{'fraction_non_alphanumeric': 0.011904761904761904, 'fraction_numerical': 0.0, 'mean_word_length': 5.138686131386861, '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}}
Transverse modes of a laser resonator with Gaussian mirrors.

Analytical methods are presented for transverse mode analysis of a laser resonator having spherical mirrors with a Gaussian reflectivity profile. The modes of this type of resonator have a form similar to that of the conventional Gaussian modes, but it is necessary to define an additional beam parameter to meet the self-consistency requirement for resonator modes. Stability of both the conventional complex beam parameter and the additional parameter is discussed. It is predicted mathematically that small perturbations in the new beam parameter will cause the intensity profile of the higher-order modes to evolve into that of the fundamental mode. Mode losses and discrimination are also discussed. The results may be useful in the design of regenerative laser amplifiers.