Exploring Aperiodic Order in Photonic Time Crystals

TL;DR

This paper develops a theoretical framework for analyzing aperiodic order in photonic time quasicrystals, revealing complex wave dynamics and spectral features that could inform advanced photonic device design.

Contribution

It extends the trace and anti-trace map formalism to temporal aperiodic structures, specifically analyzing the Thue-Morse sequence in photonic time crystals.

Findings

Identification of multiscale spectral response in PTQCs

Observation of localization effects in aperiodic time structures

Comparison of aperiodic and periodic photonic time crystals

Abstract

We present a theoretical framework for analyzing aperiodically ordered photonic time quasicrystals (PTQCs), which are the temporal analogs of spatial photonic quasicrystals. Using a general two-symbol substitutional sequence to model temporal modulations, we extend the trace and anti-trace map formalism used for spatial photonic quasicrystals to the temporal domain. Focusing on the Thue-Morse sequence as a representative example, we examine the band structure and wave-transport properties, discussing their physical origins and highlighting both similarities and key differences with conventional periodic photonic time crystals. Furthermore, we investigate the peculiar features of PTQCs, such as multiscale spectral response and localization effects. Our findings provide valuable insights into the complex interplay between aperiodic order and wave dynamics in time-varying media, highlighting its potential to enable the development of advanced photonic devices.