The Propagation And Focusing Properties Of Vector Beams

In recent years, vector beams have attracted significant interest due to the uniquefeature compared with homogeneously polarized beams. Two extreme cases of vectorbeams are radially polarized (RP) and azimuthally polarized (AP) beams. A RP beamcan be focused to generate a strong longitudinal and non-propagating electric field atthe focal plane. Moreover, an AP beam can be focused into a hollow dark spot.Recently, beams with more complicate polarization distribution such as radial-variantvector fields with hybrid states of polarization (SoPs) becomes the focus ofinvestigations due to their unique features. These peculiar properties are useful formany applications such as optical data storage, particle trapping and acceleration,high-resolution microscopy, material processing, and determination of singlefluorescent molecule orientation, etc. Therefore, for the investigation on propagationand focusing properties of these vector beams have important theoretical and practicalsignificance.In this paper, we investigate the focusing properties of hybridly polarized laserbeams through a high numerical aperture objective. Moreover, the propagation andfocusing properties of partially coherent vector beams including radially polarizedand azimuthally polarized beams are theoretical and experimental investigated.Numerical calculations are performed to compare the influence of correspondingparameters on the propagation and tight focusing properties.1.By using the Richards-Wolf vector diffraction theory, we theoretically investigatethe tight focusing properties of hybridly polarized vector beams. Some numericalresults are obtained to illustrate the intensity, phase and polarization of tightly focusedhybridly polarized vector beams. It is shown that the shape of the focal pattern maychange from an elliptical beam to a ring focus with increasing radial index. The phasedistribution around the tightly focused ring is shown to be the helical phase profile,indicating that the radial-variant spin angular momentum (SAM) of hybridlypolarized vector beams can be converted into the radial-variant orbital angularmomentum (OAM). 2. By using the Debye vector diffraction theory, a super-length optical needle (~14λ)of strong transversally polarized field with homogeneous intensity along the opticalaxis and sub-diffraction beam size (~0.9λ) can be generated by focusing a hybridlypolarized vector beam through a dielectric interface with an annular high numericalaperture (NA) lens. Moreover, it is found that the polarization of the cross sectionnear the focal plane is radial-variant. Such kind of non-diffracting optical needle mayhave applications in atom-optical experiments, such as with atom trap and atomswitches.3.Based on the extended Huygens-Fresnel method by adopting a beamcoherence-polarization matrix, the propagation and focusing properties of partiallycoherent vector beams including radially polarized and azimuthally polarized beamsare theoretical and experimental investigated. The beam profile of partially coherentradially or azimuthally polarized beam can be shaped by adjusting the initial spatialcoherence length. The dark hollow, flat-topped, and Gaussian beam spots can beobtained, which will be useful in trapping particles.