Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica

Ultrafast light-material interactions near the damage threshold are often studied using postmortem analysis of damaged dielectric materials. Corresponding simulations of ultrashort pulse propagation through the material are frequently used to gain additional insight into the processes leading to such damage. However, comparison between such experimental and numerical results is often qualitative, and pulses near to but not exceeding the damage threshold leave no permanent changes in the material for postmortem analysis. In this article, a series of experiments is presented that measures the near- and far-field properties of a 140-fs laser pulse after propagation through a fused silica sample in which a noncritical electron plasma was generated. Concurrently, results from simulations in which the laser pulse was numerically constructed according to the nearfield beam profile and frequency resolved optical gating (FROG) trace are presented. It is found that to extract a quantitative comparison of such data, cylindrical symmetry of the laser pulse in simulations should be abandoned in favor of a fully $3+1\mathrm{D}$ Cartesian representation. Further comparison of experimental and calculated damage thresholds shows that time-corrective effects predicted by the Drude model play a critical role in the physics of both pulse evolution and plasma formation. The influence of resulting spatiotemporal dependences of the pulse in far-field measurements leads to unretrievable FROG traces. However, it is shown through both simulation and experiment that the use of an appropriate beam aperture will eliminate this effect when measuring the temporal pulse amplitude.

Figure 1

Experimental setup.

Figure 2

Single-shot damage thresholds (surface and bulk) as a function of collision time as determined by simulation for the full solution of Eq. (1) [solid (black) line], the solution of Eq. (1) where the operator $\widehat{G}=1$ [dashed (red) line], and the front surface damage threshold [dotted (blue) line]. Inset: Normalized Drude absorption cross section $\sigma$ as a function of collision time for an 800-nm field in fused silica.

Figure 3

Peak plasma densities generated in the $x$-$z$ ($y=0$) and $y$-$z$ ($x=0$) planes for (a, b) the 30-$\mu$J pulse without Drude dispersion corrections, (c, d) the 30-$\mu$J pulse with Drude dispersion corrections, and (e, f) the 80-$\mu$J pulse with Drude dispersion corrections.

Figure 4

Isometric surface plot of the peak plasma density value, ${10}^{20}$ cm${}^{-3}$, as a function of the spatial coordinates in the material, for the case of an 80-$\mu$J single-shot laser pulse.

Figure 5

Normalized beam profiles. (a) measured beam profile before the first lens. (b) Simulated beam profile before the first lens. (c) Measured beam profile with a pulse energy of 10 $\mu$J. (d) Simulated beam profile with a pulse energy of 10 $\mu$J. (e) Measured beam profile for 80 $\mu$J. (f) Ssimulated beam profile for 80 $\mu$J.

Figure 6

(a) Normalized simulated beam profile of the 80-$\mu$J pulse immediately after the sample and (b) simulated 80-$\mu$J beam profile after the recollimating lens if a 25-$\mu$m radial block [see white circle in (a)] is applied immediately after the sample.

Figure 7

Amplitude and phase of the complex field at $y=0$ after the sample. Amplitude and phase (a, b) for 1 $\mu$J input pulse energy, (c, d) for 10 $\mu$J input pulse energy, (e, f) for 22 $\mu$J input pulse energy, and (g, h) for 50 $\mu$J input pulse energy.

Figure 8

Amplitude and phase of the field at the center of the beam (a) at the rear sample surface, (b) when a 25.4-mm (1-in.) aperture is applied, and (c) when a 4-mm aperture is applied. All amplitudes are normalized to the small front pulse at the left. Plots of different colors represent initial pulse energies of 1 $\mu$J [dotted (black) curve], 10 $\mu$J [dashed (gray) curve], 22 $\mu$J [dashed (black) curve], 35 $\mu$J [solid (gray) curve], and 50 $\mu$J [solid (black) curve].

Figure 9

Measured and retrieved FROG traces for a pulse energy of (a, b) 10 $\mu$J, (c, d) 40 $\mu$J, and (e, f) 45 $\mu$J. The destruction threshold of the sample was observed at 45 $\mu$J (3.8 J/cm${}^2$).

Figure 10

Measured FROG traces with the corresponding autocorrelation signals (solid line) and FROG traces found from the solution for an apertured beam. (Measured and retrieved FROG traces for a pulse energy of (a, b) 1 $\mu$J, (c, d) 10 $\mu$J, (e, f) 35 $\mu$J, and (g, h) 46 $\mu$J. The destruction threshold for this sequence was 55 $\mu$J (4.7 J/cm${}^2$). Complex field solutions for this set are shown in Fig. 11.

Figure 11

Complex field amplitude (bottom plots) and phase (top plots) retrieved from FROG traces (shown in Fig. 10) measured for different pulse energies. The front of the pulse is on the left (earlier in time). Errors for the retrieval processes are listed in Table .