Monday, September 10, 2012

1209.1449 (Yisong Yang et al.)

Existence of Optical Vortices    [PDF]

Yisong Yang, Ruifeng Zhang
Optical vortices arise as phase singularities of the light fields 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 Schr\"{o}dinger 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. Some interesting explicit estimates relating vortex winding number, wave propagation constant, and magnitude of potential function are also derived.
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