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.
The focusing spot beyond diffraction limit is critical to plasmonic direct-writing lithography. To improve the speed and precision of plasmonic direct-writing lithography, we design a new periodically repeated circular hole/elliptical ring plasmonic structure named as split-focusing structure used for producing two focusing spots under the incidence of linearly polarized plane wave at 633nm wavelength. It consists of SiO2 substrate and coated silver film with holes and slits of different shapes. By designing appropriate structure parameters to excite localized surface plasmon resonance, two split subwavelength spots are produced on the focal plane. Finite-difference time-domain (FDTD) method is used for numerical simulation. The simulation result indicates that the focal length of structure is 36nm and the full width at half maximum (FWHM) of single spot is 50nm. Both split spots can be used for direct writing so the speed of photoetching will be raised. The dual spots are both in circular shape, which is beneficial to improve the pattern precision. The influence of structure parameters on focusing performance is also analyzed to guide the practical fabrication of structure. The split-focusing structure designed in this paper also owns application values in data storage and non-contact sensing.
As the numerical aperture (NA) of the projection objective increases continually and the exposure pattern feature size decreases gradually, the polarization illumination is introduced into the lithography system. Therefore, it is necessary to design a wide field-of-view (FOV) wave plate to eliminate the effect of oblique incident light on the phase delay of the traditional zero order wave plate effectively. The quarter-wave plate with 20° FOV based on birefringent optical crystals has been designed in our laboratory by Dong et al. In order to obtain a wider FOV, we explore a previously reported Ag patch ultrathin quarter-wave plate whose performances were not analyzed by finite-difference time-domain (FDTD) method. In this paper, we mainly investigate three performances of the Ag patch quarter-wave plate consisting of FOV, achromatic band and achromatic band transmission. The simulation results indicate that when phase difference error is controlled at ±2° (1) the range of FOV of the quarter-wave plate is ±29° at 632nm; (2) the achromatic band ranges from 618nm to 658nm at normal incidence; (3) the achromatic band transmission ranges from 11% to 30%. Compared with the traditional wave plate made of birefringent crystals, the achromatic band and transmission is slightly lower but the FOV of this quarter-wave plate is much wider. Thus, this Ag patch nanoscale wide FOV quarter-wave plate can be effectively used in high NA lithography projection exposure systems to reduce the polarization aberration caused by oblique incidence of light.