{'fraction_non_alphanumeric': 0.01303538175046555, 'fraction_numerical': 0.0, 'mean_word_length': 5.554878048780488, '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}}
Multiphoton excitation of fluorescence in spherical particles: angular distribution of scattered radiation

The angular distribution of spontaneous fluorescence excited inside a spherical microparticle by femtosecond laser radiation is considered. The distribution of the internal optical field of a particle is investigated at the multiphoton excitation of fluorescence. The position and the effective volume of fluorescence sources in a particle are calculated numerically as functions of the particle radius in the cases of one-, two-, and three-photon excited fluorescence. The equation determining the relation between the mean brightness of fluorescence from the front and rear hemispheres of a particle is derived within the framework of geometric optics. It is shown that if a fluorescence source is located near the shadow hemisphere of a particle, asymmetry appears in the angular distribution of spontaneous fluorescence in the forward and backward directions. This asymmetry becomes more pronounced, as the number of photons taking part in the process increases.