Reflection and Transmission of Electromagnetic Waves by Stratified Moving Media

1971 ◽  
Vol 49 (22) ◽  
pp. 2785-2792 ◽  
Author(s):  
J. A. Kong
Keyword(s):  
Velocity Profile ◽  
Electromagnetic Waves ◽  
Stratified Medium ◽  
Moving Medium ◽  
Reflection And Transmission ◽  
Special Cases ◽  
Moving Media ◽  
Boundary Solutions ◽  
Nonuniformly Moving

The problem of reflection and transmission of electromagnetic waves by a stratified n-layer parallely moving medium has been solved. It includes the moving stratified medium and the nonuniformly moving medium with a stratified velocity profile as special cases. The results also reduce to all previous works with medium motion parallel to the boundary. Solutions are facilitated by the introduction of propagation matrices. Reflected and transmitted field intensities are calculated, and a detailed discussion on simple cases that have not been treated before is given to illustrate the general formalism.

The propagation of electromagnetic waves in a stratified medium

1929 ◽  
Vol 25 (1) ◽  
pp. 97-120 ◽  
Author(s):  
D. R. Hartree
Keyword(s):  
Refractive Index ◽  
Reflection Coefficient ◽  
Electromagnetic Waves ◽  
Stratified Medium ◽  
Simple Extension ◽  
Angle Of Incidence ◽  
First Approximation ◽  
Special Cases ◽  
Cartesian Coordinate ◽  
The Given

The equations of propagation of electromagnetic waves in a stratified medium (i.e. a medium in which the refractive index is a function of one Cartesian coordinate only—in practice the height) are obtained first from Maxwell's equations for a material medium, and secondly from the treatment of the refracted wave as the sum of the incident wave and the wavelets scattered by the particles of the medium. The equations for the propagation in the presence of an external magnetic field are also derived by a simple extension of the second method.The significance of a reflection coefficient for a layer of stratified medium is discussed and a general formula for the reflection coefficient is found in terms of any two independent solutions of the equations of propagation in a given stratified medium.Three special cases are worked out, for waves with the electric field in the plane of incidence, viz.(1) A finite, sharply bounded, medium which is “totally reflecting” at the given angle of incidence.(2) Two media of different refractive index with a transition layer in which μ2 varies linearly from the value in one to the value in the other.(3) A layer in which μ2 is a minimum at a certain height and increases linearly to 1 above and below, at the same rate.For cases (2) and (3) curves are drawn showing the variation of reflection coefficient with thickness of the stratified layer.Case (3) may be of some importance as a first approximation to the conditions in the Heaviside layer.

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.

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