Single attosecond pulse and xuv supercontinuum in the high-order harmonic plateau

It is proposed that single attosecond pulses be generated by gating high-order harmonic emission with fields whose ellipticity varies rapidly with time. The laser pulse with a time-dependent ellipticity is created from two $5\text{−}\mathrm{fs}$ laser pulses centered at $750\mathrm{nm}$ and separated by $5\mathrm{fs}$. One of the laser pulses is left-circularly polarized and the other is right-circularly polarized. Numerical simulations show that when neon atoms are driven by such laser pulses, the generated high-order harmonic spectrum in the 25th to the 85th orders are a supercontinuum that corresponds to single attosecond pulses. A simple analytical expression is derived for estimating the high-harmonic radiation time.

Figure 1

The time-dependent ellipticity of the laser pulse formed by the combination of a left-hand circularly polarized pulse and a right-hand circularly polarized pulse. The pulse duration for each pulses is ${\tau }_p$ and the delay between them is $T_d$.

Figure 2

(a) Comparison of the high-order harmonic spectrum from a single atom (solid line) with the result of the three-dimensional propagation (dot line). The gas target is neon gas driving by a linearly polarized laser pulse. The pulse duration is $5\mathrm{fs}$ centered at $0.75\mu \mathrm{m}$. The peak intensity is $6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The carrier-envelope phase of the laser pulse is 0 radian. (b) Effects of propagation on the high harmonic pulses at the plateau region (centers at $55\hslash \omega$) and at the cutoff region (centers at $85\hslash \omega$). The spectrum window is $9.9\mathrm{eV}$. The solid line corresponds to the single atom calculation and the dot line is from the three-dimensional propagation simulation. (c) The effects of the carrier-envelope phase on the high harmonic spectra. The dot line and solid line correspond to $\varphi =0$ and $\varphi =\pi ∕2$, respectively.

Figure 3

(a) The high-order harmonic spectra from neon atoms driving by a laser pulse with a time-dependent ellipticity. The dot line corresponds to the single atom calculation and the solid line is from the three-dimensional propagation simulation. The laser pulse is formed by the combination of a left-hand circularly polarized pulse and a right-hand circularly polarized pulse. The pulse duration for both pulses is $18.75\mathrm{fs}$ and the delay between them is $25\mathrm{fs}$. The peak intensity is $6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The carrier-envelope phase of the laser pulse is 0 radian. (b) The high harmonic pulses centered at two different frequencies: $55\hslash \omega$ and $85\hslash \omega$. The spectrum window is $9.9\mathrm{eV}$. The solid line correspond to the single atom calculation and the dot line is from the three-dimensional propagation simulation.

Figure 4

(a) The high-order harmonic spectra from neon atoms driving by a laser pulse with a time-dependent ellipticity. The solid line corresponds to the single atom calculation and the dot line is from the three dimensional propagation simulation. The laser pulse is formed by the combination of a left-hand circularly polarized pulse and a right-hand circularly polarized pulse. The pulse duration for both pulses is $5\mathrm{fs}$ and the delay between them is $5\mathrm{fs}$. The peak intensity is $6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ . The carrier-envelope phase of the laser pulse is $\varphi =\pi ∕2$ radian. (b) The high harmonic pulses centered at four different frequencies: $25\hslash \omega$, $45\hslash \omega$, $65\hslash \omega$, and $85\hslash \omega$. The spectrum window is $9.9\mathrm{eV}$. The results are obtained from the single atom calculation. (c) The attosecond pulses from the three-dimensional propagation simulation.

Figure 5

(a) The high-order harmonic spectra from neon atoms driving by a laser pulse with a time-dependent ellipticity formed by the combination of a left-hand circularly polarized pulse and a right-hand circularly polarized pulse. The pulse duration for both pulses is $5\mathrm{fs}$ and the delay between them is $5\mathrm{fs}$. The peak intensity is $6\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$. The dot line is when the carrier-envelope phase of the laser pulse is $\pi ∕2$ radian and the solid line is when the phase equals zero. (b) The high harmonic pulses centered at $85\hslash \omega$. The spectrum window is $9.9\mathrm{eV}$. The upper curve (dot line) is when the carrier-envelope phase is $\pi ∕2$ radian. The lower curve (solid line) is for the phase equaling zero and its intensity is normalized to the upper one.