Dispersion-Mediated Space-Time States

TL;DR

This work presents a dispersion-aware framework for space-time scattering at uniformly moving interfaces between dispersive media. By enforcing phase matching and two physical criteria—group-velocity restriction and media passivity—it identifies physically allowed frequency transitions, revealing dispersion-mediated space-time states that have no nondispersive analog. A Fourier-domain formulation yields complete solutions for both monochromatic waves and broadband pulses, demonstrated on Drude and Lorentz models, and enabling dispersion-engineered control of wave propagation. The results provide a rigorous foundation for realistic space-time metamaterials and have immediate relevance to epsilon-near-zero platforms, offering pathways to dispersion-engineer wave manipulation in optical regimes.

Abstract

Space-time varying media enable unprecedented control over electromagnetic waves, yet most existing studies assume idealized, nondispersive materials and thus fail to capture the intrinsic frequency dispersion of realistic platforms. Here, we develop a general framework for dispersive space-time varying systems that rigorously identifies the physically allowed frequency transitions of waves scattered at moving interfaces. Unlike previous approaches, our method is valid for arbitrary dispersion profiles, including resonances, and does not rely on the commonly used frame hopping approach, allowing treatment of multiple-velocity and accelerated systems. Applying this framework to canonical Drude and Lorentz media, we uncover a family of dispersion-mediated space-time states that arise from the multiple frequency transitions permitted by material dispersion. These states extend beyond conventional nondispersive scattering, revealing qualitatively new regimes of space-time scattering behavior. Beyond the frequency transitions, we derive the scattering coefficients for dispersive moving interfaces and provide a Fourier-domain formulation that yields a complete electromagnetic scattering solution for both monochromatic waves and broadband pulses. Our results establish a rigorous foundation for the design of realistic space-time metamaterials, with immediate relevance to emerging experiments in epsilon-near-zero optical platforms and open pathways for dispersion-engineered wave manipulation.

Figures (2)

• Figure 1: Dispersion-mediated space-time states for the lossless Drude model [Eq. \ref{['eq:Refractive_Index_Profile_Free_Electron_Plasma_Model']}] with $n_{\infty,1} = 1$, $\omega_{\text{p},1} = 5$, $n_{\infty,2} = 1.5$ and $\omega_{\text{p},2} = 10$, computed according to the conditions in Tab. \ref{['tab:Summary_Conditions_Frequency_Transitions']}. (a) Scattering regimes of the space-time states as a function of the modulation velocity, $v_{\text{m}}$, and the incident frequency, $\omega_{\text{i}}$. The dashed lines indicate the nondispersive velocity limits. (b) Space-index perspective for each space-time state with corresponding spectral transition diagrams, where some of the solutions of Eq. \ref{['eq:Frequency_Transitions_Example']} are crossed out since they do not satisfy the conditions in Tab \ref{['tab:Summary_Conditions_Frequency_Transitions']}.
• Figure 2: Dispersion-mediated space-time states for the lossless Lorentz dispersion model with parameters $n_{\infty,1} = 1, \omega_{\text{p},1}=4, \omega_{0,1} =3, n_{\infty,2} = 1.5, \omega_{\text{p},2} = 8$ and $\omega_{0,2} = 3$, computed according to the conditions in Tab. \ref{['tab:Summary_Conditions_Frequency_Transitions']}. The dashed lines indicate the nondispersive velocity limits.