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Scattering at Interluminal Interfaces

Scattering at interluminal modulation interfaces, where a sharp space-time perturbation moves at a velocity lying between the wave velocities of the two surrounding media, has remained an open problem for decades. This regime is somewhat reminiscent of the Cherenkov regime, in which the velocity of a charged particle exceeds the phase velocity of light in a medium. However, because it involves two media and a moving interface, it gives rise to richer and more complex scattering dynamics, with a single scattered wave when the incident wave propagates in the same direction as the interface and three scattered waves when they propagate in opposite directions. Existing studies address only limited non-magnetic configurations, and a general formulation has yet to be established. In this paper, we present a complete and general solution to scattering in the interluminal regime using a symmetric decomposition approach based on subluminal and superluminal limit interfaces, together with a space-time impulse response. This approach provides clear physical insight into the scattering features of the interluminal regime. Our results bridge the long-standing gap between the subluminal and superluminal regimes and elucidate the fundamental mechanisms underlying interluminal scattering.