Gap solitons in spatiotemporal photonic crystals

TL;DR

This paper introduces a generalized framework for nonlinear pulse propagation in spatiotemporal photonic crystals, revealing new gap soliton solutions that connect static and dynamic photonic crystal behaviors.

Contribution

It extends the concept of nonlinear periodic structures to systems with arbitrary spacetime refractive index variations and derives novel gap soliton solutions using a modified massive Thirring model.

Findings

Derived coupled mode equations for spatiotemporal photonic crystals

Found new gap soliton solutions bridging static and dynamic regimes

Established a theoretical link between different types of photonic crystal solitons

Abstract

We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow nonstationary gratings, by coupled mode equations which are a generalization of the traditional equations used for stationary photonic crystals. Novel gap soliton solutions are found by solving a modified massive Thirring model. They represent the missing link between the gap solitons in static photonic crystals and resonance solitons found in dynamic gratings.