Temporal Interface in Dispersive Hyperbolic Media

TL;DR

This paper explores how a monochromatic wave interacts with a temporally varying hyperbolic dispersive medium, revealing frequency conversion and wave direction changes through theoretical analysis and simulations.

Contribution

It introduces a novel analysis of wave behavior at a temporal interface in hyperbolic dispersive media with layered structures, combining analytical and numerical methods.

Findings

Frequency conversion into three pairs of frequencies

Generation of forward and backward waves

Insights into energy flow at the temporal interface

Abstract

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 the 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-average Poynting vectors for such FW and BW waves and discuss some of the salient features of such temporal interface.