Planar binary-phase lens for super-oscillatory optical hollow needles

Optical hollow beams are suitable for materials processing, optical micromanipulation, microscopy, and optical lithography. However, conventional optical hollow beams are diffraction-limited. The generation of sub-wavelength optical hollow beams using a high numerical aperture objective lens and pupil filters has been theoretically proposed. Although sub-diffraction hollow spot has been reported, nondiffracting hollow beams of sub-diffraction transverse dimensions have not yet been experimentally demonstrated. Here, a planar lens based on binary-phase modulation is proposed to overcome these constraints. The lens has an ultra-long focal length of 300 λ . An azimuthally polarized optical hollow needle is experimentally demonstrated with a super-oscillatory transverse size (less than 0.38 λ /NA) of 0.34 λ to 0.42 λ , where λ is the working wavelength and NA is the lens numerical aperture, and a large depth of focus of 6.5 λ . For a sub-diffraction transverse size of 0.34 λ to 0.52 λ , the nondiffracting propagation distance of the proposed optical hollow needle is greater than 10 λ . Numerical simulation also reveals a good penetrability of the proposed optical hollow needle at an air-water interface, where the needle propagates through water with a doubled propagation distance and without loss of its super-oscillatory property. The proposed lens is suitable for nanofabrication, optical nanomanipulation, super-resolution imaging, and nanolithography applications.