Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters

When the pupil filters are used to improve the performance of the imaging system, the conversion efficiency is a critical characteristic for real applications. Here, in order to take full advantage of the subwavelength focusing property of the radially polarized higher-order Laguerre-Gaussian (LG) beam, we introduce the multi-zone binary phase pupil filters into the imaging system to deal with the problem that the focal spot is split along the z axis for the small size parameter of the incident LG beam. We provide an easy-to-perform procedure for the design of multi-zone binary phase pupil filters, where the zone numbers of π phase are uncertain when the optimizing procedure starts. Based on this optimizing procedure, we successfully find the set of optimum structures of a seventeen-belt binary phase pupil filters and generate the excellent focal spot, where the depth of focus, the focal spot transverse size, the Strehl ratio, and the sidelobe intensity are 9.53λ, 0.41λ, 41.75% and 16.35% in vacuum, respectively. Most importantly, even allowing the power loss of the incident LG beam truncated by the pupil of the imaging system, the conversion efficiency is still as high as 37.3%. Theoretical calculations show that we succeed to have sufficient conversion efficiency while utilizing the pupil filters to decrease the focal spot and extend the depth of focus.