Research On Diffraction Properties Of Optical Vortex Field

A vortex beam possesses the exp(ilφ) form of phase distribution, and its topologicalcharges are l. Each of the photon orbital angular momentum is l. Study on the characteristicsof distribution and evolution, accurate determination the topological charge number l of avortex beam has important application value in finding other methods to generate vortexbeams and applying vortex beams to optical micro-manipulation, atomic optics, biomedicine,nonlinear optics, optical information transmission.In this paper, the diffraction method has been used. By means of different diffractionaperture, diffraction optical intensity distribution characteristics of the vortex beams that havedifferent topological charge numbers are analyzed.Based on the understanding of the basic principle, the characteristics of optical intensitydistribution and phase distribution of vortex beam, the common methods to generate vortexbeams, such as mode conversion methods, hologram methods, spiral phase plate method andspatial light modulator method, are summed. The principles, optical structure, relative meritsand application conditions of various methods are analyzed. The complex amplitudeexpressions of ideal vortex beam, plane vortex beam and annular vortex beam are givenrespectively.In Fraunhofer diffraction conditions, diffracted by square aperture, sinusoidal amplitudeaperture, circular aperture and annular aperture respectively, the differences of optical fielddistributions of vortex beams which have different topological charges, are analyzed. Thediffraction results shows that, by using flat-topped vortex beam which is diffracted by asquare aperture or sinusoidal amplitude aperture, the topological charges can be determinedaccording to the diffraction pattern. The main process to determine topological charges by thismethod is that, calculating diffraction intensity distribution of vortex beam with differenttopological charge through square amplitude grating with different spatial frequencies,observation the diffraction bright spots, and counting the diffraction pattern peripheral bright spots. The numbers of bright spot represent the topological charge numbers of an incidentvortex beam actually. For comparison purposes, the diffraction of vortex beam by a circularaperture and an annular aperture are calculated also. The differences in diffraction intensitydistribution of different topological charge are compared. Furthermore, the differencebetween diffraction pattern of integer order and non-integer order vortex beam by an annularaperture is given. The result shows that the diffraction intensity distribution range increaseswith topological charge numbers. On the same diffraction order, the diffraction pattern of anannular aperture is clear than a circular aperture, and annular aperture diffraction have higherorders than circular aperture diffraction.For more complex apertures, the diffraction distribution of Laguerre-Gaussian beam by asquare matrix aperture and multi-circular aperture arranged in ring are calculated respectively.By comparing the Fraunhofer diffraction intensity distribution characteristics in differentapertures, the similarities and differences are found out. Calculation shows that diffractionintensity distribution depends on topological charge and diffraction aperture. The topologicalcharge number of vortex beam can be determined accurately by changing the aperture inexperiments. Using a complex aperture can get better diffraction effect than using a simpleaperture.