Synthesis of ultrashort laser pulses for high-order harmonic generation

We present a technique for the synthesis of ultrashort laser pulses with approximately one cycle (FWHM) of temporal duration. These pulses are characterized by a certain degree of chirp. We show that these pulses produce both an enhancement of the high-order harmonic generation (HHG) cutoff and a noticeable increase of the yield, when interacting with an atomic system. Additionally, the asymmetric nature of the driven pulses plays an important role in the efficiency and cutoff extension of the high-order harmonics generated. Starting from the HHG spectra, we demonstrate it is possible to retrieve isolated attosecond pulses by spectral filtering. The analysis and interpretation of the different characteristics present in the HHG driven by this kind of pulse was carried out invoking classic arguments. Furthermore, a more complete description and validation of the HHG properties is performed by a quantum analysis, based on the integration of the time-dependent Schrödinger equation in full dimensionality.

Figure 1

Potential experimental setup to carry out the proposed pulse synthesis.

Figure 2

Wavelet analysis of the (a) synthesized and (b) filtered pulses. Temporal profiles of the (c) synthesized and (d) filtered (in red) pulses.

Figure 3

Temporal profile of the four pulses synthesized in the present study. (a) Pulse 1 is obtained with $L_1=25\mu \mathrm{m}$, $L_2=30\mu \mathrm{m}$ and it is up-chirped; (b) pulse 2 with $L_1=25\mu \mathrm{m}$, $L_2=30\mu \mathrm{m}$ and down-chirped; (c) pulse 3 with $L_1=20\mu \mathrm{m}$, $L_2=30\mu \mathrm{m}$ and up-chirped; (d) pulse 4 with $L_1=20\mu \mathrm{m}$, $L_2=30\mu \mathrm{m}$ and down-chirped. Note that the temporal region corresponding to higher frequencies was removed ($t>6$ optical cycles).

Figure 4

3D-TDSE HHG spectra in argon driven by the four synthesized pulses of Fig. 3 (red lines). (a) Pulse 1 [Fig. 3]; (b) pulse 2 [Fig. 3]; (c) pulse 3 [Fig. 3]; and (d) pulse 4 [Fig. 3]. In Fig. 4 the HHG spectrum (black line) for a conventional Gaussian pulse is included. Additionally, in all the panels the HHG spectra (blue lines) of their “equivalent pulses” are represented (see the text for details). The laser intensity is the same for all cases, $I={10}^{14}$ ${\mathrm{W}/\mathrm{cm}}^2$. The valley in the respective spectra around 40 eV is due to the Cooper minimum in argon [35].

Figure 5

Classical total electron energies (in eV) as a function of ionization (red points) and recombination (green points) times for the four synthesized pulses of Fig. 3. The black arrows show the travel times of the electron trajectories at the cutoff energy. The $I_p$ (15.7 eV) of the argon atoms is displayed with blue arrows (note that one optical cycle is 2.66 fs).

Figure 6

Time-frequency analysis of the HHG spectra of Fig. 4. The classical electron energies at the recombination time is superimposed (solid black lines). The driving pulses are also plotted (solid gray line). The laser intensity is the same for all cases, $I={10}^{14}$ W/${\mathrm{cm}}^2$.

Figure 7

HHG generated by (a) pulse 1 and (b) pulse 3 and the corresponding attosecond pulses (c) and (d), respectively, using a 20 eV filter in the cutoff region.