{'fraction_non_alphanumeric': 0.021534320323014805, 'fraction_numerical': 0.0, 'mean_word_length': 5.642857142857143, '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}}
Nonparaxial free-space diffraction from oblique end faces of single-mode optical fibers.

We investigate free-space diffraction of light that emanates from obliquely cleaved end faces of single-mode fibers. Emphasis is placed on precise prediction of the wave-front sphericity of fiber-generating waves in the nonparaxial Fresnel propagation region spanning an entire hemispherical observation surface. Rayleigh-Sommerfeld scalar diffraction theory is used to produce an analytic closed-form solution with a nonparaxial approximation. The result allows the wave front's sphericity and the amplitude distribution of fiber-generating waves to be evaluated precisely with less computation than for existing numerical or infinite-series solutions.