Optical probing of ultrafast laser-induced solid-to-overdense-plasma transitions

Abstract

Understanding the solid target dynamics resulting from the interaction with an ultrashort laser pulse is a challenging fundamental multi-physics problem involving atomic and solid-state physics, plasma physics, and laser physics. Knowledge of the initial interplay of the underlying processes is essential to many applications ranging from low-power laser regimes like laser-induced ablation to high-power laser regimes like laser-driven ion acceleration. Accessing the properties of the so-called pre-plasma formed as the laser pulse's rising edge ionizes the target is complicated from the theoretical and experimental point of view, and many aspects of this laser-induced transition from solid to overdense plasma over picosecond timescales are still open questions. On the one hand, laser-driven ion acceleration requires precise control of the pre-plasma because the efficiency of the acceleration process crucially depends on the target properties at the arrival of the relativistic intensity peak of the pulse. On the other hand, efficient laser ablation requires, for example, preventing the so-called "plasma shielding". By capturing the dynamics of the initial stage of the interaction, we report on a detailed visualization of the pre-plasma formation and evolution. Nanometer-thin diamond-like carbon foils are shown to transition from solid to plasma during the laser rising edge with intensities < 10¹⁶ W/cm². Single-shot near-infrared probe transmission measurements evidence sub-picosecond dynamics of an expanding plasma with densities above 10²³ cm^-3 (about 100 times the critical plasma density). The complementarity of a solid-state interaction model and kinetic plasma description provides deep insight into the interplay of initial ionization, collisions, and expansion.

Fig. 1. Single-shot space and time-resolved probe transmission measurement.

a The pump laser’s temporal intensity contrast. The color-shaded regions (1) and (2) are related to the modeling discussed in Fig. 2e. The feature at $t_{\mathrm{pump}}~-5\mathrm{ps}$ is an artifact from the measurement, cf. Materials and methods. b The experimental arrangement. The pump pulse is focused at normal incidence on the target, while the probe pulse is obliquely incident under an angle $\alpha =37^{\circ }$. The inset shows the pump focus’s normalized spatial intensity profile. c 1D-spatially and temporally resolved relative transmission $T_r$ of the probe for a 10 nm-thick DLC foil measured using a 1D-spatially resolving (SR) imaging spectrometer and a chirped probe pulse. The wavelength on the top axis is converted into time on the bottom axis where $t_{\mathrm{p}robe}=0\mathrm{p}s$ is arbitrarily chosen and corresponds to the arrival of the probe wavelength λ ≈ 920 nm. The inserted yellow curve is the normalized spatial intensity profile of the pump pulse in the transverse y-direction (cf. inset in b)

Fig. 2. Measured and computed probe absolute transmission T(t) through the interaction region (y = 0 µm) induced by the pump laser pulse on DLC foils, and the calculated plasma electron densities.

a–d Measured (blue) and calculated (red) $T\left(t\right)$ for DLC foils of thicknesses from 5 to 50 nm. The measurements are averaged over four shots with peak intensities $I_{\mathrm{p}eak}~{10}^{15}-{10}^{16}{\mathrm{W/cm}}^2$. The blue shaded region is the standard deviation over all shots for each foil. The red curve is computed using the TSI model with $I_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}\sim {10}^{15}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ and plotted as a function of $t_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$. The measured and calculated curves are aligned at their inflection points where the relative transmission is 50 %. The red arrows delimit the time intervals for SSI and PIC steps in the TSI model. e Computed time-dependent probe transmission for different interaction models for different DLC foil thicknesses (5 nm: black, 10 nm: red, 20 nm: blue and 50 nm: green): the dashed line, the triangles and the solid line correspond to PIC only, SSI only (up to $n_e$ ≈ ${20n}_c$) and the TSI model, respectively. The blue and orange arrows correspond to the time intervals given by the shaded regions with the same colors in the laser temporal intensity profile in Fig. 1a. f Maximum electron densities $n_e^{\max }$ as a function of $t_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$ corresponding to the different simulations shown in (e). The density obtained from the SSI model does not depend on the foil thickness by construction and is therefore shown in violet. The shaded grey regions in (e) and (f) indicate where the extended SSI model (up to $n_e$ ≈ ${70n}_c$) was used

Fig. 3. Computed plasma properties during the interaction from the TSI model for DLC foils of 5 and 50 nm thicknesses.

Here, the pump laser propagates in positive z-direction. a Time-dependent electron density from the SSI model, lattice ($T_l$), and electron ($T_e$) temperatures from the TTM model for all thicknesses and $T_e$ for 5 and 50 nm thicknesses from PIC simulations. b and c show the spatiotemporal dynamics of the electron and the carbon ion densities for 5 and 50 nm thick foils, respectively. The black and green dashed lines correspond to maximum electron densities $n_e^{\max }$ as a function of $t_{\mathrm{p}\mathrm{u}\mathrm{m}\mathrm{p}}$ for 5 nm and 50 nm thicknesses, respectively