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Critical Power for Temporal-Pulse Collapse in Third-Harmonic Generation

The self-trapping critical power of light propagation is one of the key physical quantities characterizing nonlinear-beam propagation. Above the critical power, the spatial and temporal profiles of the beam deviate from its original shapes. Therefore, the critical power is considered an important indicator in nonlinear optical phenomena, such as filamentation and laser processing. However, although the concept of the critical power has been established for fundamental waves, it remains unclear if the power-dependent phenomena can also be observed in harmonic generation because of the complex interplay of nonlinear-propagation effects and ionization-plasma effects. In this study, we find the critical power for the third-harmonic generation; the criterion for whether or not temporal-pulse collapse occurs in the third-harmonic generation is determined only by the incident power. Experiments show that a certain incident power exists, at which the third-harmonic power exerts a specific dependence, independent of the focusing conditions. This incident power is approximately six times lower than the self-trapping critical power of the fundamental pulse, which indicates that it is unique to the third-harmonic generation. Numerical calculations reveal that at this incident power, the third-harmonic pulse begins to collapse temporally. Furthermore, the numerical calculations reproduce the experimental results without the nonlinear effects of the fundamental pulse, dispersion effect, and ionization-plasma effects. This shows that the pulse collapse is due to the interference effects from the third-order nonlinear term, which disappears after long-distance propagation due to phase mismatch, and higher-order nonlinear terms. This study demonstrates the existence of the critical power for harmonic pulses and show that higher-order nonlinear effects on the harmonics can yield a universal phenomenon.