The Focusing Properties Of Cylindrical Vector Beams

In recent years, there have been increasing interests in the tight focusing ofcylindrical vector beams, due to their unusual properties and potential applications ofthe resulting light configuration. Cylindrical vector light beam is a special vectorbeam with a cylindrical symmetry distribution of the intensity and polarization. Therehave been increasing interests in generation and tight focusing of light beams withradially and azimuthally polarized fields. They may find many applications, such asoptical trapping, material processing, particle acceleration and high-resolutionmicroscopy etc, due to their unusual properties.In this paper, we investigate the focusing properties of radially polarized andazimuthally polarized laser beams with different rings through a high numericalaperture objective. Numerical calculations are performed to compare the influence ofcorresponding parameters on the tight polarization properties.By using the Richards-Wolf vector diffraction theory, we investigate the propertiesof a double-ring-shaped azimuthally polarized beam that is tightly focused by anannular high numerical aperture objective. It is shown that sub-wavelength focal spotsof great application can be obtained near the focus, the influence of correlatedparameters of the incident beam and the maximal angle of the highnumerical-aperture objective are investigated in great detail. It is also found thatlonger depth of focus (nearly26) can be generated near the focus. These propertiesof this paper will have many significant applications.We investigate the focusing properties of double-ring-shaped azimuthally polarizedand radially polarized ultrashort pulsed laser beams. By using the Richards-Wolfvector diffraction theory, the intensity and the velocity of double-ring-shapedazimuthally polarized and radially polarized ultrashort pulsed laser beams werecalculated in great detail. It is shown that pulse velocity exceeds the velocity of lightin vacuumcoccurs near the focus. Moreover, theoretical analysis predicts that thevelocity at the focal point varies drastically with NA and correlated parameters,slower or faster than light speed in vacuum. It was shown that the spatial and temporal properties of a focused ultrashort laser pulse may influence the resolution ofa produced image, Moreover, we investigate the focusing properties of radiallypolarized ultrashort pulsed laser beams through a high numerical aperture objective. Itis shown that slow light phenomenon occurs near focus. This is, in the focus, theultrashort light pulse slows down near the focus. It is also shown that the differentfield components of the focused pulsed beams exhibit different speed.By using the Richards-Wolf vector diffraction theory, we investigate the focusingproperties of higher-order radially polarized laser beams through an high numericalaperture with a diffractive optical element. Expressions for the intensity distributionin the focal field are derived, and numerical calculations are performed to comparethe influence of corresponding parameters on the tight focusing properties. It isshown that3D optical chain along optical axis can be obtained near the focus byspatially modulating the phase of incoming beam. The influence of correlatedparameters of the incident beam and the maximal angle of the highnumerical-aperture objective are investigated in great detail.Based on the Collins formula, expressions of intensity distribution in the focalregion are derived, and the interaction forces between light and the Rayleigh particleusing the Rayleigh scattering theory. Numerical calculations are shown to comparethe different radiation forces of a partially coherent radially polarized doughnut beamand a partially coherent linear polarized beam. It is found that the radiation forces inthe focal field are obviously different with the different correlation width.