Abstract
The existence and stability of three-wave solitons, both (1+1) and (2+1) dimensional, that result from a double-resonance (type I plus type II) parametric interaction in a purely quadratic nonlinear medium are investigated. We demonstrate the existence of a family of stable solitons for a broad parameter range in the double-resonance model. Further, these solitons exhibit multistability, a property that is potentially useful for optical switching applications. We introduce a way to measure the quality of multistability and use this measure to compare the double-resonance model with single-resonance models in χ(2) media. We also discuss the modulational instability of the double-resonance system and present physical estimates of the power required for soliton generation.
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