Research On The Propagation And Focusing Characteristics Of Partially Coherent Vortex Beam

The power-exponent-phase vortex beam(PEPVB)is a new type of optical vortex beam,and its phase exp[i 2l?((?)2?)~n]is determined by the power exponent n and the topological charge l.When n=1,the power-exponent-phase vortex beam(PEPVB)degenerates into vortex beam.The partially coherent power-exponent-phase vortex beam(PEPVB)has the common characteristics of the partially coherent beam and the power-exponent-phase vortex beam.Compared with traditional coherent beams,partially coherent beams exhibit some novel physical characteristics:reducing beam speckle effect,reducing beam scintillation through random media,beam wander and self-repairing,etc.,in‘ghost'imaging,coherent diffraction imaging and particle capture have broad application prospects.The propagation and focusing characteristics of partially coherent beams are the basis of the application of partially coherent light fields.Therefore,we studied the propagation and focusing characteristics of partially coherent vortex beams in this thesis.The specific research content is as follows:(1)The basic theories and methods of partially coherent beam propagation have been investigated,which include theory of scalar light fields propagation,theory of vector light fields propagation and basic theory of partially coherent light fields,and lay a foundation for the study of partially coherent vortex beams.(2)The propagation characteristics of partially coherent vortex beams have been studied.Based on the Fresnel-Kirchhoff diffraction integral theory and the vector Rayleigh-Sommerfeld diffraction integral theory,the cross-spectral density functions of the source field and after the propagation in free space as well as complex optical system characterized by the ABCD matrix under the paraxial approximation are derived,respectively.(3)The propagation characteristics of partially coherent vortex beams in atmospheric turbulence have been researched.Based on Kolmogorov's atmospheric turbulence medium theory,we establish a theoretical model of partially coherent vortex beams in atmospheric turbulence,and numerically study the propagation characteristics of scalar and vector partially coherent vortex beams in atmospheric turbulence.(4)A theoretical model for the propagation and tight focusing of partially coherent radially polarized power-exponent-phase vortex beams(PEPVB)has been established,and an efficient numerical calculation program has been written based on numerical calculation software such as MATLAB to simulate and study the propagation characteristics of partially coherent radially polarized power-exponent-phase vortex beams(PEPVB)in free space and in the ABCD optical system.The evolution of the light intensity,the evolution of the degree of polarization and the evolution of the spectral coherence have been analyzed.What's more,the tight focusing characteristics of partially coherent radially polarized power-exponent-phase vortex beams(PEPVB)have been simulated and studied.We analyzed and revealed the relationship between the tight focusing characteristics of different related structures Schell-mode radially polarized power-exponent-phase vortex beams(PEPVB)and the power exponent n as well as the topological charge l.This project will lay a theoretical foundation for the application of partially coherent radially polarized power-exponent-phase vortex beams in optical capture and other fields,and is of great significance to the promotion of the theory and application of new vector light fields.