Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T07:18:28.224Z Has data issue: false hasContentIssue false
  • English
  • Français

The velocity of a wave packet in an anisotropic absorbing medium

Published online by Cambridge University Press:  13 March 2009

Kurt Suchy†
Kurt Suchy†
Affiliation:
Groupe de Recherches Ionosphériques du Centre National de la Recherche Scientifique 4 avenue do Neptune, 94 Saint-Maur, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The field of a pulsed beam (a ‘wave packet’), travelling through a medium with moderate absorption, is calculated by the saddle-point method. The packet velocity (i.e. the velocity of the spatial amplitude maximum) has the same direction as the velocity Re (∂ω/∂k), a generalization of the group velocity ∂ω/∂k in non-absorbing media. It differs from the absolute value of this velocity by a correction factor depending on the absorption, beam width and pulse duration. This factor is unity for vanishing absorption and infinite beam width. The velocity Im (∂ω/∂k) has no apparent physical meaning.

Type
Research Article
Information
Journal of Plasma Physics , Volume 8 , Issue 1 , August 1972 , pp. 33 - 51
Copyright
Copyright © Cambridge University Press 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Allis, W. P., Buchsbaum, S. J. & Bers, A. 1963 Waves in Anisotropic Plasmas. M.I.T. PressGoogle Scholar
Altman, C. 1971 Reciprocity relations for electromagnetic wave propagation through birefringent stratified media. Int. Symp. Electromag. Wave Theory, Tbilisi.Google Scholar
Argence, E., Rawer, K. & Suochy, K. 1955 Les théorèmes d'équivalence de l'absorption ionosphérique. C.R. Acad. Sci. (Paris) 241, 505.Google Scholar
Baerwald, H. G. 1930 Über die Fortpflanzung von Signalen in dispergierenden Systemen. 2. Verlustarmo kontinuierliche Systeme. Ann. Phys. (Leipzig) 7, 731.CrossRefGoogle Scholar
Barsukow, K. A. & Ginzburg, V. L. 1964 The direction of the ray and the group velocity in an absorbing anisotropic medium. Izvestiya vysshikh uchebnykh zavedenii. Radio. fizika, 7, 1187. (In Russian.)Google Scholar
Bertoni, H., Felsen, L. B. & Hessel, A. 1971 Local properties of radiation in lossy media. IEEE Trans. Antennas and Propagation AP-19, 226.CrossRefGoogle Scholar
Brillouin, L. 1914 Über die Fortpflanzung des Lichtes in dispergierenden Medien. Ann. Phys. (Leipzig) 44, 203. (Also 1960 Wave Propagation and Group Velocity, ch. 3, pp. 43–83. Academic.)Google Scholar
Budden, K. G. 1963 Lectures on magneto-ionic theory. Geophysics. The Earth's Environment (ed. De Witt, C., Hieblot, J. and Lebeau, A.), pp. 61–139. Gordon and Breach.Google Scholar
Budden, K. G. & Jull, G. W. 1964 Reciprocity and nonreciprocity with magnetoionic rays. Canad. J. Phys. 42, 113.CrossRefGoogle Scholar
Budden, K. G. & Terry, P. D. 1971 Radio ray tracing in complex space. Proc. Roy. Soc. A 321, 275.Google Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, vol. 2. Interscience.Google Scholar
Crisp, M. D. & Hilbert, D. 1971 Concept of group velocity in resonant pulse propagation. Phys. Rev. A 4, 2104.CrossRefGoogle Scholar
Crisp, M. D. 1972 Propagation of step-function light-pulses in a resonant medium. Phys. Rev. A 5, 1365.CrossRefGoogle Scholar
Gershman, B. N. & Ginzburg, V. L. 1962 Electromagnetic wave propagation in an anisotropic dispersive medium. Izvestiya vysshikh uchebnykh zavedenii. Radiofizika, 5, 31.Google Scholar
(Also 1964 The propagation of Electromagnetic waves in plasmas, pp. 461–476. Pergamon.)Google Scholar
Ginzburg, V. L. 1962 The law of conservation of energy in the electrodynamics of media with spatial dispersion. Izvestiya vysshikh uchebnykh zavedenii. Radiofizika, 5, 573.Google Scholar
(Also 1964 The propagation of Electromagnetic waves in plasmas, pp. 496–500. Pergamon.)Google Scholar
Grad, H. 1949 On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2, 331.CrossRefGoogle Scholar
Hines, C. O. 1951 Wave packets, the Poynting vector and energy flow. J. Geophys. Res. 56, 63; 197; 207; 535.CrossRefGoogle Scholar
Johnston, T. W. 1970 Anisotropic plasma pressure and the dielectric tensor. J. Plasma Phys. 4, 283.CrossRefGoogle Scholar
Jones, D. S. 1966 Generalised Functions. McGraw-Hill.Google Scholar
Jones, R. M. 1970 Ray theory for lossy media. Radio Sci. 5, 793.CrossRefGoogle Scholar
Marcus, M. 1960 Basic theorems in matrix theory. Nat. Bureau Standards, Appl. Math. Ser. 57.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, vol. 1. McGraw-Hill.Google Scholar
Rawer, K. & Suchy, K. 1967 Radio Observations of the Ionosphere. Handbuch der Physik (ed. Flügge, S.), vol. 49 (2), pp. 1–546. Springer.Google Scholar
Roehner, B. 1971 Détermination explicite do la direction do phase stationnaire lors do la transmission d'uno onde électromagnétique d'un milieu isotrope absorbant à un autre. Ann. Géophysique. (To be published.)Google Scholar
Smirnow, W. L. 1960 Lehrgang der höheren Mathematik, vol. 1 (3). Berlin: Doutsoher Verlag der Wissensehaften.Google Scholar
Smith, R. L. 1970 The velocities of light. Am. J. Phys. 38, 978.CrossRefGoogle Scholar
Storey, O. & Roehner, B. 1970 La direction do phase stationnairo dans un milieu absorbant. C.R. Acad. Sci. (Paris) B 270, 301.Google Scholar
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.Google Scholar
Suchy, K. 1972 Ray tracing in an anisotropic absorbing medium. J. Plasma Phys. 8, 53.CrossRefGoogle Scholar