Abstract
We discuss the classical and quantum theory of time refraction in a generic nonstationary medium. The classical description is based on temporal Fresnel and Snell’s formulas, which are similar and in some sense symmetric from their spatial counterparts. Temporal mirror effects are considered. The quantum formulation of time refraction is based on time-dependent Bogoliubov transforms, describing the evolution of the creation and destruction field operators. Photon pair creation and the associated entanglement properties are discussed. The influence of boundary conditions, the connection of time refraction with the dynamic Casimir effect, and radiation from superluminal non-accelerated optical boundaries are also discussed.
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