Tightly Focusing Properties Of Vortex Beams

Researches on and applications of the optical vortex beams have recently generated great research interest, which has resulted in a new branch of singular optics in modern optics. Optical vortex beams possess wave-front dislocations where the phase values are undefined (also referred to as phase singularities) and the amplitude vanishes to zero. Such beams can be generated by using the spatial light modulators or the spatial phases plates, and possess a helical phase structure. It has been known that such vortex beams carry orbital angular momentum and can be applied to trap and rotate particles and related applications. And the dark optical vortices can become the physical instrument to create optical vortex tweezers. The unique and novel properties of vortex beams have opened a variety of new possibilities for singular optics applications. So it is of great theoretical and realistic significance to investigate the propagation properties of vortex beams.The vectorial Debye diffraction integral method is introduced in the first chapter. Since Bessel-Gaussian (BG) beams of the non-zero order can be set as vortex beams, the tightly focusing properties of BG beams of the non-zero order under several conditions are studied in detail.The focusing properties of cylindrically polarized BG beams focused by a high numerical-aperture objective is studied. The light field expressions of cylindrically polarized BG beams focused by a high numerical-aperture objective are derived. Numerical calculations are taken to analyze the influences of varying values of the parameters on the light intensity distribution at the focal plane and in the vicinity of focus. By adjusting the values of corresponding parameters, the intensity distribution in the focal region can be controlled, and bottle beams and flat-topped beams are obtained which possess the characteristics of vortex and will have many significant applications.The tightly focusing of vortex beams through a dielectric interface and an uniaxial birefringent crystal are investigated. For the tightly focusing of linearly polarized vortex beams through a dielectric interface, the intensity distribution near the focus is analyzed by performing numerical calculations. The influences of numerical aperture (NA) of the objective and the probe depth on the focal shift are discussed. And the dependence of the intensity distribution in the cross section of the beams on the propagation distance z is also studied. For the tightly focusing of radially and azimuthally polarized vortex beams through a dielectric interface, the influence of NA on the full width at half maximum of the focal spot and focal hole is analyzed. The tightly focusing of radially and azimuthally polarized vortex beams through a unaxial birefringent crystal is studied under the approximation of small birefringence. The contour plots of intensity distribution near the focus and in the real focal plane are illustrated by performing numerical calculations. Moreover, the Strehl ratio in the real focal plane as a function of birefringence is also analyzed.The focusing properties of partially coherent BG beams through a high NA objective are studied based on vectorial Debye theory. Expressions of intensity distribution, degree of coherence and degree of polarization are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the distribution of intensity, degree of coherence and degree of polarization in the focal region. It is shown that the intensity, degree of coherence and degree of polarization in the focal region are all influenced by varying effective coherent length of incident beams and maximal angle determined by the NA of the objective. And the linearly polarized incident field is found to be depolarized after focused by a high NA objective.The expressions for distribution of light field and orbital angular momentum (OAM) of tightly focused vortex beams have been derived. Distribution of phase and OAM of tightly focused vortex beams are investigated. The phase distribution of the field component in the x direction near focus is typically analyzed by presenting phase contours. Moreover, the dependence of distribution of phase contours and OAM in the focal plane on NA has been shown. And the distribution of OAM along the z-axis is studied, finding that the optimal location for applications of OAM of vortex beams along the z-axis is just near the focal plane.