Scattering and Chirping at Accelerated Interfaces

TL;DR

The paper tackles electromagnetic scattering from arbitrarily accelerated interfaces in space-time varying media by developing exact analytical solutions directly in the laboratory frame using a suitable change of variables. It reveals that acceleration induces time-dependent Doppler shifts, producing frequency chirping, and it systematically derives scattering formulas for subluminal, interluminal, and superluminal regimes, including explicit boundary-condition-based expressions and Doppler relations. The authors also solve the inverse synthesis problem to design interface trajectories that realize prescribed chirp profiles, with explicit interface-motion equations and a chirp-admissibility constraint. Validation via full-wave FDTD demonstrates agreement with the theory for subluminal and interluminal cases, and the work discusses feasible experimental routes in microwave and optical platforms, highlighting applications in space-time signal processing and dynamic pulse shaping.

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.

Figures (4)

• Figure 1: Generalization of electromagnetic wave scattering from uniformly moving interfaces to accelerated interfaces, parametrized by a trajectory, $z{\left[t\right]}$, and normalized modulation velocity, $\beta{\left[t\right]} = \dd{z{\left[t\right]}}/\dd{(ct)}$. (a) Left: space-time diagram of an accelerated interface, whose time-varying positive velocity sweeps through all three velocity regimes---subluminal ($\left|\beta{\left[t\right]}\right| < 1/n_{2}$), interluminal ($1/n_{2} \leq \left|\beta{\left[t\right]}\right| \leq 1/n_{1}$) and superluminal ($\left|\beta{\left[t\right]}\right| > 1/n_{1}$), assuming $n_{1} < n_{2}$. Right: corresponding local constant-velocity reference cases for a forward-propagating wave in the first medium, each represented by the related space-time diagrams (left insets) and spectral transition diagrams (right insets). (b) Same as (a) but for a negative modulation velocity.
• Figure 2: Illustration examples for the analysis problem [Eqs. \ref{['eq:Analysis_Subluminal_Solutions', 'eq:Analysis_Superluminal_Solutions', 'eq:Analysis_Interluminal_Co_Solutions', 'eq:Analysis_Interluminal_Contra_Solutions']}] of electromagnetic scattering at arbitrary accelerated interfaces (Fig. \ref{['fig:Overview']}) in different velocity regimes, showing the space-time evolution, time-domain waveforms far from the interface and corresponding spectra. (a) Single interface with an S-shape trajectory. (b) Space-time cavity.
• Figure 3: Full-wave finite-difference time-domain (FDTD) validation of the analysis problem [Eqs. \ref{['eq:Analysis_Subluminal_Solutions', 'eq:Analysis_Superluminal_Solutions', 'eq:Analysis_Interluminal_Co_Solutions', 'eq:Analysis_Interluminal_Contra_Solutions']}], showing the space-time evolution, time-domain waveforms far from the interface and corresponding spectra. (a) Constant, proper-accelerated interface. (b) Backwards oscillating trajectory.
• Figure 4: Illustrative examples of the synthesis problem [Eqs. \ref{['eq:Synthesis_Full_Trajectory']}] illustrated through space-time diagrams, time-domain scattered waveforms far from the interface and corresponding spectrograms. (a) Linear chirp. (b) Oscillatory chirp.