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We study Maxwell's equations on a 4-manifold where the electromagnetic mediumis modelled by an antisymmetric (2, 2)-tensor kappa with real coefficients. Inthis setting the Fresnel surface is a fourth order polynomial surface in eachcotangent space that acts as a generalisation of the light cone determined by aLorentz metric; the Fresnel surface parameterises electromagnetic wave-speedsas a function of direction. The contribution of this paper is the completepointwise description of all electromagnetic medium tensors that satisfy thefollowing conditions:  (i) kappa is invertible,  (ii) kappa is skewon-free,  (iii) kappa is birefringent, that is, the Fresnel surface of kappa is theunion 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.

Non-dissipative electromagnetic medium with a double light cone