Nonlinear Bloch wave dynamics in photonic Aharonov–Bohm cages

Nana Chang,Sinan Gundogdu,Sergej Flach,Dimitris G Angelakis,Supeng Kou,Aleksandra Maluckov,Daniel Leykam

doi:10.1063/5.0037767

Abstract

We study the properties of nonlinear Bloch waves in a diamond chain waveguide lattice in the presence of a synthetic magnetic flux. In the linear limit, the lattice exhibits a completely flat (wavevector k-independent) band structure, resulting in perfect wave localization, known as Aharonov–Bohm caging. We find that in the presence of nonlinearity, the Bloch waves become sensitive to k, exhibiting bifurcations and instabilities. Performing numerical beam propagation simulations using the tight-binding model, we show how the instabilities can result in either the spontaneous or controlled formation of localized modes, which are immobile and remain pinned in place due to the synthetic magnetic flux.

Highlights

Nonlinear waves are general solutions of nonlinear partial differential equations such as the Korteweg–de Vries, cubic nonlinear Schrödinger, sine-Gordon, or Boussinesq equations,1 which describe wave processes in diverse fields ranging from nonlinear optics, hydrodynamics, and plasma to biological systems; the theory of general relativity; and the topological theory of knots
We study the properties of nonlinear Bloch waves in a diamond chain waveguide lattice in the presence of a synthetic magnetic flux
We have studied the dynamics of nonlinear waves in the diamond chain waveguide lattice in the presence of a synthetic magnetic flux and nonlinearity, which exhibits perfect wave localization (Aharonov–Bohm caging) in the linear limit

Summary

INTRODUCTION

Nonlinear waves are general solutions of nonlinear partial differential equations such as the Korteweg–de Vries, cubic nonlinear Schrödinger, sine-Gordon, or Boussinesq equations, which describe wave processes in diverse fields ranging from nonlinear optics, hydrodynamics, and plasma to biological systems; the theory of general relativity; and the topological theory of knots. A new front for nonlinear wave dynamics in lattices has been opened by recent advances in creating artificial gauge fields for light, which can be used to manipulate photonic band structures to control their dispersion and topological properties, leading to many opportunities for both fundamental studies and device applications, such as the creation of edge states. The aim of this study is to shed further light on the effect of artificial gauge fields on nonlinear wave dynamics in photonic lattices, focusing on the diamond chain lattice. We study the effect of nonlinearity on delocalized nonlinear Bloch wave excitations of the Aharonov–Bohm cage lattice, comparing against the properties of the flux-free diamond chain lattice.

MODEL AND NONLINEAR BLOCH MODES

DYNAMICS OF NONLINEAR BLOCH WAVES

CONTROLLED GENERATION OF LOCALIZED NONLINEAR MODES

CONCLUSIONS