Scattering at Interluminal Interface

Interest for spacetime structures has recently been revived, following developments in metamaterials and ultrafast optics. Such structures essentially consist of successions of space-time interfaces for which the theory is still incomplete, in particular in the regime where the interface velocity lies between the wave velocities in the two media involved. This paper addresses this `interluminal' regime, providing exact scattering solutions for both approaching and receding interfaces. The solutions are verified to be consistent with the transmission matrix perspective and to be continuous at the limits of the subluminal and superluminal regimes.