Instantaneous modulations in time-varying complex optical potentials

TL;DR

This paper investigates how a time-varying, homogeneous dielectric medium affects light's spectral and dynamical properties, revealing modulation effects linked to PT symmetry and potential applications in various wave systems.

Contribution

It introduces a theoretical framework for analyzing light in non-stationary PT-symmetric optical potentials, highlighting instantaneous amplitude, frequency, and modulation phenomena.

Findings

Demonstrates modulation of light amplification and attenuation over time.

Predicts splitting of extrema in frequency modulation.

Shows shrinkage of the modulation period.

Abstract

We study the impact of a spatially homogeneous yet non-stationary dielectric permittivity on the dynamical and spectral properties of light. Our choice of potential is motivated by the interest in PT-symmetric systems as an extension of quantum mechanics. Because we consider a homogeneous and non-stationary medium, PT symmetry reduces to time-reversal symmetry in the presence of balanced gain and loss. We construct the instantaneous amplitude and angular frequency of waves within the framework of Maxwell's equations and demonstrate the modulation of light amplification and attenuation associated with the well-defined temporal domains of gain and loss, respectively. Moreover, we predict the splitting of extrema of the angular frequency modulation and demonstrate the associated shrinkage of the modulation period. Our theory can be extended for investigating similar time-dependent effects with matter and acoustic waves in PT-symmetric structures.