Fundamental and harmonic emission from the rear side of a thin overdense foil irradiated by an intense ultrashort laser pulse

The emission of fundamental and harmonic radiation from the rear side of thin foils in the thickness range $50–460\mathrm{nm}$ irradiated by intense frequency doubled Ti:sapphire laser pulses of the duration of $150\mathrm{fs}$ and intensities up to a few ${10}^{18}\mathrm{W}∕{\mathrm{cm}}^2$ was investigated. Following up a previous study of the rear side harmonic emission [Teubner et al., Phys. Rev. Lett. 92, 185001 (2004)], we measured the emission efficiencies, polarization properties, and the spectral shapes of the fundamental frequency and the second harmonic. Rear side emission is only observed when the obliquely incident laser light is $p$-polarized. Particle-in-cell (PIC) simulations indicate that the foils remain strongly overdense during the interaction with the laser pulse and that the rear side emission is caused by energetic electron bunches which are generated at the front side by resonance absorption. They are accelerated into the foil and drive strong plasma oscillations at the fundamental and higher harmonic frequencies.

Figure 1

(a) Scheme of the experiment. (b) Measured reflected and re-emitted harmonics [19].

Figure 2

Experimental setup.

Figure 3

Measured conversion efficiency of re-emitted light. (a) Dependence of the re-emitted fundamental, second and seventh harmonic on the foil thickness at the maximum intensity of the experiment $(1.5\times {10}^{18}\mathrm{W}∕{\mathrm{cm}}^2)$. (b) Dependence of the fundamental conversion on the incident laser pulse intensity for the three different foil thicknesses.

Figure 4

Measured spectral line shapes of the re-emitted fundamental. (a) Spectra at three different incident laser intensities and fixed foil thickness $(=200\mathrm{nm})$. (b) Spectra at two different foil thicknesses and fixed incident intensity $(=1.5\times {10}^{18}\mathrm{W}∕{\mathrm{cm}}^2)$. In addition to the re-emitted spectra the incident spectrum is displayed.

Figure 5

(Color) Intensity of the calculated re-emitted spectra (red lines) at different densities: $n_e∕n_c=84$ in (a), $=27$ in (b), and $=4.2$ in (c). Foil thicknesses are $0.2\lambda$ in (a), $0.6\lambda$ in (b), and $4\lambda$ in (c) corresponding to a fixed mass per area. The green line in (a) is the calculated re-emitted spectrum for incident $s$-polarized light (the dashed and solid green lines are the $p$- and $s$-polarized components, respectively). To compare the shape of simulated spectra with the experiment, we have added into each diagram (a, b, and c) the measured conversion efficiencies at the different orders (the open circles with error bars, allready shown in Fig. 1).

Figure 6

(Color) Electron and ion density (normalized to $n_c$) at different times ($t=0$, 50, and 100, times are normalized to the period of the incident light, $=1.33\mathrm{fs}$ at ${\lambda }_0=400\mathrm{nm}$). At the positions labeled by 1–5 the Fourier spectra of the density are plotted in Fig. 7.

Figure 7

Fourier transform of the electron density at the positions 1–5 indicated in Fig. 6. $n_e∕n_c$ is the electron density (normalized to the critical density) at these positions. Note the change in the scale of the ordinate for the different positions. The plotted density amplitudes are normalized to the critical density.

Figure 8

(a) Intensity and (b) density scale length $L$ (at $n_e=n_c$) versus time for an incident pulse with constant intensity. In (b) the optimum gradient for resonance absorption is indicated.

Figure 9

(Color) The total electric field (in the direction of the normal of the foil) as a function of space at $t=50$ (black line) and a half period later ($t=50.5$, blue line). In addition the density is plotted (red line, ordinate at the right side). The inset shows the electric field as a function of time at the position $x∕{\lambda }_0=7.2$, corresponding to $n_e=n_c$.

Figure 10

Calculated re-emitted conversion efficiencies for comparison with Fig. 3. (a) Efficiencies of the fundamental, the second and seventh harmonics as a function of the foil thickness $(a_0=0.5)$. (b) The re-emitted fundamental as a function of $a_0$ at different foil thicknesses.

Figure 11

Calculated spectral line shapes of the re-emitted fundamental. (a) Spectra at two different incident laser intensities and fixed foil thickness $\left(200\mathrm{nm}\right)$. (b) Spectra at two different foil thicknesses and fixed incident intensity $(a_0=0.5)$. In addition to the re-emitted spectra the incident spectra are displayed.