{'fraction_non_alphanumeric': 0.01287128712871287, 'fraction_numerical': 0.0, 'mean_word_length': 4.777142857142858, '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}}
Diffraction catastrophes and wave caustics of multimode fibers

A set of interference ring patterns is formed by two laser beams after the Mach-Zander interferometer. The first of these beams passes along a short multimode fiber. This fiber is excited by off-axis rays. The second field is a referent Gaussian beam. The reference beam is set near a cusped point of a wave caustics. A conversion of a single ring interference pattern into three ring interference patterns is the result of the displacement of the Gaussian beam near the vicinity of the cusped point. There is only one degenerated ring-interference pattern in an interior caustic region. This optical phenomenon turns out to be a bifurcational process which could be explained by means of the interference between the quasiplane wave having a wavefront with the singularity region in the form of the Whitney's cusp and the Gaussian beam. A model theoretical computation of wave caustics interference and a fundamental Gaussian beam has been done.