Existence of Optical Vortex Solitons in Pair Plasmas

Optical vortices arise as phase dislocations of light fields and they are of importance in modern optical physics. In this study, we employ the calculus of variations method to develop an existence theory for the steady state vortex solutions of a nonlinear Schrodinger type equation to model light waves that propagate in a medium with a new focusing-defocusing nonlinearity. First, we demonstrate the existence of positive radially symmetric solutions by constrained minimization, where we give some interesting explicit estimates related to vortex winding numbers and the wave propagation constant. Second, we establish the existence of saddle-point solutions through a mountain-pass argument.