Absorption and opacity threshold for a thin foil in a strong circularly polarized laser field

We show that a commonly accepted transparency threshold for a thin foil in a strong circularly polarized normally incident laser pulse needs a refinement. We present an analytical model that correctly accounts for laser absorption. The refined threshold is determined not solely by the laser amplitude, but by other parameters that are equally or even more important. Our predictions are in perfect agreement with particle-in-cell simulations. The refined criterion is crucial for configuring laser plasma experiments in the high-field domain. In addition, an opaque foil steepens the pulse front, which can be important for numerous applications.

Figure 1

1D PIC simulation results for the interaction of a strong circularly polarized Gaussian laser pulse ($\lambda =1\mu \mathrm{m}, a_0=500$, FWHM duration $30\mathrm{fs}$) with a thin hydrogen foil (thickness $d=0.1\lambda$). (a) foil electron density $n_0=140n_c$ (areal density ${\sigma }_0\approx 88$)—the foil is opaque; (b) foil electron density $n_0=80n_c$ (areal density ${\sigma }_0\approx 50$)—the foil is transparent.

Figure 2

Time dependencies of the laser front [hatched in Fig. 1] energy (${\varepsilon }_f$), the ion energy (${\varepsilon }_i$), and the reflected energy (${\varepsilon }_r$) for the simulation presented in Fig. 1.

Figure 3

Estimations vs 1D PIC simulation results for transparency threshold areal density for different pulse durations and ion charge-to-mass ratios. Dimensionless field amplitude $a_0=500$, laser carrier wavelength $\lambda =1\mu \mathrm{m}$, foil thickness $d=0.1\lambda$. Left panel: linear pulse profile; right panel: Gaussian pulse profile.

Figure 4

2D PIC simulation results. $a_0=500$, transverse waist radius $w=6\lambda , \lambda =1\mu \mathrm{m}, d=0.1\lambda , H^{+}$ ions. (a), (b), (d): electron density (red, continuous color bar), and laser field (grey, discrete color bar) distributions for laser pulse FWHM 30 fs [(a) and (d)] and 15 fs [(b)], target density $n_0=140n_c$ [(a) and (b)] and $n_0=300n_c$ [(d)]; insets (the same legends as in Fig. 1): a sectional view at $y=0$. (c): electron density distributions at subsequent moments of time for different target densities. Left: $n_0=140n_c$ and $t=12$ fs, 18 fs, 26 fs; right: $n_0=300n_c$ and $t=12$ fs, 18 fs, 26 fs, 46 fs.