Longitudinal optical phonons in photonic time crystals containing a stationary charge

TL;DR

This paper explores how stationary charges in photonic time crystals can excite and amplify longitudinal optical phonons, revealing a new way to manipulate waves in these structures with minimal refractive index modulation.

Contribution

It demonstrates that stationary charges can excite longitudinal phonons in photonic time crystals and that a momentum bandgap can be achieved with minimal refractive index modulation, expanding wave control capabilities.

Findings

Stationary charges excite longitudinal phonons in PTCs.

A momentum bandgap can be created with minimal refractive index modulation.

Longitudinal modes can be amplified within the PTCs.

Abstract

Lorentzian-type media support optical phonons that oscillate with longitudinal polarization parallel to the wave direction, at a wave vector-independent frequency at which the permittivity becomes zero. Here, we study the interactions between the longitudinal optical phonons and Lorentzian medium-based dispersive photonic time crystals (PTCs). We demonstrate that a stationary charge embedded in the PTCs can excite these longitudinal modes through the conversion of the static polarization field induced by the charge. Furthermore, the PTCs can develop a momentum bandgap across the entire wave vector space to amplify the longitudinal modes. Remarkably, this infinite momentum bandgap can be established with minimal temporal modulation of the refractive index when creating the PTCs. Our approach expands the range of waves that can be manipulated in PTCs and shows potential for observing momentum bandgap phenomenon in realistic optical experiments, where the modulation depth of the refractive index is severely constrained.