# Scattering at Interluminal Interface

## TL;DR

This paper develops exact scattering solutions for interluminal spacetime interfaces, filling a theoretical gap in understanding wave interactions when interface velocity is between wave velocities in the media.

## Contribution

It provides the first complete theoretical analysis of interluminal interfaces, including solutions valid across subluminal, interluminal, and superluminal regimes.

## Key findings

- Exact scattering solutions for interluminal interfaces
- Verification of solutions with transmission matrix approach
- Continuity of solutions at subluminal and superluminal limits

## Abstract

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.