Self-steepening-induced stabilization of nonlinear edge waves at photonic valley-Hall interfaces

Localized nonlinear modes at valley-Hall interfaces in staggered photonic graphene can be described in the long-wavelength limit by a nonlinear Dirac-like model including spatial dispersion terms. It leads to a modified nonlinear Schr\"odinger equation for the wave field amplitude that remarkab...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Authors: Smolina, Ekaterina O, Smirnov, Lev A, Leykam, Daniel, Smirnova, Daria A
Format: Article
Language:English
Subjects:
Amplitudes
Direct numerical simulation
Edge waves
Graphene
Graphical user interface
Mathematical models
Nonlinear systems
Nonlinearity
Perturbation
Photonics
Plane waves
Stabilization
Valleys
Wave propagation
Waveguides
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Summary:Localized nonlinear modes at valley-Hall interfaces in staggered photonic graphene can be described in the long-wavelength limit by a nonlinear Dirac-like model including spatial dispersion terms. It leads to a modified nonlinear Schr\"odinger equation for the wave field amplitude that remarkably incorporates a nonlinear velocity term. We show that this nonlinear velocity correction results in a counter-intuitive stabilization effect for relatively high-amplitude plane-wave-like edge states, which we confirm by calculation of complex-valued small-amplitude perturbation spectra and direct numerical simulation of propagation dynamics in staggered honeycomb waveguide lattices with on-site Kerr nonlinearity. Our findings are relevant to a variety of nonlinear photonic systems described by Dirac-like Hamiltonians.
ISSN:2331-8422
DOI:10.48550/arxiv.2305.06544