Generalized total internal reflection at dynamic interfaces

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