Light bullets in moir\'e lattices

TL;DR

This paper predicts the existence of stable three-dimensional light bullets in photonic moiré lattices with Kerr nonlinearity, highlighting how lattice periodicity affects their stability and energy thresholds.

Contribution

It introduces the concept of light bullets in moiré lattices and analyzes their stability depending on lattice commensurability and eigenmode localization.

Findings

Stable light bullets exist in incommensurate moiré lattices without energy threshold.

Periodic moiré lattices support stable light bullets only above a certain energy threshold.

Lattice periodicity determines the stability and localization properties of 3D nonlinear states.

Abstract

We predict that photonic moir\'e lattices produced by two mutually twisted periodic sublattices in the medium with Kerr nonlinearity can support stable three-dimensional light bullets localized in both space and time. Stability of light bullets and their properties are tightly connected with the properties of linear spatial eigenmodes of moir\'e lattice that undergo localization-delocalization transition (LDT) upon increase of the depth of one of the sublattices forming moir\'e lattice, but only for twist angles corresponding to incommensurate, aperiodic moir\'e structures. Above LDT threshold such incommensurate moir\'e lattices support stable light bullets without energy threshold. In contrast, commensurate, or periodic, moir\'e lattices arising at Pythagorean twist angles, whose eigenmodes are delocalized Bloch waves, can support stable light bullets only above certain energy threshold. Moir\'e lattices below LDT threshold cannot support stable light bullets for our parameters. Our results illustrate that periodicity/aperiodicity of the underlying lattice is a crucial factor determining stability properties of the nonlinear three-dimensional states.