Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons

TL;DR

This paper develops a systematic tight-binding approach for longitudinally driven photonic lattices, revealing topologically protected edge states and solitons with unidirectional propagation, supported by asymptotic analysis and numerical simulations.

Contribution

It introduces a new method for deriving tight-binding models in driven photonic lattices, including complex sublattice rotations and topological edge states.

Findings

Topologically protected unidirectional edge modes identified.

Asymptotic analysis links edge modes to Schrödinger equations.

Numerical simulations confirm theoretical predictions.

Abstract

A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by varying/rotating the waveguides, longitudinally, along the direction of propagation. Different sublattice rotation and structure are allowed. Linear Floquet bands are constructed for intricate sublattice rotation patterns such as counter rotation, phase offset rotation, as well as different lattice sizes and frequencies. An asymptotic analysis of the edge modes, valid in a rapid-spiraling regime, reveals linear and nonlinear envelopes which are governed by linear and nonlinear Schrodinger equations, respectively. Nonlinear states, referred to as topologically protected edge solitons are unidirectional edge modes. Direct numerical simulations for both the linear and nonlinear edge states agree with the asymptotic theory. Topologically protected modes are found; they possess unidirectionality and do not scatter at lattice defect boundaries.