Mechanisms of third harmonic generation through pulse cumulative effect from femtosecond laser filament in air

We experimentally observed a spectral broadening of the third harmonic in the long-wavelength range accompanied by intensity enhancement as the laser repetition rates increased. A correction for the simulation of the third harmonic at different repetition rates is proposed. Simulation and analysis confirm that the pulse accumulation effect changes the spatiotemporal evolution of the electric field within the filament, thus enhancing the cross-phase modulation and self-phase modulation of the third harmonic, leading to the broadening of the third harmonic, with a quantitative analysis establishing the cross-phase modulation as the dominant mechanism. These findings provide a comprehensive physical framework for understanding third harmonic generation in a high-repetition-rate filament. The demonstrated repetition-rate-dependent mechanism presents new opportunities for advancing intense UV pulse generation techniques, with promising applications in precision laser machining and remote UV detection technology.