Gradient catastrophe of nonlinear photonic valley-Hall edge pulses

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...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Smirnova, Daria A, Smirnov, Lev A, Smolina, Ekaterina O, Angelakis, Dimitris G, Leykam, Daniel
Format: Article
Language:English
Subjects:
Domain walls
Frequency shift
Nonlinearity
Pulse propagation
Solitary waves
Topology
Valleys
Wave equations
Wave packets
Wave propagation
Waveguides
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.10569