Study On The Focal Field Modulations Of Tightly Focused Radially Polarized Beam

Compared with the tightly focusing properties of scalar beams,cylindrical vector beams behave many novel properties when focused by a high numerical-aperture lens.Combined with the modulations of amplitude,phase and polarization on the incident cylindrical vector beams through a pupil filter on the pupil plane,many special optical distributions such as axial multiple foci,optical needle and focal array on the focal plane are able to be obtained in the vicinity of the geometrical focus of the lens,which meet with practical applications in micro and nano fabrication,microscopy imaging and particle manipulation.Hence,it is quite a meaningful issue to improve the properties of these special optical fields through designing pupil filter and further explore the potentials of tightly focused cylindrical vector beams.As one of cylindrical vector beams,radially polarized beam behaves strong longitudinal component near the focus under tightly focusing condition.This thesis focused on the modulations of radially polarized beam under tightly focused condition,in which different kinds of pupil filter were designed on the pupil plane to modulate the tightly focused field,and improve the modulation schemes of axial multiple foci,longitudinally polarized optical needle and foci array on the focal plane.The main contents of this thesis are as following:First,we studied the modulating approach for multiple foci on optical axis with controllable positions and intensity ratios.Here,we explored the design method for multi-belt diffractive optical element(DOE),and proposed a decomposed optimization method to solve the problem of designing multi-belt DOE with optimization.In this decomposed optimization,genetic algorithm was adopted and multi-belt DOE was decomposed to the combination of several sub-DOEs with less belts for optimization,which consequently reduced the optimization complexity and improved the solving efficiency.With this method,we optimized a series of multi-belt DOEs to modulate the tightly focused radially polarized beam,and three,five,seven and nine focal spots on the optical axis were obtained respectively.By varying the inner radius of DOE,that is adjusting the phase distributions on the DOE,we achieved multiple foci on the optical axis with controllable positions and intensity ratios.Then,we studied the modulating approach of longer,high uniform and longitudinally polarized optical needle.Here,we proposed a design method with the interferences between multiple foci on the optical axis and merged them to form an optical needle.In this method,we firstly modulated multifocal spots on the optical axis with similar intensity,shape and size through a multi-zone phase pupil filter;then we took advantage of the interference among multifocal spots and merged them to form an optical needle with high uniformity through optimizing multifocal positions with genetic algorithm.Meanwhile,the length of optical needle could be adjusted flexibly through changing the amount of multifocal spots,which met the requirements of designing longer,high uniform and longitudinally polarized optical needle or high uniform and longitudinally polarized optical needle with specified length.In the end,we studied the modulating approach for large-scale,high uniform foci array with weak side lobes on the focal plane.Here,we designed a complex pupil filter through manipulating pupil function,which modulated foci arrays on the focal plane with accurate focal positions,high uniformity and weak side lobes.The focal distributions can be adjusted through varying several parameters in the pupil function.Then,through multiplying several pupil functions,that is superposing several designed pupil filters to obtain a new complex filter,we found that large-scale multifocal arrays were modulated on the focal plane,and we further studied the modulating approach for large-scale,equidistant foci array.Considering the implementation complexity of designed complex pupil filter,at last we proposed a preliminary discussion on the implementation feasibility of this kind of complex filter with spatial light modulators.The modulating approaches proposed in this thesis for achieving axial multiple foci with controllable positions and intensity ratios,longer,high uniform and longitudinally polarized optical needle,and large-scale foci array with high uniformity and weak sides further tapped the tightly focusing properties of radially polarized beam,which also provided powerful theoretical basis for applications of cylindrical vector beams in many areas such as micro and nano fabrication,microscopy imaging and particle manipulations.