{'fraction_non_alphanumeric': 0.023117569352708058, 'fraction_numerical': 0.0066050198150594455, 'mean_word_length': 5.158536585365853, '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}}
Optical vortex lasers by the coherent superposition of off-axis multiple-pass transverse modes in an azimuthal symmetry breaking laser resonator

Optical vortex (OV) laser is generated by the superposition of coherently phase-locked off-axis laser beamlets in a nearly semi-spherical optical resonator with intra-cavity azimuthal symmetry breaking (ASB) optics. Due to the ASB, this laser resonator rejects radiation to resonate on-axis but supports off-axis beamlets belonging to the multiple-pass transverse (MPT) modes. These independent off-axis MPT modes, which are experimentally proven to retrace V-shaped paths in the resonator span ring-shaped intensity distribution and are coherently phase-locked to form an OV with a wavefront dislocation mirroring the topological charge (TC) of the ASB optics. Pumped by a conventional diode laser without critical beam shaping, we successfully generate randomly polarized OV having an annular intensity distribution and a positive unit TC of more than 99.9% at a central wavelength of 1064 nm when the power of pump laser goes above 1.52 W. The build-up of the deterministic phase relation among the independent MPT modes is demonstrated by spatial coherence measurement of the laser from a perturbed ASB resonator. This ASB resonator not only provides an easy approach to generate intrinsic vortex laser with power scalability but also serves as an useful platform to shape laser beams structurally, to study the laser dynamics and to combine radiations coherently.