Quadratic Ring-Shaped Solitary Waves

Abstract

Cascaded χ⁽²⁾: χ⁽²⁾ parametric interactions of intense signals in materials with quadratic nonlinearity offer a rich variety of interesting phenomena one of which is the formation of solitons [1–9]. Investigation of the evolution of spatial solitons in χ⁽²⁾ nonlinear media (NLM) is much more preferable because of the possibility for easier experimental observation. Two basic types of solitons exist in this case: bright-bright [1, 2] and dark-dark [5, 6]. An interesting feature of the spatial case of beam propagation is that it can be extended into two transverse dimensions (2D) [7–9].