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
Full-text PDF Free Access
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.
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B. D. H. Tellegen, The gyrator, a new electric network element, Philips Res. Rep., 3, 81–101 (1948)
LL. G. Chambers, Propagation in a gyrational medium, Quart J. Mech. Appl. Math. 9, 360–370 (1956)
B. S. Gourary, Dispersion relations for tensor media and their application to ferrites, J. Appl. Phys. 28, 283–288 (1957)
D. Polder, On the theory of ferromagnetic resonance, Phil. Mag. 40, 99–115 (1949)
E. Astrom, On waves in an ionized gas, Arkiv Fysik 2, 443–157 (1951)
C. O. Hines, Wave packets, the Poynting vector and energy flow, J. Geophysics Res. 56, 63, 107, 207, 535 (1951)
T. H. Stix, The theory of plasma waves, McGraw-Hill, New York, 1962, pp. 45–52
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D. A. Watkins, Topics in electromagnetic theory, Wiley, New York, 1958, pp. 12–14
E. H. Wagner, Uber Gruppengeschwindigkeit, Energiestromdichte und Energiedichte in der Rontgenbezw Lichtoptik der Kristalle, Zeit. fur Physik 154, 352–360 (1959)
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)
C. G. Montgomery, R. H. Dicke and E. M. Purcell, Principles of microwave circuits, McGraw-Hill, New York, 1948, pp. 151–152
J. S. Toll, Causality and the dispersion relation: logical foundations, Phys. Rev. 104, 1760–1770 (1956)
J. A. Stratton, Electromagnetic theory, McGraw-Hill, New York, 1941, p. 137
L. Brillouin, Wave propagation and group velocity, Academic Press, New York, 1960, pp. 88–93
A. Tonning, Energy density in continuous electromagnetic media, IRE Trans, on Antennas and Propagation, AP-8, 428–434 (1960)
M. Leontovitch, Generalization of the Kramers-Kronig formulas to media with spatial dispersion, Soviet Physics-JETP 13, 634–637 (1961)
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Article copyright:
© Copyright 1968
American Mathematical Society
