Propagation of bogolons in superfluid light: time-like effects in non-uniform optical media

We consider the evolution of bogolons in superfluid light, propagating in a non-uniform optical medium. This non-uniformity is perceived as a temporal change of the superfluid. We focus on sharp non-uniformities, due to the existence of boundaries between two optical media. This leads to time-refraction of bogolons, a process similar to time-refraction of photons. Time-refraction leads to a change of the bogolon “frequency”, with the formation of a reflected signal. Fresnel-type of formulas for the reflection and transmission coefficients are derived. The case of two successive boundaries, forming a barrier, is also examined. As in photon optics, the reflection and transmission coefficients oscillate as a function of the barrier length. Time-refraction and time crystals are two distinct physical configurations leading to the emission of bogolon-pairs.