Study On Tightly Focusing Characteristics Of Hollow Cylindrical Vector Beams

Cylindrical vector beams, which can be decomposed into radially polarized and azimuthally polarized components, possess axial symmetry in polarization. Recently, tightly focusing performances of the cylindrical vector beams have attracted singnificant attention. These unique properties can be extensively utilized for high-density data storage, second-harmonic generation, Raman spectroscopy, particle manipulation, nanolithography, laser cutting, material processing, particle acceleration, high-resolution imaging, all-optical magnetic recording and spin wave operations, etc. Therefore, it is of great practical significance to explore and optimize the tightly focusing performances of the cylindrical vector beams. In this thesis, based on the vector diffraction theory and the inverse Faraday effect, we study systematically, respectively, the tightly focusing properties associated with both the optical field and light induced magnetization field of hollow radially polarized beams, azimuthally polarized beams, radially polarized vortex beams and azimuthally polarized vortex beams by means of the modulation of special binary filters and interference effect to optical wavefront. The primary research contents are as follows:On the basis of the vector diffraction theory, we explore tightly focused hollow radially polarized beams that can form subwavelength longitudinally polarized optical needle. The tightly focusing performances of radially polarized LBG beams, LG and BG modes are compared in a clear aperture. To improve the focusing performances, special three-ring phase filters are designed and optimized. Moreover, the effects of the proposed three-ring phase filter on the focusing performances of the radially polarized LBG beams are discussed, as well as the mechanism to form both longitudinally polarized optical needle with subwavelength latral size and dark hollow field with wavelength scale are illustrated. Based on Rayleigh scattering theory, the radiation forces on the particles with different refractive indexes exerted by these two kinds of special field structures are calculated, and the conditions to stably trap two types of particles are analyzed. To obtain rich focused structures simultaneously, a systematic study on the tightly focusing performances of radially polarized HG beams with various beam orders is performed. Firstly, the dependence of values of the transverse full width at half maximum on the beam order and truncation parameter is given, and the condition for generating a flat-topped beam is dissected. Additionally, special five-ring phase filters are designed by using the global search optimization algorithm, thus super-resolution longitudinally polarized optical needle is created. Finally, in view of self-design three-ring amplitude filters, we simulate numerically that the impacts of different beam orders on the tightly focusing features of the radially polarized HG beams. The reasons to develop a quasi-periodic optical chain and super-resolution longitudinally polarized light needle with long focal depth are elaborated with the aid of interference theory.Realization of subwavelength transversally polarized optical needle by tightly focused hollow azimuthally polarized beams is researched. The effects of variant truncation parameters and polarization states on the tightl y focusing features of double-ring-shaped azimuthally LG polarized vortex beams are dissected. To suppress the side lobe effectively and eliminate focal shift, seven-ring vortex complex filters are designed by virture of the global search optimization algorithm. Under such a circumstance, the transversally polarized light needle with super-resolution scale and long focal depth can also be obtained. The spatial variation regulation of the azimuthal angle and the ellip ticity is obtained by calculating the Stokes polarization parameters, which further validate that the polarization orientation of the focal field is transverse.Creation of three-dimensional super-resolution transversally polarized field by 4π high numerical aperture focusing radially polarized HG vortex beams is investigated. We firstly study the dependence of focusing characteristics on the beam order in the case of single-objective high numerical aperture focusing configuration. In order to form a subwavelength transversally polarized focal spot, the use of 4π high numerical aperture objective to focusing the radially polarized HG vortex beams is presented. Based on the interference traits between various components of two counter-propogating HG vortex beams, the physical mechanisms to achieve three-dimensional super-resolution transversally polarized field are clarified qualitatively. Also, the local field with transversal polarization is further validated by calculating the average field distributions. To illustrate the reasonableness of the numerical simulation results, the analytical expressions on the field distributions of 4π high numerical aperture focusing radially polarized HG vortex beams are deduced.Based on vector diffraction theory and inverse Faraday effect, we explore that pure longitudinal magnetization field can be created by tightly focusing hollow cylindrical vector and vortex beams. Firstly, the generation of purely longitudinally polarized magnetization needle with subwavelength lateral size and super-long focal depth by tightly focusing azimuthally polarized Airy vortex beams is examined. We also analyze the influences of the radius of the primary ring and the scaling factor of Airy beams, and the vortex direction of spiral phase plate on magnetization field distributions. Moreover, in order to effectively manipulate and transport multiple atoms and efficiently record and store multi-layer magneto-optic data, the formation of single/double channel pure longitudinal polarized magnetization chain with subwavelength lateral size by adopting special vortex annular filters is proposed for the first time. We discuss the modulation of the phase difference between inner circle and outer ring on moving direction and distance of the proposed magnetization chains. Finally, we propose that pure longitudinal magnetization field with three-dimensional super-resolution can be induced by 4π high numerical aperture objectives focusing radially polarized HG vortex beams, and the physical mechanisms of the well-defined magnetization distribution are elucidated in three aspects. Also, the light-induced magnetization with locally longitudinal polarization is further verified by calculating the average magnetization distributions. The dependence of the values of transversal and axial full width at half maximum on the beam order and the truncation parameter is explored, which makes spherical and subwavelength longitudinal magnetization field possible.