{'fraction_non_alphanumeric': 0.022082018927444796, 'fraction_numerical': 0.0015772870662460567, 'mean_word_length': 5.414141414141414, '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}}
Minimal dispersion refractive index profiles.

The analogy between optics and quantum mechanics is exploited by considering a 2-D quantum system whose Schroedinger equation is closely related to the wave equation for light propagation in an optical fiber. From this viewpoint, Marcatili's condition for minimal-dispersion-refractive-index profiles, and the Olshansky- Keck formula for rms pulse spreading in an alpha-profile fiber may be derived without recourse to the WKB approximation. Besides affording physical insight into these results, the present approach points out a possible limitation in their application to real fibers.