Shaping of attosecond pulses by phase-stabilized polarization gating

We demonstrate that the characteristics of the high-order harmonic spectra generated by few-cycle carrier-envelope phase-stabilized pulses can be finely adjusted by controlling the time-dependent ellipticity. The experimental measurements show evidence for the generation of single, pairs, and trains of attosecond pulses by controlling the time window of linear polarization of the driving pulses. The influence of the carrier-envelope phase on the generation process in different confinement configurations is interpreted and analyzed using a nonadiabatic stationary phase model. We show that the xuv emission depends critically on particular aspects of the fundamental electric field that allows us to steer the electron trajectories on the time scale of tens of attoseconds.

Figure 1

(Color online) xuv spectra generated in neon using a polarization-modulated pulse (pulse duration of 5 fs, $\delta =5.04\text{fs}$, intensity $I=5\times {10}^{14}\text{W}/{\text{cm}}^2$, and $\beta =0°$) for two CEPs (see text).

Figure 2

(Color online) Calculated xuv spectra in neon for two different CEPs: $\psi =0$ (black solid line) and $\psi =\pi /2$ (red dashed line). The other parameters are the same as those in Fig. 1.

Figure 3

(Color online) xuv spectra generated in argon using a polarization-modulated pulse (pulse duration of 5 fs and $\delta =5.58\text{fs}$) as a function of the CEP shift of the ir pulse for (a) $\beta =-15°$ and (b) $\beta =15°$.

Figure 4

xuv spectra for two different CEPs corresponding to the solid and dashed lines of Fig. 3a.

Figure 5

(Color online) Calculated xuv spectra in argon as a function of the CEP shift of the ir pulse for (a) $\beta =-15°$ and (b) $\beta =15°$ (pulse duration of 5 fs and $\delta =5.58\text{fs}$).

Figure 6

(Color online) (a) Projection of the electric field on the major axis of the rotating polarization ellipse for $\beta =-15°$ (blue dotted line) and $\beta =15°$ (black solid line). Real parts of the ionization times (black solid curves) and of the recombination times (red dotted curves) for paths (1a) and (8a) [panel (b)] and for paths (1b) and (8b) [panel (c)] corresponding to $\beta =15°$ for different xuv photon energies. The dashed lines indicate the photon energy of 32.3 eV.

Figure 7

Recombination time differences $\Delta t$ as a function of the photon energy for the different path pairs corresponding to $\beta =-15°$ (solid lines) and $\beta =15°$ (dotted lines). The vertical arrows indicate the direction of increasing number path pairs. Other parameters as in Fig. 3.

Figure 8

(Color online) Difference of the real parts of the ionization times $\Delta t_0$ at 32.3 eV for the eight path pairs corresponding to $\beta =-15°$ (square) and $\beta =15°$ (triangle) using the nonadiabatic stationary phase methods (black solid lines) and a constant intensity field including the “effective chirp” (blue dotted lines).

Figure 9

(Color online) Intensity profile [panel (a)] (black dashed-dotted line) and modulus of ellipticity [panel (b)] (black dashed-dotted line) for the parameters of Fig. 3. Real part of the ionization times (black solid curves) and of the recombination times (red dotted curves) for paths (1a) and (1b) $\left(\beta =15°\right)$ for different xuv photon energies [panel (a)]. The solid and open circles correspond to the “average” intensity and average ellipticity at instants ${\overline{t}}_{j\text{a}}$ and ${\overline{t}}_{j\text{b}}$ $\left(j=1,4,7\right)$, respectively. Dashed horizontal line: photon energy of 32.3 eV [panel (a)].

Figure 10

(Color online) Difference of the real parts of the time in the continuum $\Delta \tau$ at 32.3 eV for the eight path pairs corresponding to $\beta =-15°$ (square solid line) and $\beta =15°$ (triangle solid line) according to the nonadiabatic stationary phase method. $\Delta {\tau }^I$ (open square red dotted line), $\Delta {\tau }^{\epsilon }$ (open circle green dotted line), and $\Delta {\tau }^{\epsilon }+\Delta {\tau }^I$ (diamond magenta dotted line).

Figure 11

(Color online) Temporal intensity profile of double attosecond pulses calculated using the nonadiabatic numerical model (see text) for three CEPs, of the ir field. Same parameters of Fig. 5b. Inset: electric field evolution of the attosecond wave form for the CEPs $\psi =3\pi /8$ (red dashed line) and $\psi =3\pi /4$ (blue dotted-dashed line).

Figure 12

(Color online) xuv spectra generated in argon using a polarization-modulated pulse (pulse duration of 5 fs and $\delta =5.58\text{fs}$) as a function of the CEP shift of the ir pulse for (a) $\beta =-30°$ and (b) $\beta =30°$.

Figure 13

(Color online) Calculated xuv spectra in argon (pulse duration of 5 fs and $\delta =5.58\text{fs}$) as a function of the CEP shift of the ir pulse for (a) $\beta =-30°$ and (b) $\beta =30°$.

Figure 14

xuv spectra for $\beta =\pm 30°$ corresponding to the solid lines of (a) Fig. 12a and (b) Fig. 12b.

Figure 15

(Color online) Harmonic spectra associated to the short paths on the leading (solid black line) and falling (red dotted line) edges of the pulse for (a) $\beta =-30°$ and (b) $\beta =30°$. The vertical dashed lines indicate the position of the odd harmonics of the fundamental frequency.