{'fraction_non_alphanumeric': 0.029411764705882353, 'fraction_numerical': 0.0028011204481792717, 'mean_word_length': 5.008403361344538, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Creation of super-resolution hollow beams with long depth of focus using binary optics

In this letter, we propose a method for designing super-resolution hollow beams (SHBs) with long depth of focus (DOF) using an M-ring 0-π pure-phase binary optical element (BOE) and a focusing lens when a linearly polarized Bessel–Gaussian beam incident. We also introduce a custom-made method for SHBs with long DOF to iteratively obtain optimal 0-π phase distribution. Moreover, it is shown that the hollow beams can provide great flexibility by controlling spot size and DOF through adjustment of the BOE parameters, including different ring numbers and positions, and also have significant potential for particle trapping.