A paraxial theory of third harmonic generation by a finite spot size laser in a tunnel ionizing gas is developed. The laser, with intensity close to tunnel ionization threshold, creates plasma whose density rises in a stepwise manner in every half wave period, giving a strong second harmonic component in electron density. The density beats with the oscillatory velocity at the fundamental to produce a nonlinear current, driving the third harmonic. The region of harmonic generation is localized near the laser axis. Further, the strong radial nonuniformity, created in electron density by the ionization process, causes defocusing of the laser, limiting the efficiency of harmonic generation.
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Verma et al. (2009) studied this question.
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