{'fraction_non_alphanumeric': 0.01726263871763255, 'fraction_numerical': 0.0, 'mean_word_length': 5.151515151515151, '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}}
Numerical simulation of Fresnel-regime wave propagation: the light-tube model

The numerical simulation of the propagation of optical wave fields for large propagation distances can require increasingly larger numbers of numerical samples because of the diffraction spreading of the wave. Such spreading can be avoided if a positive lens is used to confine the propagating field to a tube between input and back focal plane. A one-to-one mapping allows the confined light-tube propagation to be substituted for the unconfined free-space propagation, with a resulting reduction in number of samples required. With proper choice of lens focal length, the number of samples needed for propagation from input to far field remains essentially constant at approximately twice the space-bandwidth product of the input.