Dispersion-Mediated Space-Time States

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.