Solitons near avoided mode crossing in $\chi^{(2)}$ nanowaveguides

TL;DR

This paper models $$ waveguides with three modes near avoided crossing, revealing new soliton solutions, their stability, and spectral features, supported by simulations of two-color soliton generation.

Contribution

Introduces a coupled-mode model for $$ waveguides near avoided crossing, predicting novel solitons and analyzing their dynamics and spectral properties.

Findings

Existence of avoided-crossing solitons with unique spectral features

Continuous wave solutions are prevalent and modulationally unstable

Simulations confirm two-color soliton generation from single pulses

Abstract

We present a model for $\chi^{(2)}$ waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.