3D+1 Parametric Bright Vortex Solitons. Optical Mesons

Abstract

Using the method of separation of variables, we developed a vector nonparaxial theory from the nonlinear wave equations in strong field approximation of a Kerr media. Investigating three waves on different frequencies, which satisfied the condition 2w3=w1+w2, we found that exact localized vortex parametric soliton solutions existed for the set of four nonlinear 3D+1vector wave equations. The solutions are obtained for a fixed angle between the main frequencies and the signal waves A=60 deg. This method is applicable for angular functions, which satisfy additional conditions. It is shown that exact parametric vortex solitary waves exist for solution with eigenrotation momentum L=1. The method is generalized for arbitrary number of signal waves appearing symmetrically in pairs in respect to w3. The existence of such type of vortex solitons, in the case of degenerate four-wave mixing is discussed. As all of the waves are localized and have momentum L=1, they are called optical mesons.