{'fraction_non_alphanumeric': 0.016726403823178016, 'fraction_numerical': 0.005973715651135006, 'mean_word_length': 4.86013986013986, '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}}
Improved coupled-mode theory of directional couplers

In this letter, we present an improved coupled-mode theory applied to the optical-fiber directional coupler with a large overlap between the evanescent electromagnetic fields of two fibers. The analysis is based on a method of the quantum mechanics for the hydrogen molecule ion, where a new couple of local orthogonal modes corresponding to the fiber 1 and 2 are introduced. We may obtain the coupled-mode equations of local modes and the simple formulas of the output powers from coupler, in which, the overlap integral between the evanescent fields of two fibers is taken account of as an second order approximation. A new conclusion from this theory is that a coupling ratio with 100% can't be reached for a lossless coupler with a sufficiently small distance between two fibers.