Propagation And Focusing Properties Of Vortex Beams

Beams with spiral phase front are regarded as vortex beams. Vortex beams posses phase singularity, and each photon of vortex beams carries orbital angular momentum (OAM). Vortex beams have important potential applications in many fields, such as particle trapping and manipulation, optical information encoding and transmission, and atomic optics etc. Therefore, vortex beams have been the focus of investigations. In this thesis, we have studied the propagation and focusing properties of vortex beams, the contents include the following sections.The intensity distribution of vortex beams with special polarization distribution formed by a4Pi configuration is investigated. The result of radially polarized vortex beams shows that, special focal patterns can be generated by properly chosen the topological charge and polarization direction of incident vortex beams. For example, subwavelength spherical focal spot and spherical dark core beam, and well-defined spherical dark core beam array and hollow beam with length of30λ. The result of azimuthally polarized first order vortex beams shows that, a spherical focal spot can be produced by introducing a filter, and the position of the focal spot can be controlled by the phase retardation of two incident beams.The intensity evolution of partially coherent vortex beams on propagation in non-Kolmogorov atmospheric turbulence is numerically simulated. The results show that, after a sufficiently long propagation distance, the central-dipped intensity profile of vortex beam will evolve into the Gaussian shape in turbulent atmosphere. The distance required depends on the topological charge and correlation properties of vortex beams and the generalized refractive-index structure parameter and spectral index of the turbulent atmosphere. Generally, the distance is longer with a larger topological charge, higher coherence, and weaker turbulence. The analytic expression of the degree of polarization of on-axis point of stochastic electromagnetic vortex beams is derived. It is shown that the evolution of polarization of vortex beams in atmosphere is different from that of non-vortex beams, and is influenced by the correlation length and the topological charge of the incident vortex beams. However, after a sufficiently long propagation distance in turbulence, the degree of polarization of vortex beams will tend to the magnitude of source beam.The scintillation index of vortex beam in simulated and real atmospheric turbulence is experimentally measured. The result in simulated atmospheric turbulence produced by rotating ground glasses shows that, the fluctuation of the intensity can be effectively reduced by vortex beams. In particular, the reduction of scintillation is more pronounced for vortex beams with larger topological charge. The measurement on the scintillation of Gaussian beams and vortex beams propagating in real turbulent atmosphere shows that the scintillation index of a Gaussian beam around optical axis increases gradually as propagation distance increases from100m to400m. The scintillation of vortex beam with topological charge of4increases with the increment of the propagation distance, and achieves the maximum value at a fixed distance. The scintillation decreases as the propagation distance continues to increase. It is shown that for the beams propagating in distance of400m in weaker turbulence atmosphere, the scintillation of a Gaussian beam is smaller than that of a vortex beam, however the scintillation of a Gaussian beam is larger than that of a vortex beam in stronger turbulence.The diffraction properties of an elliptic vortex beam incident on a square Fresnel zone plate (FZP) are studied. Some interesting beam patterns are obtained by choosing the proper parameters. A diamond beam is produced under the illumination of a circular Gaussian beam, and a rhombus beam is produced under the illumination of an elliptic Gaussian beam. A dark hollow beam is generated as the incident beam is a vortex beam, and the shape of the central dark core depends on the topological charge and the elliptic coefficient.The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical aperture are studied. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges, and the direction of the rotation depends on the symbol of the topological charge. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane.The concept of a quadratic vortex beam is proposed, in which phase term of the beam is given by exp(imθ2). The phase of the quadratic vortex beam increases with azimuthal angle nonlinearly. This change in phase produces several unexpected effects. The result of beam with phase term of exp exp[imθ2/(2π)] shows that, such beam possess m phase singularities. The phase singularities will shift in the transverse beam plane on propagation.