Scattering and Chirping at Accelerated Interfaces

TL;DR

This paper derives exact solutions for electromagnetic wave scattering at arbitrarily accelerating interfaces, revealing complex effects like multiple scattering and frequency chirping, and demonstrates how to design interface trajectories for specific chirping profiles.

Contribution

It provides the first exact laboratory-frame solutions for arbitrarily accelerating interfaces and introduces methods to engineer desired frequency modulations through tailored acceleration.

Findings

Acceleration causes multiple velocity regimes and scattering events.

Generalized frequency chirping can be achieved via specific interface trajectories.

Framework enables advanced wave control in space-time media.

Abstract

Space-time varying media with moving interfaces unlock new ways to manipulate electromagnetic waves. Yet, analytical solutions have been mostly limited to interfaces moving at constant velocity or constant proper acceleration. Here, we present exact scattering solutions for an arbitrarily accelerating interface, derived directly in the laboratory frame through a suitable change of variables. We show that acceleration introduces rich effects that do not occur with uniform motion, including transitions between multiple velocity regimes, multiple scattering events and generalized frequency chirping. We also solve the inverse problem of designing an interface trajectory that produces a desired chirping profile, demonstrating how tailored acceleration can synthesize complex frequency modulations. These results provide a fundamental framework to understand and control wave interactions with accelerated boundaries, opening pathways for advanced applications in space-time signal processing and dynamic pulse shaping.