Generalized Total Internal Reflection at Dynamic Interfaces

TL;DR

This paper provides a comprehensive analysis of total internal reflection at various dynamic interfaces, deriving formulas for critical angles and validating them through simulations, with implications for advanced optical and quantum technologies.

Contribution

It introduces a generalized framework for TIR at dynamic interfaces, including new criteria and analytical formulas validated by simulations.

Findings

Closed-form formulas for critical angles at dynamic interfaces

Validation of formulas through FDTD simulations

Insights into physics using Fresnel-Fizeau drag and spacetime frequency transition

Abstract

Recent research developments in the area of spacetime metamaterial structures and systems have raised new questions as to how the physics of fundamental phenomena is altered in the presence of spacetime modulation. In this context, we present a generalized and comparative description of the phenomenon of total internal reflection (TIR) at different dynamic interfaces. Such interfaces include, beyond the classical interfaces corresponding to the boundaries of moving bodies (moving interface -- moving matter systems), interfaces formed by a traveling-wave step modulation of an electromagnetic parameter (e.g., refractive index) (moving interface -- stationary matter systems) and fixed interfaces between moving-matter media (stationary interface -- moving matter systems). We first resolve the problem using the evanescence of the transmitted wave as the criterion for TIR and applying the conventional technique of relative frame hopping (between the laboratory and rest frames), which results in closed-form formulas for the relevant critical (incidence, reflection, phase refraction and power refraction) angles. We then introduce the concept of catch-up limit between the dynamic interface and the transmitted wave as an alternative criterion for the critical angle. We use this approach both to analytically verify the critical angle formulas, further validated by full-wave (FDTD) analysis, and to explain the related physics, using Fresnel-Fizeau drag and spacetime frequency transition considerations. These results might find various applications in ultra-fast optics, gravity analogs and quantum processing.