{'fraction_non_alphanumeric': 0.030456852791878174, 'fraction_numerical': 0.005076142131979695, 'mean_word_length': 5.069230769230769, '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}}
Lens coupling in fiber-optic devices: efficiency limits.

GRIN-rod lenses, ball lenses, and plano-convex rod lenses are currently proposed for fiber-optic devices. From analyses of the aberrations of these lens types it turned out that equivalent lenses in a well-designed coupling have nearly the same aberration. We derive valuable relations between the coupling efficiency and the optimal lens parameters. For each above-mentioned lens type, coupling efficiencies of 95% (0.2-dB insertion loss) can be obtained if typical communication fibers are incorporated. We also present a lens connector that has been fabricated in a factory-type production line. Its performance reaches the theoretical limits. Finally the influence of misalignments in the lens coupling system is investigated.