The Propagation Of The Optical Vortices In Optically Induced2D Photonic Lattice

Vortices are localized nonlinear excitations that carry screw phase dislocations and nonzero angular momentum, which attract much attention for their orbital angular momentum can be used to manipulate the microscopic particles, do as the information for the quantum coding and the information transmission, etc. In nonlinear optics, a vortex beam can self-trap into a vortex soliton in self-defocusing materials. However, it would decays into the fundamental solitons flying along the tangent direction in self-focusing materials because of the azimuthal modulation instabilities. Recently, people find that vortex beams can form vortex solitons which can propagate stably in photonic lattices with self-focusing nonlinearity, which opens a new area for studying the vortex beams.In addition, photonic lattice is a kind of optical periodic structures that can control the propagation of the beams, which have potentially important application in all-optical exchange, light switch and so on.This paper has mainly studied the dynamics of a vortex beam in optically induced square lattice and Bessel lattice. It investigates the influence of the lattice and the conditions under which the vortex solitons could form. The nonlinear Schrodinger equations that describe the propagation of the vortex beams are got by the Maxwell equations and the mechanism of photorefractive effect and can be numerical solved by optimized ADI-BPM. The contents and achievements are outlined as follows:1. We investigate vortex beams propagation in square photonic lattice with self-focusing nonlinearity. Vortices would decay into the fundamental solitons without the lattice. When there has the lattice, both on-site and off-site single-charged vortices can form the discrete vortex solitons that can propagate stably under appropriate conditions. Charge-flipping of double-charged vortices could be observed during the propagation and the vortex solitons are quasi-stable. When the intensity of the input beams is too low, energy coupling along the axial could be found in the single point of incidence. But after raising the intensity, there will form the vortex solitons.2. We investigate vortex beams propagation in square photonic lattice with self-defocusing nonlinearity. On-site single-charged vortices could form the discrete vortex solitons whose four parts are focusing between the lattice points under appropriate conditions. Charge-flipping of double-charged vortices could also be observed during the propagation.3. We investigate single-charged vortex beams propagation in Bessel lattice. As the radial symmetry of the lattice, the input beam could evolve into a ring-like vortex soliton after the depth of the lattice and the intensity of the bias field all appropriate when the energy of the input beam is all located in the first ring of the lattice.