Non-dissipative electromagnetic medium with a double light cone

Abstract

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is modelled by an antisymmetric (2, 2)-tensor kappa with real coefficients. In this setting the Fresnel surface is a fourth order polynomial surface in each cotangent space that acts as a generalisation of the light cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speeds as a function of direction. The contribution of this paper is the complete pointwise description of all electromagnetic medium tensors that satisfy the following conditions: (i) kappa is invertible, (ii) kappa is skewon-free, (iii) kappa is birefringent, that is, the Fresnel surface of kappa is the union of two distinct light cones. We show that there are only three classes of mediums with these properties. Moreover, we give explicit expressions in local coordinates for each class.

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• First principles approach to the Abraham-Minkowski controversy for the momentum of light in general linear non-dispersive media
• The Kummer tensor density in electrodynamics and in gravity
• On skewon modification of light cone structure
• Non-minimal Einstein-Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor
• The Inverse Problem of Quartic Photonics
• Characterisation and representation of non-dissipative electromagnetic medium with a double light cone
• Photon propagator in skewon electrodynamics
• Contact topology and electromagnetism: The Weinstein conjecture and Beltrami-Maxwell fields