Vol. 51

Latest Volume
All Volumes
All Issues

Electromagnetic Media with No Dispersion Equation

By Ismo Veikko Lindell and Alberto Favaro
Progress In Electromagnetics Research B, Vol. 51, 269-289, 2013


It has been known through some examples that parameters of an electromagnetic medium can be so de ned that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satis ed identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. In addition to the previously known examples, a novel class of Case 1 media with no dispersion equation is seen to emerge through the analysis making use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.


Ismo Veikko Lindell and Alberto Favaro, "Electromagnetic Media with No Dispersion Equation," Progress In Electromagnetics Research B, Vol. 51, 269-289, 2013.


    1. Kong, J. A., Electromagnetic Wave Theory, 353, EMW Publishing, Cambridge, MA, 2005.

    2. Hehl, F. W. and Y. Obukhov, Foundations of Classical Electrodynamics, Birkhäuser, Boston, 2004.

    3. Balakin, A. and W. Zimdahl, "Optical metrics and birefringence of anisotropic media," Gen. Relativ. Gravit., Vol. 37, No. 10, 1731-1751, 2005.

    4. Obukhov, Y., T. Ramos, and G. Rubilar, "Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field ," Phys. Rev. E, Vol. 86, 031703, 2012.

    5. Lindell, I. V., L. Bergamin, and A. Favaro, "Decomposable medium condition in four-dimensional representation," IEEE Trans. Antennas Propag., Vol. 60, No. 1, 367-376, 2012.

    6. Dahl, M., "Characterization and representation of non-dissipative electromagnetic medium with two Lorentz null cones," J. Math. Phys., Vol. 54, 011501, 2013.

    7. Lämmerzahl, C. and F. W. Hehl, "Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics," Phys. Rev. D, Vol. 70, 105022, 2004.

    8. Itin, Y., "Nonbirefringence conditions for spacetime," Phys. Rev. D, Vol. 72, 087502, 2005.

    9. Favaro, A. and L. Bergamin, "The non-birefringent limit of all linear skewonless media and its unique light-cone structure," Ann. Phys., Vol. 523, No. 5, 383-401, Berlin, 2011.

    10. Dahl, M., "Determination of an electromagnetic medium from the Fresnel surface ," J. Phys. A: Math. Theor., Vol. 45, 405203, 2012.

    11. Lindell, I. V., "The class of bi-anisotropic IB media," Progress In Electromagnetics Research, Vol. 57, 1-18, 2006.

    12. Lindell, I. V. and A. H. Sihvola, "Uniaxial IB-medium interface and novel boundary conditions," IEEE Trans. Antennas Propag., Vol. 57, No. 3, 694-700, Mar. 2009.

    13. Lindell, I. V., L. Bergamin, and A. Favaro, "The class of electromagnetic P-media and its generalization," Progress In Electromagnetics Research B, Vol. 28, 143-162, 2011.

    14. Favaro, A., Recent advances in electromagnetic theory, Ph.D. Thesis, Imperial College, London, 2012.

    15. Lindell, I. V., On electromagnetic fields in skewon-axion media, ICEAA' 12, 58-61, Cape Town, South Africa, Sep. 2012.

    16. Deschamps, G. A., Electromagnetics and differential forms, Proc. IEEE, Vol. 69, No. 6, 676-696, 1981.

    17. Lindell, I. V., Differential Forms in Electromagnetics, Wiley, New York, 2004.

    18. Post, E. J., Formal Structure of Electromagnetics, North-Holland Pub. Co., 1962, Reprinted: Dover, New York, 1997.

    19. Lindell, I. V., "Electromagnetic wave equation in differential-form representation," Progress In Electromagnetics Research, Vol. 54, 321-333, 2005.

    20. Obukhov, Y., T. Fukui, and G. Rubilar, "Wave propagation in linear electrodynamics," Phys. Rev. D, Vol. 62, 044050, 2000.

    21. Rubilar, G., "Linear pre-metric electrodynamics and deduction of the light cone," Ann. Phys., Vol. 11, No. 10-11, 717-782, Leipzig, 2002.

    22. Itin, Y., "On light propagation in premetric electrodynamics: The covariant dispersion relation," J. Phys. A, Vol. 42, 475402, 2009.

    23. Gibbs, J. W. and E. B. Wilson, Vector Analysis, Charles Scribner's Sons, 1909, Reprinted: Dover, New York, 1960.

    24. Lindell, I. V., Methods for Electromagnetic Field Analysis, 2nd Ed., IEEE Press, New York, 1995.

    25. Schuller, F., C. Witte, and M. Wohlfarth, "Causal structure and algebraic classification of non-dissipative linear optical media," Ann. Phys., Vol. 325, 1853-1883, NY, 2010.

    26. Dahl, M., "A restatement of the normal form theorem for area metrics," Int. J. Geometric Methods in Modern Phys., Vol. 9, No. 5, 1250046, 2012.

    27. Lindell, I. V., "Inverse for the skewon medium dyadic," Progress In Electromagnetics Research, Vol. 63, 21-32, 2006.