Study Of Tightly Focusing Properties Of Multi-gaussian Correlated Vector Beam

Coherence and polarization are two important properties of light.In past several decades,researchers were studying these two properties separately,until the unified theory of coherence and polarization was introduced.Polarization is the basic property of light beam,which is considered as a manifestation of correlation involving components of the fluctuating electric field at a single point.It is usually assumed that the state of polarization of a light beam is invariant as the beam propagates,until James showed that the degree of polarization of a light beam generated by a partially coherent source may change on propagation in free space in 1994.This discovery is of great important,and among such non-uniform polarized beam whose polarization varies with spatial position,the cylindrical polarized beam,whose axissymmetric polarization matches symmetry of focusing system lens well,has unique focus intensity distribution.Specially,azimuthally polarized beam,whose polarization is perpendicular to radius,shows annular focus intensity distribution;While the focus intensity distribution of radially polarized beam,whose polarization is parallel to radius,can be decomposed into annular transversal component and center longitudinal component.Coherence is regarded as a consequence of correlations between some components of the fluctuating electric field at two points,or two moments of one point.According to the coherence width,light beam could be divided into three types: complete coherent beam,like Laser;complete incoherent beam,like sunlight;and partially coherent beam whose coherence width is between those of two types above,typically like partially coherent Gaussian Shell-model beam.Comparing to completely coherent beam and completely incoherent beam,partially coherent beam has its own advantages,which makes it the research focus in past several decades.Classic Gaussian Shell-model beam,whose intensity distribution at the source plane and spatial correlation distribution are both Gaussian distribution,shows several superiorities in many applications.Based on the realizability conditions,a series of beams with special spatial correlation distribution(or “special correlated beam” for short)was introduced and studied consecutively.Special correlated beam,which is based on classic Gaussian Shell-model beam and combined with special spatial correlation distribution,realizes more flexible modulation than classic Gaussian Shell-model beam,and has potential use in laser process and remote detection.After unified theory of coherence and polarization was introduced,partially polarized partially coherent beam became a heat study among researchers.In this paper,we introduce radially polarized multi-Gaussian correlated Shell-model beam,whose intensity distribution of light source is Gaussian distribution,while spatial correlation distribution is multi-Gaussian distribution.After deriving the realizability conditions of multi-Gaussian radially polarized beam,we also calculated the focus intensity distribution of such beam passing through high-NA tight focusing system.It is found that by modulating parameters of light source’s spatial correlation appropriately,focus intensity distribution could be controlled to produce light field of flat-top shape.It is also found that,after inserting binary optics,the depth of uniform focus intensity distribution was further increased in longitudinal direction.Such results provide a novel way for shaping both transverse and longitudinal field distributions,which has potential use in particle acceleration and laser machining.The basic structure of this paper is as follows:In chapter 1,we briefly review the research progress of partially coherent beam with special correlation function and vector polarized beam whose polarization varies with spatial position.In chapter 2,we introduce the basic theory knowledge of partially coherent beam,which includes mutual coherence function and cross spectral density function,the characterizations of partially coherent vector beams and the basic theory knowledge of tight focusing.After that,we derivate the tight focusing propagation function of linear polarized beam.In chapter 3,referring to non-uniform polarized vector beam whose polarization varies with spatial position,we select azimuthally polarized beam and radially polarized beam to derivate their tight focusing function,and to study the effect of beam parameters on the tight focusing properties.In chapter 4,referring to partially coherent beam with special correlation function,we select multi-Gaussian correlated beam to study its realizability conditions and the paraxial propagation properties.In chapter 5,we introduce multi-Gaussian correlated radially polarized beam,and study its realizability conditions.We also study the focusing properties of such beam after passing through tight focusing system,and the effect of beam parameters on the tight focusing properties.Besides,we further study the effect of inserting binary optics on the tight focusing properties of radially polarized Bessel-Gaussian correlated Shell-model beam,and radially polarized multi-Gaussian correlated Shell-model beam.In chapter 6,we have the conclusion and some prospection.