Electromagnetic mediums with a double light cone structure
Seminar Room 2, Newton Institute Gatehouse
If we are given an electromagnetic medium we can compute the speed of a propagating signal. For example, in homogeneous medium we can compute the phase velocity of a planewave. A more challenging problem is to understand the converse problem: If we know the behaviour of signal speed in all possible directions, what can we say about the medium?
The problem has a natural formulation on a 4-manifold representing spacetime. Then the Fresnel surface describes propagation speed in an electromagnetic medium. For example, in an isotropic medium the Fresnel surface is a Lorentz light cone. Conversely, A. Favaro and L. Bergamin have proven that isotropic medium is the only medium with this property (within a suitable class of linear mediums). The purpose of this talk is to describe the analogous problem when the Fresnel surface is the union of two Lorentz light cones. Uniaxial crystals like calcite is one example. In addition, we find two other medium classes with the same property.