Existence Of Vortices In Nonlinear Optics

Optical vortices arise phase singularities of the light field and are of central interest in modern optical physics. In this paper, some existence theorems are established for stationary vortex wave solutions of a general class of nonlinear Schrodinger equations. There are two types of results. The first type concerns the existence of positive-radial-profile solutions which are obtained through a constrained minimization approach. The second type addresses the existence of saddle-point solutions through a mountain-pass-theorem or min-max method so that the wave propagation constant in an open interval.The structure of this paper is as follows:Chapter1states the introduction of this thesis.Chapter2according the constrained minimization approach, get the existence of positive-radial-profile solutions.Chapter3in a certain range of β, by using the mountain-pass-theorem to prove the existence of saddle-point solutions.