Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Dispersion relations, stored energy and group velocity for anisotropic electromagnetic media


Author: H. Kurss
Journal: Quart. Appl. Math. 26 (1968), 373-387
DOI: https://doi.org/10.1090/qam/99846
MathSciNet review: QAM99846
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Abstract | References | Additional Information

Abstract: The Hermitian and skew-Hermitian components of the susceptibility matrix of a general linear electromagnetic medium are represented as Hilbert transforms of each other. These so-called dispersion relations lead to a priori inequalities which must be satisfied by the susceptibility of a passive medium in a frequency interval in which the medium is lossless. One such inequality states that the stored energy density for a given $ E\left( \omega \right)$ and $ H\left( \omega \right)$ is always greater than in free space. This is also verified directly from the usual gyrotropic susceptibilities of ferrites and plasmas.


References [Enhancements On Off] (What's this?)

  • [1] L. D. Landau and E. M. Lifshitz, Electrodynamics of continuous media, Pergamon, New York, 1960, pp. 247-267
  • [2] L. Page and N. I. Adams, Electrodynamics, D. Van Nostrand, New York, 1940, p. 405
  • [3] B. D. H. Tellegen, The gyrator, a new electric network element, Philips Res. Rep., 3, 81-101 (1948)
  • [4] LL. G. Chambers, Propagation in a gyrational medium, Quart J. Mech. Appl. Math. 9, 360-370 (1956)
  • [5] B. S. Gourary, Dispersion relations for tensor media and their application to ferrites, J. Appl. Phys. 28, 283-288 (1957)
  • [6] D. Polder, On the theory of ferromagnetic resonance, Phil. Mag. 40, 99-115 (1949)
  • [7] Ernst Åström, On waves in an ionized gas, Ark. Fys. 2 (1951), 443–457. MR 0040995
  • [8] C. O. Hines, Wave packets, the Poynting vector and energy flow, J. Geophysics Res. 56, 63, 107, 207, 535 (1951)
  • [9] Thomas Howard Stix, The theory of plasma waves, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0153425
  • [10] W. P. Allis, S. J. Buchsbaum and A. Bers, Waves in anisotropic plasmas, M.I.T. Press, Cambridge, Mass., 1963, pp. 95-131
  • [11] F. E. Borgnis and C. H. Papas, Electromagnetic waveguides and resonators, Handbuch der Physik. Herausgegeben von S. Flügge. Bd. 16, Elektrische Felder und Wellen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958, pp. 285–422. MR 0106022
  • [12] D. A. Watkins, Topics in electromagnetic theory, Wiley, New York, 1958, pp. 12-14
  • [13] E. H. Wagner, Uber Gruppengeschwindigkeit, Energiestromdichte und Energiedichte in der Rontgenbezw Lichtoptik der Kristalle, Zeit. fur Physik 154, 352-360 (1959)
  • [14] H. L. Bertoni and A. Hessel, Group velocity and power flow relations for surface waves in plane-stratified anisotropic media, IEEE Trans, on Antennas and Propagation, AP-14, 344-352 (1966)
  • [15] C. G. Montgomery and R. H. Dicke (eds.), Principles of Microwave Circuits, McGraw-Hill Book Company, Inc., New York, N. Y., 1948. MR 0032476
  • [16] John S. Toll, Causality and the dispersion relation: logical foundations, Phys. Rev. (2) 104 (1956), 1760–1770. MR 0083623
  • [17] J. A. Stratton, Electromagnetic theory, McGraw-Hill, New York, 1941, p. 137
  • [18] Léon Brillouin, Wave propagation and group velocity, Pure and Applied Physics, Vol. 8, Academic Press, New York-London, 1960. MR 0108217
  • [19] A. Tonning, Energy density in continuous electromagnetic media, IRE Trans, on Antennas and Propagation, AP-8, 428-434 (1960)
  • [20] M. Leontovič, Generalization of the Kramers-Kronig formulas to media with spatial dispersion, Soviet Physics JETP 13 (1961), 634–637. MR 0129281


Additional Information

DOI: https://doi.org/10.1090/qam/99846
Article copyright: © Copyright 1968 American Mathematical Society


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