A rigorous distribution-theory derivation shows that at a temporal interface the fields satisfy jump conditions that yield a generalized Snell's law and explicit reflection/transmission coefficients.
Shalaev, Daniele Faccio, and Matteo Clerici
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Refraction laws in temporal media
A rigorous distribution-theory derivation shows that at a temporal interface the fields satisfy jump conditions that yield a generalized Snell's law and explicit reflection/transmission coefficients.