
Boundary Effect ◽  
Inhomogeneous Plasma ◽  
Simple Zero ◽  
Wave Guide ◽  
Wave Number ◽  
Axially Symmetric ◽  
Radial Wave

Propagation of axially symmetric E-type and H-type modes of electromagnetic waves in a radially inhomogeneous plasma inside a wave guide is considered. For E-type modes conditions for the propagation of slow surface waves along the plasma–dielectric interface have been obtained. Approximate expressions for fields for wavelengths much smaller than the ratio of the gradient of the permittivity to the permittivity of the plasma are also given.It is also shown that if the dielectric constant ε(r) of the plasma vanishes along a particular surface r = r0, the electromagnetic fields for E-type modes behave singularly along this surface. In particular, if ε(r) has a simple zero at r0 ≠ 0, the radial and the longitudinal electric fields become singular as 1/ε(r0) and log ε(r0) respectively at r0. On the other hand, if ε(r) has a multiple zero at r0, the singularities of the above-mentioned fields will be as strong as a multiple pole at r0.Turning-point phenomena are also observed when the radial wave number [Formula: see text] vanishes along a surface. It is shown that the fields are oscillatory in the region [Formula: see text] and evanescent in the region [Formula: see text] for both E-type and H-type modes. The treatment of the singular behavior of the fields at ε(r) = 0, and of the turning-point phenomena at [Formula: see text], does not consider any boundary effect; therefore the results obtained here will be valid also for an inhomogeneous plasma column in free space.

scholarly journals Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves

2012 ◽  
Vol 111 (5) ◽  
pp. 053105 ◽  
Author(s):  
Yaroslav Urzhumov ◽  
Nathan Landy ◽  
David R. Smith
Keyword(s):  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Three Dimensional

scholarly journals The quantum theory of dispersion in metallic conductors

1929 ◽  
Vol 124 (794) ◽  
pp. 409-422 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Classical Electrodynamics ◽  
Metallic Conductivity

1. Formulation of the problem. - The propagation of electromagnetic waves in a homogeneous isotropic medium showing metallic conductivity has been treated phenomenologically on the basis of classical electrodynamics. If in Maxwell's equations for the electromagnetic field curl E = - 1/ c ∂B/∂ t , curl H = 1/ c (∂D/∂ t + 4πI), div D = 4πρ, div B = 0, we assume that D = εE, B = μH, I = σE, (1) where e is the dielectric constant, u the permeability and q the electrical conductivity, we get curl E = - μ/c ∂H/∂ t , curl H = 1/ c (ε ∂E/∂ t 4πσE), div E = 4πρ/ε. div H =0.

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