SRX Physics

SRX Physics / 2010 / Article

Research Article | Open Access

Volume 2010 |Article ID 832487 |

Pierre Hillion, "Pseudo-TE/TM Waves in a Self-Dual Chiral Medium", SRX Physics, vol. 2010, Article ID 832487, 5 pages, 2010.

Pseudo-TE/TM Waves in a Self-Dual Chiral Medium

Received25 Sep 2009
Accepted20 Oct 2009
Published17 Nov 2009


Using successively the conventional Gibbs and the differential-form formulations of Maxwell's equations, we analyze the electromagnetic fields in a self-dual chiral material (invariance under the exchanges [(EH), (DB), (εμ)]. We prove that such a medium supports pseudo-TE/TM waves (only a component is null with two relations between four of the five other components). An interesting example is supplied by the Courant-Hilbert quasi-undistorted progressing waves: their form does not change along propagation; only their amplitude could change.


  1. I. V. Lindell, Differential Forms in Electromagnetics, John Wiley & Sons, Hoboken, NJ, USA, 2004.
  2. I. V. Lindell and L. H. Ruotanen, “Duality transformations and Green dyadics for bi-anisotropic media,” Journal of Electromagnetic Waves and Applications, vol. 12, no. 9, pp. 1131–1152, 1998. View at: Publisher Site | Google Scholar
  3. E. J. Post, Formal Structure of Electromagnetism, North Holland, Amsterdam, The Netherlands, 1962.
  4. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 2, Interscience, New York, NY, USA, 1962.
  5. P. Hillion, “Nondispersive solutions of the Klein-Gordon equation,” Journal of Mathematical Physics, vol. 33, no. 5, pp. 1817–1821, 1992. View at: Publisher Site | Google Scholar | MathSciNet
  6. P. Hillion, “Nondispersive solutions of the Dirac equation,” Journal of Mathematical Physics, vol. 33, no. 5, pp. 1822–1830, 1992. View at: Publisher Site | Google Scholar | MathSciNet
  7. A. P. Kiselev, “Modulated Gaussian beams,” Radiophysics and Quantum Electronics, vol. 26, no. 8, pp. 1014–1020, 1983. View at: Google Scholar
  8. A. Bossavit, “Differential forms and the computation of fields and forces in electromagnetism,” European Journal of Mechanics B, vol. 10, no. 5, pp. 474–481, 1991. View at: Google Scholar
  9. Z. Ren and A. Razek, “Computation of 3D-electromagnetic field using differential forms based on elements,” International Journal of Numerical Analysis and Modeling, vol. 9, pp. 81–98, 1996. View at: Google Scholar
  10. A. Stein, Y. Tong, M. Desbrun, and J. L. Marsden, “Geometric computational electrodynamics with variational integrators and discrete differential forms,” View at: Google Scholar
  11. W. A. Rodrigues, Jr. and J. Y. Lu, “On the existence of undistorted progressing waves of arbitrary speed 0v<,” Foundations of Physics, vol. 27, no. 3, pp. 435–508, 1997. View at: Google Scholar
  12. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Physical Review A, vol. 39, no. 4, pp. 2005–2033, 1989. View at: Google Scholar
  13. H. E. Moses and R. T. Prosser, “Acoustic and electromagnetic bullets,” SIAM Journal on Applied Mathematics, vol. 50, no. 5, pp. 1325–1340, 1990. View at: Publisher Site | Google Scholar | MathSciNet

Copyright © 2010 Pierre Hillion. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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