Research Of Propagation Properties Of Vortex Beams In A High NA Focusing System

A beam with helical phase distribution is called a vortex beam,and the beam carries orbital angular momentum.Vortex beams which carry orbital angular momentum have important applications in optical micro-manipulation,free space optical communication,imaging and other fields.Based on Richard and Wolf's vector diffraction theory,the propagation properties of vector vortex electromagnetic beams in a high NA focusing system are deduced and studied in this paper.The purpose is to expand the theory of singularity optics and enrich the understanding of vortex electromagnetic waves.The work of this paper mainly focuses on the following four aspects:Firstly,this paper summarizes the research on the vortex electromagnetic beams done in the field of engineering practice in the past 30 years,makes a classification about the research progress of vector vortex beams in several different application fields,and illustrates the research significance of vector vortex beams.Secondly,the basic concepts and theories of vortex beams are summarized in detail,including the derivation process of Laguerre-Gauss beams and Gauss beams and their relationship,and the important diffraction theory in optical field is introduced.Then,the special properties of the phase singularity,polarization singularity,wavefront spacing,Gouy phase and off-axis vortices are summarized and compared.Then,the expressions of the focused field of four main polarization modes(linear polarization,circular polarization,radial polarization and azimuthal polarization)are deduced for the first time,and the expressions of the wavefront spacing of the field components on different axis are calculated.The effects of different polarization modes on the wavefront spacing of the optical axis in the high NA focused field are analyzed and summarized.The results show that there may be nine different field components and five different Gouy phase and wavefront spacing distributions in the focused field;polarization state,half-aperture angle and beam waist size have great influences on the wavefront spacing,and the influence trends are different;in the strong focusing system with larger numerical aperture,the wavefront spacing will become more larger and more uneven;Finally,the effects of different parameters in the focused field of linearly polarized beams with an off-axis vortex on the variation of polarization modes on the axis are studied for the first time.The results show that the polarization mode on the optical axis of the focused field can be different along the propagation axis,and it is mainly related to the Gouy phase on the axis and the position of the off-axis singularity of the beam.By changing the position of the off-axis singularity,the shape of the polarization ellipse can be changed without changing the direction of the polarization ellipse,and the off-axis singularity of the vortex beam can be changed without changing the direction of the polarization ellipse.The position of the offaxis vortex in the incident beam corresponds to the linear polarization inclination at the focal point in the focused field.These results are helpful to understand the distribution of Gouy phase and wavefront spacing and the evolution of polarization modes in the focused field of vortex beams,and are also helpful to improve the accuracy of interferometry and give constructive view on polarization control in experiments.