Toward attosecond pulse synthesis from solids: Spectral shaping, field autocorrelation, and two-color harmonic generation

Harmonic generation from solid surfaces is a promising tool for producing high-energy attosecond pulses. We report shaping of the harmonic spectrum to achieve the bandwidth necessary for attosecond pulse generation. The shaping is demonstrated for lower as well as for higher harmonics using single and two-pulse pumping. The measured harmonic field autocorrelation function exhibits attosecond spikes in good agreement with the harmonic spectrum. Double slit experiments reveal a high spatial coherence of the harmonic beam.

Figure 1

Pump beam is focused onto the target with the help of the parabolic mirror PM1. The aperture AP1 together with the beam stop BS blocks the driver radiation [53]. The aperture AP2 with the diameter of 25 mm cuts out the central part of the pump beam. Long working distance microscope objectives MO1 and MO2 are used for monitoring the energy distribution in the focal plane of PM1 and the target positioning (autofocus), respectively.

Figure 2

LiF spectrometer: PM2, M1, $\mathrm{M}{1}^{\prime }$ [54], and M2 are a parabolic mirror and concave spherical mirrors, respectively. P1 and P2 are LiF prisms. Insertion of P2 compensates for the dispersion of P1. The mask MS placed in the focal plane of the mirror M1 adjusts the harmonic intensities. PS is a phosphor screen. The double slit DS is used to measure the harmonic temporal and spatial coherence.

Figure 3

CCD images (a), (b) and the corresponding harmonic spectra (c), (d). Panels (a) and (c) show the initial spectrum and (b) and (d) the spectrum corrected by the mask MS.

Figure 4

(a) Spectrally resolved harmonic interference patterns. Top to bottom: second, third, and fourth harmonic patterns, respectively. (b), (c) Visibility V of the harmonic interference pattern as functions of $I_p$ (b) and the distance $R$ between the slits (c). The solid black ($•$) and open red ($○$) circles correspond to the second harmonic with $R=2.5$ mm and 5 mm, respectively; ($\blacksquare$) represents the visibility of the third harmonic with $R=0.5$ mm. The blue triangles ($▿$) correspond to the second harmonic at the pump intensity of $3\times {10}^{17}{\mathrm{W}/\mathrm{cm}}^2$. Panel (d) shows the interference pattern of the overlapping second, third, and fourth harmonic.

Figure 5

Panels (a), (b), and (c) show the interference patterns and their profiles for (a) second, (b) overlapping second and third, and (c) overlapping second, third, and fourth harmonic. The black solid curves correspond to experimental profiles. The green dotted curve in (a) depicts the normalized function $I\left(x\right)$ with $x=\tau c{F}_{M2}/R$. The red dashed lines and the blue open circles represent profiles calculated with $\mathrm{Re}\left[\gamma \right(\tau \left)\right]$, which was obtained using the Wiener-Khinchin theorem and (5), respectively. The right axes for the profiles in (b) and (c) represent $\mathrm{Re}\left[\gamma \right(\tau \left)\right]$. Panel (d) shows a simulated pulse train corresponding to (c) with a compensated attochirp. For the chirp compensation an additional fused silica platelet FS with the thickness of $\approx 700 \mu \text{m}$ was placed in front of the mask MS and the filter UG11 [panel (d), inset].

Figure 6

(a) Two-pulse HOHG. The intensity of the driver at the frequency ${\omega }_d$ is much higher than that of the probe at the frequency ${\omega }_p$. In addition to the multiples of ${\omega }_d$ also hybrid harmonics at the frequencies $n{\omega }_d+{\omega }_p$ are observed. (b) Experimental setup. The parabolic mirror PM1 focuses the beams onto the target. The aperture AP1 and the beam stop BS are placed in the 400 nm beam. The aperture AP2 controls the intensity of the 800 nm beam on the target. The microscope objectives MO1 and MO2 (i) monitor the focal energy distributions, (ii) control autofocusing, and (iii) monitor the beam overlapping.

Figure 7

Two-pulse harmonic spectra. The aperture AP2 [Fig. 6] was closed ($○$) and had the diameters of 50 mm (completely open) ($---$) and 6.8 mm (—). The probe intensities were ${10}^{18} {\mathrm{W}/\mathrm{cm}}^2$ ($---$) and about ${10}^{16} {\mathrm{W}/\mathrm{cm}}^2$ (—).

Figure 8

Grating spectrometer (a): the toroidal grating images the plasma spot on the target spectrally resolved onto the CCD camera. The harmonic spectra (b) as recorded by the CCD camera: aperture AP2 [Fig. 6] closed ($○$) and open (—). Panel (c) shows $K=R_{\mathrm{G}}\times {\text{Eff}}_{\mathrm{CCD}}$ as a function of frequency. The green circles ($•$) in (b) represent the energy of the individual harmonics integrated over the corresponding harmonic peak and corrected for $K$.