Vortex beams have drawn much attention for their distinct properties. When vortex beams propagate along optical axis, they exhibit complicated physical phenomena. Under tight focusing condition, we investigate the defocusing behavior of two superposed vortex beams with opposite but arbitrary topological charge. The results reveal that the intensity distribution of the focus will be petal-shaped if the two topological charges have opposite sign, where the number of intensity lobes in the focal plane is |m− n + 2| . Meanwhile, we find that the focusing intensity of topological charge m = −n would not appear the helical structure when a defocusing occurs. Otherwise, the defocusing would result in the helical structure of intensity when m ≠ −n , and the rotation of helical structure depends on the sign of m + n . Of which clockwise rotation of defocus intensity is related to the negative m + n , and anti-clockwise direction corresponds to the positive m + n . Furthermore, the helical degree of the helical intensity also depends on the magnitude of m + n . The interesting results obtained in this paper will lead to further advances in the field of optical vortices.
Optical vortices have been applied in many fields for their distinct properties. In this paper, we explore the focusing intensity distribution of the radially and azimuthally polarized vortex beam (VB) with varying beam waist parameter. The results reveal that low beam waist parameter is beneficial to form a super-resolution spot. In the condition of the high beam waist parameter, the focusing intensity of radially and azimuthally polarized VB along the longitudinal direction would split to multi-spots. Meanwhile, the focal plane intensity distribution become non-symmetrical as well as expansion when the beam waist parameter increase. Therefore, appropriate beam waist must be chosen for the two kind beam in actually application. Furthermore, we also investigate the focal properties affected with helical phase TC. The results reveal that the focal spot size of radially polarized VB along the longitudinal gradually increases with the order of helical phase. The peak intensity ratio of the longitudinal and transverse field of radially polarized VB holds a maximum value when helical phase order l = 0 and becomes to minimum when l =1 , then gradually increases with the order of helical phase. For the azimuthally polarized VB, when l =1 , the focal intensity would exhibit an excellent small solid spot. The results obtained in this paper are useful for application of radially and azimuthally polarized VB.
Based on concept of eye space, we proposed an idea to achieve multi-view autostereoscopic display with densest viewpoints (for largest tolerance) which reaches physical limitation of density. The physical limitation of separation between two neighboring view-points is one eye spacing for largest tolerance in binocular view based display; the display can be achieved by using light-shutter-screen with fast-enough-switching and a circuit hardware called address driving matrix. The idea is applied for both binocular view based and depth map based display. For the former (binocular view), one shutter screen is placed at front of 2D-display screen with address driving matrix and two video streams of left and right eyes; for the latter (not binocular view, a kind of quasi-holography display), two shutter screens are placed at front of 2D-display screen with one 2D video stream and one depth map (depth map can be generated from two video streams of left and right eye or be obtained from a depth camera), in this case, each of all screens (besides each of shutter screens, 2D-display screen also) need separate address driving matrix, and the physical limitation of separation of view-points is further reduced to half of eye spacing for largest tolerance. Current technologies are ready for building the address driving matrix, but not ready yet for the fast- enough-switching, for example, current LCD is not fast enough for this purpose. Therefore, this will bring many challenges and new opportunities for those physicist and engineers who work in area of fast light switch (not only limited in LCD), besides in autostereoscopic display.