Light propagation through random hyperbolic media.

We analyze electromagnetic field propagation through a random medium that consists of hyperbolic metamaterial domains separated by regions of normal "elliptic" space. This situation may occur in a problem as common as 9 μm light propagation through a pile of sand, or as exotic as electromagnetic field behavior in the early universe immediately after the electroweak phase transition. We demonstrate that spatial field distributions in random hyperbolic and random "elliptic" media look strikingly different. Optical field is strongly enhanced at the boundaries of hyperbolic domains. This effect may potentially be used to evaluate the magnitude of magnetic fields which existed in the early universe.