Anderson Localization in Photonic Time Crystals

TL;DR

This paper demonstrates that temporal disorder in photonic time crystals induces Anderson localization in time, causing electromagnetic fields to emerge and decay exponentially, revealing a novel temporal localization phenomenon.

Contribution

It introduces the concept of Anderson localization in the time domain within photonic time crystals with temporal disorder, a novel extension of spatial localization concepts.

Findings

Temporal disorder leads to Anderson localization in time.

Electromagnetic fields can emerge and decay exponentially over time.

The phenomenon extends Anderson localization to a three-dimensional fluctuating medium.

Abstract

Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially homogeneous media in which the refractive index changes periodically in time, leading to the formation of bands in the wave number domain. By analogy to Anderson localization in space, one might expect that the presence of temporal disorder in photonic time crystals would lead to Anderson localization in the time domain. Here, we show that indeed periodic modulations of the refractive index with the addition of temporal disorder lead to Anderson localization in time, where an electromagnetic field can emerge from the temporally modulated medium at a certain moment in time and then decay exponentially over time. Thus, we are dealing with a situation where, in a fluctuating three-dimensional medium, the birth and death of waves can occur, and the mechanism of this phenomenon corresponds to Anderson localization.