Imaging electron angular distributions to assess a full-power petawatt-class laser focus

We present a technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate ($\theta ,\varphi$) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, but also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few $\times {10}^{19}$ to a few $\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2$, an f/10 optic produced a focal spot in the paraxial regime. This allows a plane-wave parametrization of the peak intensity given by $tan{\theta }_c=2/a_0$ ($a_0$ being the normalized vector potential and ${\theta }_c$ the minimum ejection angle) to be compared with our measurements. Qualitative agreement was found using an $a_0$ inferred from the pulse energy, pulse duration, and focal spot distribution with a modified parametrization, $tan{\theta }_c=2\eta /a_0$ ($\eta =2.{02}_{-0.22}^{+0.26}$). This highlights the need for (i) better understanding of intensity degradation due to focal-spot distortions and (ii) more robust modeling of the ejection dynamics. Using single-shot detection of electrons, we showed that while there is significant shot-to-shot variation in the number of electrons ejected at a given angular position, the average distribution scales with the pulse energy in a way that is consistent with that seen with the image plates. Finally, we note that the asymptotic behavior as $\theta \to 0^{\circ }$ limits the usability of angular measurement. For 800 nm, this limit is at an intensity $\sim {10}^{21}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 1

Experimental setup (not to scale) for image plate and scintillation detectors (a). Image plates are mounted a fixed distance, $d\approx 40$ mm, after the focus with active area facing the focal spot. Scintillation detectors (not shown) are mounted in the holder, attached to a rotation table, rotating about the focus in the $\vec{E}\text{−}\vec{k}$ (i.e., $\widehat{x}\text{−}\widehat{z}$) plane a fixed distance ($\approx 138$ mm) away. Typical VEGA-3 focal spot images obtained at low power are shown in (b)–(d).

Figure 2

Scaled image plate data captured under conditions detailed in Table 1, where 1 on the color bar corresponds to peak PSL values (see text) of 7.06, 6.82, and 31.88, respectively, for (a)–(c). The laser is polarized along the $\vec{x}$ axis and $\vec{k}$ points into the page. White dots indicate the single-electron PSL level vs $\varphi$ (see text).

Figure 3

The $\varphi$-averaged line profile, $h\left(\theta \right)$ (see text), for data in Figs. 2, represented by red (far right), yellow, and dark blue (far left) curves, respectively. The dashed lines indicate exponential fits used to determine ${\theta }_c$. The dot-dashed magenta (blue) curve indicates the single-electron PSL level for the BAS-SR (BAS-MS) plates used for Figs. 2 and 2 [Fig. 2] and the shaded regions are the estimated uncertainties in these levels based on measurements in Ref. [50]. The solid data points represent our best estimate of ${\theta }_c$ and the associated uncertainty (see text).

Figure 4

Single-shot scintillation data captured with Ar gas for ${15}^{\circ }\le \theta \le {95}^{\circ }$ with 26.7 J (blue dots) and 10.2 J (green squares) of laser energy on target for the experimental conditions detailed in Table 2. The average high (low) energy data are displayed as “$*$” (“$\times$”) along with their corresponding standard deviations. The solid (dashed) orange and black lines are sigmoid fits to the small and large angle falloff, respectively, for the high- (low-)energy measurement. The large angle threshold is set by the aluminum filters used to block the plethora of low-energy electrons.

Figure 5

Normalized and background subtracted sigmoid fits for the small-angle falloff of measurements performed with ${\mathrm{N}}_2$ (violet), Ar (orange), and Xe (yellow). The solid (dashed) curves correspond to high (low) energy measurements.

Figure 6

Energy scaling, $tan{\theta }_c$ vs inferred $a_0\text{–}9.1\pm 1.1$, $7.3\pm 0.9$ and $5.7\pm 0.7$ for the three measurements in Fig. 2 shown by blue filled circles, with Eq. (3) shown by the green solid curve. The inferred $a_0$ is based on the conditions given in Table 1 (see Sec. 3b). The horizontal error bars, $\pm \delta a_0$, represent the uncertainty in calculating $a_0$ using the low-power focal spot image (Figs. 1). The vertical error bars represent the uncertainty in the measurement of $tan{\theta }_c$ (see Sec. 3a). The blue dashed line represents a numerical fit of the data to $tan{\theta }_c=2\eta /a_0$, where $\eta =2.{02}_{-0.22}^{+0.26}$; the uncertainty in $\eta$ is represented by the shaded region around the dashed curve.