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 |<i>m</i>− <i>n</i> + 2| . Meanwhile, we find that the focusing intensity of topological charge <i>m</i> = −<i>n</i> would not appear the helical structure when a defocusing occurs. Otherwise, the defocusing would result in the helical structure of intensity when <i>m</i> ≠ −<i>n</i> , and the rotation of helical structure depends on the sign of <i>m</i> + <i>n</i> . Of which clockwise rotation of defocus intensity is related to the negative <i>m</i> + <i>n</i> , and anti-clockwise direction corresponds to the positive <i>m</i> + <i>n</i> . Furthermore, the helical degree of the helical intensity also depends on the magnitude of <i>m</i> + <i>n</i> . 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.
Currently, the deteriorated lithography imaging caused by polarization aberration is increasingly prominent. Therefore
measuring the polarization aberration accurately also becomes important. However, traditional polarization aberration
measurement techniques integrated with complex apparatus such as polarimetry and polarizer which result in high cost
for lithography tools. An in situ measurement technique of polarization aberration in hyper numerical aperture (NA)
lithographic tools from the aerial image is proposed in this paper. As the polarization aberration can be decomposed into
scalar phase, apodization, retardation and diattenuation, the first two items are firstly represented by Zernike coefficients
of scalar Zernike polynomials, and the last two items are represented by Zernike coefficients of orientation Zernike
polynomials. Secondly, the linear relationships between the aerial image and the Zernike coefficients of these four items
are established from the rigorous vector imaging theory. Finally, the polarization aberration can be easily obtained by
using above relationships after the aerial images of test marks in different orientations and pitches under different
illumination settings are accurately measured. In addition, the validity of linear relationships and the performance of
proposed technique are clearly demonstrated by numerical simulation for an immersion projector with NA1.35. It is fully
expected that the proposed technique will simple to implement and will be applicable for retrieving the polarization
aberration of projector with hyper-NA.