We present a model of soliton propagation in waveguides with quadratic nonlinearity. Criteria for solitons to exist in such waveguides are developed and two example nanowaveguide structures are simulated as proof of concept. Interactions between quadratic solitons and dispersive waves are analyzed, giving predictions closely matching soliton propagation simulations. The example structures are found to support five different regimes of soliton and quasisoliton existence. Pulse propagation in these example waveguides has been simulated confirming the possibility of soliton generation at experimentally accessible powers. Simulations of multisoliton generation, Cherenkov radiation, and quasisolitons with opposite signs of dispersion in the fundamental and second harmonic are also presented here.

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We present a model for χ (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.

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We present analysis of two component solitons in Lithium Niobate nano-waveguides considering quadratic and cubic nonlinearities. We examine the role of the second harmonic component in phenomena including Cherenkov radiation and Raman acceleration.