1. Introduction

The generation of single attosecond pulses has received much attention because of its potential application as a probe for exploring extremely fast phenomena, such as electron motion in atoms and molecules [1–3]. High-order harmonic generation (HHG) in the extreme-ultraviolet (XUV) and soft x-ray regions is the most promising route for generating such ultrashort pulses, because HHG basically consists of attosecond bursts of XUV radiation emitted every half-cycle of the fundamental driving field [4]. In order to obtain an isolated single attosecond pulse, the temporal duration of the driving field must be shortened to a few optical cycles, within which either a half or one cycle contributes to generate the XUV radiation on an attosecond time scale. In fact, the demonstration of single attosecond pulse generation was realized using a state-of-the-art sub-10-fs (5–7 fs) laser system incorporating an appropriate spectral filtering [5]. Since the output energy from such a laser system is limited to several hundreds of μJ, the energy of the single attosecond pulses as estimated from the typical conversion efficiency of HHG is less than 1 nJ, which is not high enough to stimulate ultrafast nonlinear phenomena in the XUV and soft x-ray regions.

As an alternative technique, the polarization-gating of fundamental pulses has been proposed [6, 7] and broadband XUV emission has been demonstrated [8, 9]. In this technique, polarization of the driving pulse is temporally modulated from circular to linear and back to circular, which limits the XUV radiation within a time scale corresponding to the linearly-polarized portion of the driving field.

As another approach to generating ultra broadband XUV radiation, we have examined the use of a two-color field consisting of a sub-10-fs fundamental and its second harmonic fields. Two-color HHG using relatively-long conventional pulses has so far been studied both theoretically [10] and experimentally [11, 12], where the most pronounced feature is the appearance of even-order harmonic components in addition to the conventional odd-orders because of the collapse of inversion symmetry in the light-matter system. One can expect that when the driving pulse duration decreases to the sub-10-fs regime, the bandwidth of each harmonic component will broaden and overlap with its neighbors to form a less-structured continuum. In the time domain, the characteristics can be understood as a reshaping of the electric field, resulting in a shortening of the effective pulse duration that contributes to HHG [13, 14].

 

Fig. 1. Temporal profiles of the fundamental, SH and synthesized electric fields and the square of the synthesized electric field. E ₁ and E ₂ are 0.9 and 0.1, respectively.

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Here we consider a synthesized electric field consisting of a fundamental and its second harmonic (SH) fields, expressed as

where the subscript i (1 or 2) denotes the fundamental or the SH field, respectively. E _i is the electric field amplitude, τ_i is the full width at half maximum (FWHM) pulse duration assuming a Gaussian profile, ω is the carrier frequency for the fundamental, Δt is the time delay between the two pulses, ϕ is the absolute phase, and Δϕ is the relative phase between them. Figure 1 shows one example. From the top to the bottom, fundamental field, second harmonic field, synthesized field, and the square of the synthesized field, where E ₁ and E ₂ are set at 0.9 and 0.1, and τ₁ and τ₂ are 9 fs and 35 fs, respectively, fitting to the experimental condition described later in this article. ω is 2.36×10¹⁵ rad/s, corresponding to a wavelength of 800 nm and all other parameters (Δt, ϕ, and Δϕ) are set to zero. As can be seen around the central peak of the synthesized field squared, the amplitude of the nearest neighbors on both sides are well suppressed by adding a small amount of the SH field (10%) to the fundamental field. Therefore, efficient broadband XUV emission near the cutoff can be obtained even using relatively long driving pulses (~10 fs), where the SH pulse duration is allowed to be much longer than the fundamental pulse duration. Thus, this technique has the great advantage of simplifying the energy scaling. From the standpoint mentioned above, intense two-color pulses that are generated based on a sub-10-fs multi-mJ Ti:sapphire laser system using the pressure-gradient hollow fiber technique [15] can be applied to ultra broadband XUV emission, leading to the generation of single attosecond pulses. In this paper, we describe experimental results on continuum radiation in the XUV region that was generated using a two-color driving field consisting of a sub-10-fs fundamental and its SH pulses.

2. Experimental setup

The experimental setup is shown in Fig. 2. The driving laser is a well-established Ti:sapphire chirped-pulse amplification (CPA) system that can provide 20-fs pulses with an energy of 5 mJ at a center wavelength of 800 nm without locking the absolute phase. The output pulses were further shortened by means of a pressure-gradient hollow fiber pulse compression technique [16], resulting in a pulse duration of 9 fs with an energy of 2 mJ. By using a spectral phase interferometer for direct electric-field reconstruction (SPIDER), we confirmed that the dispersion induced by optical elements and air could be well precompensated by adjusting the number of reflections on the chirped mirrors. Then, the pulses were loosely focused using an f=120 cm spherical lens with a broadband (600-1000 nm) anti-reflection coating into an HHG gas cell inside a vacuum chamber. The gas cell, which was 20 mm in length, had 0.5-mm diameter pinholes at both ends in order to separate the vacuum and the gas-filled regions by differential pumping. Argon was introduced from a reserve chamber into the gas cell as the interaction medium. The beam profile at the focus was measured in a vacuum chamber using a CCD camera, and showed a nearly Gaussian intensity profile with a 1/e ² spot diameter of 130 μm. Although the focused intensity estimated from the above values is 1.2×10¹⁵ W/cm², the actual intensity in the gaseous medium would be less than half this value because the beam is self-trapped in a filament with a larger beam size [17, 18]. The harmonics that were generated were separated from the fundamental pulse using a silicon beam splitter with a reflectivity of 50% at 30 nm [19], and the residual fundamental pulse was blocked using a 200-nm-thick aluminum filter with a transmittance of 10% at 30 nm (the transmission decreases with increasing wavelength up to 70 nm) [20]. The absolute energy of the harmonics was measured using a calibrated XUV photo detector (IRD AXUV-100) placed behind the Al-filter. The harmonic spectrum was monitored using a flat-field grazing-incidence spectrometer equipped with a micro-channel plate (Hamamatsu Photonics F6959) and an analog CCD camera with an exposure time of 33 ms, which corresponded to 33 shots at 1 kHz. When sub-10-fs pulses are used to generate the XUV radiation, the pulse-to-pulse change in the absolute phase smears the structure in the integrated harmonic spectrum. Therefore, to remove the ambiguity, the harmonic spectrum was taken in a single shot by using a synchronized digital CCD camera with an exposure time of 0.9 ms.

The optical elements for generating two-color pulses were closely aligned directly in front of the entrance of the HHG chamber, as illustrated in Fig. 2. About 5% of the fundamental pulse energy was converted to the SH by a 300-μm-thick beta-barium borate (β-BBO) type-I SHG crystal. The remaining fundamental and orthogonally-polarized SH pulses were subsequently passed through an 800-μm-thick α-BBO time-plate, which adjusts the temporal overlap between the fundamental and the SH pulses at the gas cell compensating the group delay difference between them caused by the optical elements and air (~200 fs). The relative phase between them was also adjusted by slightly tilting the time-plate. Then, the delay-controlled two-color pulses were passed through a 43-μm-thick quartz dual-band wave plate (half-wave retardation for the fundamental and full-wave retardation for the SH), which rotates the polarization direction of the fundamental by 90 degrees while keeping that of the SH unchanged. The bandwidth of the dual-band wave plate is broad enough; 900 nm (FWHM) and 190 nm (FWHM) for the fundamental and the SH pulses, respectively. Thus, the polarizations were set parallel to each other. Finally, the two-color pulses were passed through a 1-mm-thick MgF₂ window in the HHG vacuum chamber. We confirmed that dispersion for the fundamental pulse was well precompensated, and that the duration was 9 fs with and without SHG. On the other hand, the SH pulse duration was 35 fs, as estimated from the acceptance bandwidth of the SHG crystal (8.5 nm at around 400 nm, corresponding to a Fourier-transform-limited pulse duration of 32 fs) and the dispersion induced by the optical materials (~176 fs² at 400 nm). Spatial overlap of the two pulses can be achieved at the gas cell in this configuration, and we actually confirmed that the waist positions for both pulses agreed to within 3 mm. The spot diameter of the SH pulse at the focus was approximately 100 μm, which was a bit smaller than the fundamental (130 μm).

 

Fig. 2. Experimental setup for two-color HHG.

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3. Results and discussion

In a preliminary experiment on HHG, we used 20-fs pulses directly from the Ti:sapphire CPA system. To maximize the harmonic intensity, the pressure of argon in the reserve chamber was optimized to 30 torr. Figure 3 shows the harmonic spectra generated using (a) a fundamental pulse alone and (b) using a two-color pulse with an added SH pulse of 0.3-mJ energy. The spectrum obtained using a one-color driving pulse shows a typical absorption-limited harmonic spectrum maximized at around the 27th-29th harmonics. By adding the SH pulse to the fundamental followed by fine-tuning of the relative phase between them, the harmonic spectrum contained the odd- and even-order components equally, as shown in Fig. 3(b). We confirmed that the even-order components disappeared when the polarizations were set perpendicular to each other by rotating the dual-band wave plate. This is because the intensity of the SH pulse is too low to affect the HHG under perpendicular polarization. Of course, the SH pulse alone cannot generate high-order harmonics in this spectral region. For both one-color and two-color HHG, the harmonic energy measured after passing through the Al-filter (transmission range: 13th-45th harmonics), was 2.5 nJ at the XUV detector, while the corresponding energy generated at the gas cell was evaluated at 50 nJ.

 

Fig. 3. Harmonic spectra generated by using (a) one-color 20-fs pulse and (b) two-color pulse (33 shots accumulated).

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We then examined the use of 9-fs fundamental pulses from a hollow-fiber pulse compressor. Figure 4(a) is a harmonic spectrum obtained using only the fundamental pulses at 800 nm. The optimum pressure of argon was 18 torr in this case. The spectral bandwidth of the individual harmonic components was broad because the driving pulse duration was as short as 9 fs. When the HHG was driven by a two-color field consisting of the 9-fs fundamental pulse and an SH pulse with an energy of 0.1 mJ, two types of spectral shapes were observed, as shown in Figs. 4(b) and (c). Note that these spectra were taken in the single-shot measurement. Most of the observed spectra have discrete structures, as shown in Fig. 4(b), and continuum radiation as shown in Fig. 4(c) appeared occasionally. This might be due to the unlocked absolute phase in our laser system, and should be stabilized in the future work.

 

Fig. 4. (a) Harmonic spectrum obtained using only 9-fs fundamental pulse. Typical spectral profiles with 9-fs two-color pulse in the case of (b) discrete and (c) continuum spectra (taken in a single shot).

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In Fig. 4(c), we observed continuum spectrum with a bandwidth of 8 nm (FWHM). The discrete components emerged at wavelengths longer than 33 nm, where the end of the discrete structure corresponds to the ionization potential plus three-times the Pondermotive energy gained by the second-highest driving field, as expected from the reshaped field in Fig. 1. The spectral bandwidth of the continuum structure is comparable to that of typical single attosecond pulses driven by few-cycle pulses [5]. If the dispersion of the XUV pulse can be compensated to the Fourier-transform-limit by an appropriate method [21], the pulse duration corresponding to the spectrum that was obtained would be 200 as. The harmonic energy within the spectrum limited by the Al filter was measured at 0.5 nJ, from which the generated energy in the gas cell was evaluated as 10 nJ.

4. Conclusion

In conclusion, we have successfully demonstrated the generation of continuum radiation in the XUV region driven by an intense two-color laser field consisting of a sub-10-fs fundamental and its SH pulses. The XUV radiation has a broadband spectrum centered at 30 nm with a spectral bandwidth of 8 nm (FWHM). The generated energy is as high as 10 nJ, which is close to the absorption-limited value in the phase-matched HHG. In this way, HHG driven by a two-color field has great potential for shortening XUV/soft x-ray pulses while also enhancing the pulse energy. This technique also allows some extension of the cut-off wavelength toward the water-window region, since the depletion of neutral atoms by ionization in the leading part of the pulse can be eliminated by using the two-color technique.