scholarly journals Propagation of wave-packets incident obliquely upon a stratified doubly refracting ionosphere

1938 ◽  
Vol 237 (781) ◽  
pp. 411-451 ◽  
Keyword(s):  
Electromagnetic Waves ◽  
Wave Packets ◽  
Wave Length ◽  
Oblique Propagation ◽  
Vertical Propagation ◽  
General Investigation

Little attempt has so far been made to apply Appleton’s magneto-ionic theory to wireless waves incident obliquely upon the ionosphere. Actually the magneto-ionic theory in the form given by Appleton (1925,1932) and others (Nichols and Schelleng 1925; Breit 1927; Goldstein 1928) is only suitable for investigating vertical propagation in the ionosphere, and it is the object of this communication to develop a generalization of Appleton’s magneto-ionic theory capable of dealing conveniently with waves incident obliquely upon the ionosphere. A general investigation into oblique propagation of electromagnetic waves through a slowly varying doubly refracting medium has already been made (Booker 1936), and the ideas there developed will now be applied to propagation through the ionosphere of wireless waves of wave-length sufficiently short (less than a kilometre, say) to regard the medium as slowly varying.

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.

scholarly journals Whistler intensities above thunderstorms

2010 ◽  
Vol 28 (1) ◽  
pp. 37-46 ◽  
Author(s):  
J. Fiser ◽  
J. Chum ◽  
G. Diendorfer ◽  
M. Parrot ◽  
O. Santolik
Keyword(s):  
Background Noise ◽  
Electromagnetic Waves ◽  
Horizontal Distance ◽  
Average Amplitude ◽  
Oblique Propagation ◽  
Lightning Current ◽  
Processing Data ◽  
Demeter Satellite ◽  
Late Evening ◽  
The Mean

Abstract. We report a study of penetration of the VLF electromagnetic waves induced by lightning to the ionosphere. We compare the fractional hop whistlers recorded by the ICE experiment onboard the DEMETER satellite with lightning detected by the EUCLID detection network. To identify the fractional hop whistlers, we have developed software for automatic detection of the fractional-hop whistlers in the VLF spectrograms. This software provides the detection times of the fractional hop whistlers and the average amplitudes of these whistlers. Matching the lightning and whistler data, we find the pairs of causative lightning and corresponding whistler. Processing data from ~200 DEMETER passes over the European region we obtain a map of mean amplitudes of whistler electric field as a function of latitudinal and longitudinal difference between the location of the causative lightning and satellite magnetic footprint. We find that mean whistler amplitude monotonically decreases with horizontal distance up to ~1000 km from the lightning source. At larger distances, the mean whistler amplitude usually merges into the background noise and the whistlers become undetectable. The maximum of whistler intensities is shifted from the satellite magnetic footprint ~1° owing to the oblique propagation. The average amplitude of whistlers increases with the lightning current. At nighttime (late evening), the average amplitude of whistlers is about three times higher than during the daytime (late morning) for the same lightning current.

Determination of the velocity of short electromagnetic waves by interferometry

1952 ◽  
Vol 213 (1112) ◽  
pp. 123-141 ◽  
Keyword(s):  
Phase Velocity ◽  
Electromagnetic Radiation ◽  
Free Space ◽  
Electromagnetic Waves ◽  
Wave Beam ◽  
Wave Length ◽  
Wave Frequency ◽  
Space Wave

A new measurement of the velocity of electromagnetic radiation is described. The result has been obtained, using micro-waves at a frequency of 24005 Mc/s ( λ = 1∙25 cm), with a form of interferometer which enables the free-space wave-length to be evaluated. Since the micro-wave frequency can also be ascertained, phase velocity is calculated from the product of frequency and wave-length. The most important aspect of the experiment is the application to the measured wave-length of a correction which arises from diffraction of the micro-wave beam. This correction is new to interferometry and is discussed in detail. The result obtained for the velocity, reduced to vacuum conditions, is c 0 = 299792∙6 ± 0∙7 km/s.

scholarly journals On electric phenomena in gravitational fields

1927 ◽  
Vol 116 (775) ◽  
pp. 720-735 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Wave Length ◽  
Gravitational Effect ◽  
Electromagnetic Theory ◽  
Relativity Theory ◽  
Elementary Functions ◽  
Field Equations ◽  
Gravitational Fields ◽  
Particular Solutions

It is a consequence of general relativity that all electromagnetic and optical phenomena are influenced by a gravitational field. Indeed, the first prediction of relativity-theory, namely, the bending of light-rays when they pass near a massive body such as the sun, was a p articular application of this principle. Evidently, therefore, the classical electromagnetic theory must be rewritten in order to take account of the interaction between electromagnetism and gravitation; but beyond laying down general principles, comparatively little progress has been made hitherto in this task, the mathematical difficulties of solving definite electrical problems in a gravitational field being somewhat formidable. The subject is, however, of some interest to atomic physics; for if we assume that the atom has a massive nucleus with electrons in its immediate neighbourhood, the behaviour of such electrons (especially with regard to radiation) will be affected by the gravitational field of the nucleus. In the present paper two kinds of gravitational field are considered, namely, the field due to a single attracting centre ( i, e ., the field whose metric was discovered by Schwarzschild) and a limiting form of it. Within these gravita­tional fields we suppose electromagnetic fields to exist. Strictly speaking, the electromagnetic field has itself a gravitational effect, i.e. , it changes the metric everywhere; but this effect is in general; small, and we shall treat the ideal case in which it is ignored, so we shall suppose the metric to be simply that of the gravitational field originally postulated. The general equations of the electro­magnetic field are obtained, and particular solutions are found, which are the analogues of well-known particular solutions in the classical electromagnetic theory; notably the fields due to electrons at rest, electrostatic fields in general, and spherical electromagnetic waves. The results of the investigation are for the most part expressible only in terms of Bessel functions and certain new functions which are introduced; but in some interesting cases the electro­magnetic phenomena can be represented in term s of elementary functions, as, for instance, the electric field due to an electron in a quasi-uniform gravitational field (equations (15) and (19) below) and the spherical electromagnetic waves of short wave-length about a gravitating centre (equation (43) below).

The velocity of propagation of electromagnetic waves derived from the resonant frequencies of a cylindrical cavity resonator

1950 ◽  
Vol 204 (1077) ◽  
pp. 260-277 ◽  
Keyword(s):  
Electromagnetic Waves ◽  
Correction Term ◽  
Wave Length ◽  
Cavity Resonator ◽  
End Effects ◽  
Steel Cylinder ◽  
A Value ◽  
Half Wave ◽  
Velocity Of Propagation ◽  
Cylindrical Cavity Resonator

The cavity resonator used in this investigation is a silver-plated steel cylinder 6.5 cm. in diameter and of adjustable length. Resonance in the H 011 mode is established at a frequency in the region of 9000 Mc./sec., and the length is then varied to give successive resonances at half wave-length intervals. The wave-length is thus determined and this, together with the frequency, the diameter and a correction term involving the sharpness of resonance, enables the velocity to be calculated. This procedure has some advantage over that used previously by Essen & Gordon-Smith in which the measurements were made with a resonator of fixed dimensions. The wave-length is determined only from differences in length, the first resonant length not being used, and in this way certain end-effects, such as those due to the coupling loops and to surface imperfections, are eliminated or greatly reduced. Moreover, by using different frequencies, or different modes at the same frequency, the diameter can be eliminated from the calculations and a value of c thus obtained in terms of frequency and length both of which can be measured with high precision. The result obtained is 299,792.5 ± 3 km./sec., and is thus in close agreement with that obtained by Essen & Gordon-Smith with a fixed cavity and also with the value of c determined recently by Bergstrand with an optical method.

Identities between reflexion and transmission coefficients and electric field components for certain anisotropic modes of oblique propagation

1971 ◽  
Vol 6 (2) ◽  
pp. 257-270 ◽  
Author(s):  
J. Heading
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Differential Equations ◽  
Electric Field ◽  
Electromagnetic Waves ◽  
Electric Polarization ◽  
Stratified Medium ◽  
Transmission Coefficients ◽  
Oblique Propagation ◽  
Integral Identities

A wide-ranging investigation is rendered possible by a judicious combination of products of electric field components and electric polarization components for two distinct modes of propagation of electromagnetic waves in an anisotropic, ionized, stratified medium. The differential equations, governing oblique propagation in these two distinct modes in such a medium, are combined to yield various integral identities when integrated throughout the medium. These lead to a large number of relations between the reflexion and transmission coefficients (for incidence from below and from above) and the fields throughout the medium, each containing as a factor just one of the components of the external magnetic field pervading the medium.

Homogenization of 3D metamaterial particle arrays for oblique propagation via a point-dipole analysis

2020 ◽  
Vol 91 (2) ◽  
pp. 20902
Author(s):  
Theodosios Karamanos ◽  
Theodoros Zygiridis ◽  
Nikolaos Kantartzis
Keyword(s):  
First Principles ◽  
Electromagnetic Waves ◽  
Three Dimensional ◽  
Point Dipole ◽  
Effective Parameters ◽  
Realistic Case ◽  
Oblique Propagation ◽  
Dipole Analysis ◽  
Anisotropic Metamaterial

A rigorous technique for the consistent calculation of the effective parameters of infinite three-dimensional metamaterial particle arrays in the realistic case of oblique wave propagation, is presented in this paper. The extracted polarizabilities of the consisting scatterer and the numerically retrieved wavenumber for the obliquely propagating electromagnetic waves are systematically inserted into a properly modified first-principles homogenization technique, thus leading to the characterization of the effective medium. Finally, the proposed methodology is applied to two popular, anisotropic metamaterial resonators.

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