Gradient catastrophe of nonlinear photonic valley-Hall edge pulses

TL;DR

This paper derives nonlinear wave equations for topological valley-Hall edge states, revealing a gradient catastrophe phenomenon caused by nonlinear self-steepening, and demonstrates the formation of stable edge quasi-solitons in such systems.

Contribution

It introduces a new understanding of nonlinear pulse dynamics in topological edge states, including the gradient catastrophe and quasi-soliton formation, validated by numerical simulations.

Findings

Edge pulses undergo gradient catastrophe due to nonlinear self-steepening.

Stable edge quasi-solitons form when spatial dispersion is considered.

Numerical modeling confirms the theoretical predictions in honeycomb waveguide lattices.

Abstract

We derive nonlinear wave equations describing the propagation of slowly-varying wavepackets formed by topological valley-Hall edge states. We show that edge pulses break up even in the absence of spatial dispersion due to nonlinear self-steepening. Self-steepening leads to the previously-unattended effect of a gradient catastrophe, which develops in a finite time determined by the ratio between the pulse's nonlinear frequency shift and the size of the topological band gap. Taking the weak spatial dispersion into account results then in the formation of stable edge quasi-solitons. Our findings are generic to systems governed by Dirac-like Hamiltonians and validated by numerical modeling of pulse propagation along a valley-Hall domain wall in staggered honeycomb waveguide lattices with Kerr nonlinearity.