Temporal interface in dispersive hyperbolic media

Spatial inhomogeneity, temporal modulation, and engineered anisotropy of parameters of electromagnetic media offer numerous opportunities for manipulating light-matter interaction over the past decades. Here, we investigate a scenario in which we deal with the temporal interface, hyperbolic anisotropy in the form of layered structures, and frequency dispersion. We theoretically investigate how a monochromatic uniform plane wave - propagating in an unbounded, homogeneous, isotropic dielectric medium - undergoes changes due to the rapid temporal variation of such medium into a hyperbolic dispersive medium formed by the stack of thin metal-dielectric bilayers, in which the metal follows the lossless Drude dispersion and the dielectric is assumed to be dispersionless. We corroborate our analytical results by numerical simulations. We observe several interesting phenomena, such as conversion of the original frequency into three pairs of frequencies, resulting in three sets of forward (FW) and backward (BW) waves. We present the amplitudes and the time-averaged Poynting vectors for such FW and BW waves and discuss some of the salient features of such temporal interface.