Measurements of fluence profiles in femtosecond laser sparks and superfilaments in air

We investigate the nonlinear propagation of multiterawatt femtosecond laser pulses at 800 nm wavelength in air, under different external focusing conditions. We profile the laser beam in the vicinity of the nonlinear focus using a technique based on the dependence of the single-shot ablation threshold for gold on the angle of incidence of the laser beam on the sample. Under very tight focusing conditions ($\mathit{f}$ number $\sim 15$) we observe the propagation regime reminiscent of the nanosecond optical breakdown. No clear individual filaments are formed across the beam, and the estimated peak intensity surges to at least $200\mathrm{TW}/{\mathrm{cm}}^2$. As the external focusing is loosened to $\mathit{f}$ number $\sim 125$, we observe the transition to the multifilamentation regime. Distinct individual filaments are formed before the linear focus while the peak intensity reaches $\sim 80\mathrm{TW}/{\mathrm{cm}}^2$. Once formed, the filaments do not coalesce into a single or few superfilaments as they pass through the focus zone. Our experimental observations are supported by numerical simulations.

Figure 1

Experimental beam profiles at different intensity levels and at different longitudinal positions relative to the linear focus of the lens for the case of very tight beam focusing with an $f$ number of about 15. The energy of the 40-fs-long input laser pulse is 100 mJ. No clear individual filaments are formed on propagation. Instead, the intensity relatively uniformly surges to at least $200\mathrm{TW}/{\mathrm{cm}}^2$.

Figure 2

Results of numerical simulations for the case with very tight external beam focusing, corresponding to the experimental results shown in Fig. 1. The ring intensity structure formed after the linear focus is the artifact of the constant-temporal-envelope approximation used in the numerical model, as discussed in the text.

Figure 3

Same as in Fig. 1, but with external beam focusing loosened to the $f$ number of about 125 and the laser-pulse energy of 120 mJ. The beam patterns show the formation of multiple individual filaments with a diameter of $\sim 100\mu \mathrm{m}$ and peak intensity reaching $80\mathrm{TW}/{\mathrm{cm}}^2$. As these filaments travel through the focus zone, an intensity pedestal builds up to the relatively high level of about $40\mathrm{TW}/{\mathrm{cm}}^2$, but the individual filaments on top of the pedestal do not coalesce into one or few superfilaments.

Figure 4

Results of numerical simulations for the case with moderately strong focusing, shown in Fig. 3. Computed beam-intensity patterns are in semiquantitative agreement with those experimentally measured.