{'fraction_non_alphanumeric': 0.07701421800947868, 'fraction_numerical': 0.008293838862559242, 'mean_word_length': 5.401515151515151, 'pattern_counts': {'":': 0, '<': 16, '<?xml version=': 0, '>': 17, '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}}
Laser Self-Focusing and Nonlinear Absorption in Expanding Clusters

An intense short-pulse laser, propagating through a clustered gas, converts the clusters into hot plasma balls on subpicosecond time scale. The polarizability of a ball scales as (omega<sub>pe</sub> <sup>2</sup>/3 - omega<sub>2</sub>)<sup>-2</sup>, where omega<sub>pe</sub> is the plasma frequency inside it and omega is the laser frequency. Initially, omega<sub>pe</sub> <sup>2</sup>/3 > omega<sup>2</sup>; however, as the clusters expand under hydrodynamic pressure, decreases, causing resonant enhancement in permittivity, first near the laser axis and later away from it. The nonuniform refractive index profile thus created leads to self-focusing of the laser. It also leads to enhanced absorption in its neighborhood that counters the self-focusing effect substantially.