Two-dimensional spatial optical solitons in bulk Kerr media stabilized by self-induced multiphoton ionization: Variational approach

The beam parameters of spatial two-dimensional solitons in a bulk medium under the influence of the combined effects of diffraction, Kerr nonlinearity, and nonlinear index change by plasma creation will be studied with the help of a variational approach. A simple analytical relation for the power of a spatial two-dimensional soliton is derived which shows a two-valued behavior in dependence on the beam diameter. The variational approximation is compared with numerical and experimental results. The solution is proven to be stable against small perturbations in the whole parameter region.