It has been known through some examples that parameters of an electromagnetic medium can be so dened 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 satised 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.
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. doi:10.1007/s10714-005-0155-3
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. doi:10.1103/PhysRevE.86.031703
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. doi:10.1109/TAP.2011.2167937
6. Dahl, M., "Characterization and representation of non-dissipative electromagnetic medium with two Lorentz null cones," J. Math. Phys., Vol. 54, 011501, 2013. doi:10.1063/1.4773832
7. Lämmerzahl, C. and F. W. Hehl, "Riemannian light cone from vanishing birefringence in premetric vacuum electrodynamics," Phys. Rev. D, Vol. 70, 105022, 2004. doi:10.1103/PhysRevD.70.105022
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. doi:10.1002/andp.201000140