Theoretical And Experimental Study On The Generation And Propagation Of Laser Beams With Orbital Angular Momentum

With the development of the theory of singular optics, laser beams with orbital angular momentum have attracted more and more attention and found their potential and important applications in nonlinear optics, atomic optics, quantum information processing, free-space optical communication, particle trapping and manipulation, etc. In this thesis, we mainly choose three types of such laser beams with orbital angular momentum: partially coherent Laguerre-Gaussian beam, anomalous vortex beam and partially coherent anomalous vortex beam.First of all, with the help of the Huygens-Fresnel principle, the focusing properties and experimental generation of partially coherent Laguerre-Gaussian beam(LG0l beam is chosen in this thesis) have been studied in detail. It has been found that the focused intensity of the LG0 l beam can be shaped through varying the initial spatial coherence, and our experimental results agree well with the theoretical predictions.Secondly, through studying the spatial autocorrelation function of full coherent light beams, the relationships among the radial and azimuthal mode indices and the number of the ring dislocations of far-field autocorrelation function are given. According to the relationship, we have proposed a two-step method to determine the topological charge of a high-order Laguerre-Gaussian(LGpl) beam. Furthermore, we analyze the effect of spatial coherence on determining the topological charge of partially coherent LG0 l beam and propose a method to determine the topological charge of a vortex beam with low coherence based on its complex degree of coherence.Thirdly, a theoretical model of an anomalous vortex beam is proposed. Analytical propagation formula for the proposed beam passing through a paraxial ABCD optical system is derived, and the propagation properties of such beam in free space are studied numerically. We report experimental generation of an anomalous vortex beam and measure its propagation properties. Our experimental results are consistent with the theoretical predictions. It is interesting to find that an anomalous vortex beam will eventually become an elegant Laguerre-Gaussian beam at the far field(or at the focal plane) in free space. Thus, generation of an anomalous vortex beam provides one way for generating an elegant Laguerre-Gaussian beam.Finally, propagation properties and correlation singularity of a partially coherent anomalous vortex beam is been studied. A theoretical model is introduced and we derive analytical expression for the cross-spectral density of a partially coherent anomalous vortex beam propagating through a paraxial optical ABCD system. The effects caused by different initial spatial coherence, beam order and topological charge on the intensity distribution of the partially coherent anomalous vortex beam have been studied theoretically. Additionally, we obtain the numerical relationship among the number of correlation singularities(coherence vortices), the topological charge and the beam order. Furthermore, we first report experimental generation of a partially coherent anomalous vortex beam.