1. Introduction

The recent years have witnessed the birth of attosecond science, in which isolated bursts of XUV radiation of attosecond duration are used to probe dynamics on a previously unexplored timescale [1, 2]. Such pulses are produced by high-harmonic generation (HHG) in noble gases starting from a high intensity short driver pulse [3, 4]. Three main characteristics of the driver pulses are important: (i) short duration, which must comprise only a few optical cycles; (ii) stability of the carrier-envelope phase (CEP), required for the generation of isolated and reproducible attosecond pulses [5, 6]; (iii) carrier wavelength optimized to enhance the HHG process. Currently, the driver pulses for HHG are at 0.8 µm, produced by Ti:sapphire lasers with chirped-pulse amplification (CPA), compressed by a hollow fiber and with active CEP stabilization; this wavelength is however not the optimum for HHG. From the three-step model for HHG [7], one can in fact derive that the ponderomotive energy of the wiggling electron scales as the square of the carrier wavelength [8], so that longer wavelengths are expected to generate higher-order harmonics. On the other hand, the quantum-mechanic diffusion of the electron wavepacket due to the longer transit time in the continuum leads to a reduction of HHG efficiency for increasing carrier wavelengths; the IR wavelength interval from 1.5 to 3 µm seems to be a good compromise between these two conflicting requirements.

In this paper we describe a system for the generation of high-energy, few-optical-cycle, CEPstabilized pulses in the IR. The system, driven by a CPA Ti:sapphire laser, starts from a passively CEP-stabilized seed generated by difference frequency generation (DFG) of a broadband continuum, which is then boosted in energy by a two stage optical parametric amplifier (OPA). It produces CEP-stabilized pulses with tunable central wavelength around 1.5 µm, up to 200-µJ energy and 15-fs duration, which make them ideally suited to be used as drivers for attosecond pulse generation through HHG. The paper first compares active and passive techniques for CEP stabilization and presents the method used in this work. Then, it describes the experimental setup for the generation of high-energy self-phase-stabilized pulses. Finally, it presents the pulse characterization measurements and discusses future developments.

2. Active vs. passive CEP stabilization

CEP stabilization methods can be divided into active and passive ones. Active methods [9, 10] rely on the fact that a femtosecond mode-locked oscillator emits a train of pulses with repetition rate ν_R which suffers a pulse-to-pulse CEP slippage Δϕ. In the frequency domain, such pulse train gives rise to a frequency comb, i.e. a superposition of longitudinal modes with frequencies ν=ν _CEO+nν _R, where ${\nu }_{\mathit{CEO}}=\frac{\Delta \varphi }{2\pi }{\nu }_R$ is the carrier-envelope-offset frequency. Generation of actively CEP-stabilized pulses can then be accomplished in three steps: (i) measurement of ν_CEO by a nonlinear interferometer; (ii) stabilization of ν_CEO by active feedback on the oscillator; (iii) picking of pulses at a fraction of ν_CEO, so that their CEP becomes reproducible from shot to shot. The selected CEP-stable pulses are then amplified either in a solid-state amplifier or in an OPA [11, 12], and a second electronic feedback loop is required to compensate for CEP fluctuations induced by the amplification process [5].

Passive methods, pioneered by Baltuška et al. [13], are based on the process of DFG, in which two pulses at frequencies ω₂ and ω₃ are mixed in a second-order nonlinear crystal to generate the difference frequency (DF): ω₁=ω₃-ω₂. The CEPs of the three pulses are linked through the parametric interaction by the relationship: ϕ ₁=ϕ ₃-ϕ ₂-π/2. If the two pulses undergoing the DFG process are derived from the same source and thus share the same CEP (ϕ ₃=ϕ+c ₃, ϕ ₂=ϕ+c ₂), then ϕ ₁=c ₃-c ₂ -π/2=const., i.e. the fluctuations of ϕ are automatically cancelled in a passive, all-optical way. Passive CEP stabilization can be realized in an OPA, in which the idler is the DF between pump and signal waves; if pump and signal are derived from the same source, then the idler is phase-stable. CEP stabilization of the idler has been achieved in OPAs pumped either by the fundamental frequency (FF) or by the second harmonic (SH) of Ti:sapphire [13, 14, 15]. DFG between pulses generated by two OPAs sharing the same CEP has also been demonstrated [16]. These are all inter-pulse DFG schemes, as they involve mixing of two separate frequency-shifted pulses, synchronized by a delay line; in this case, any fluctuation of the path-length difference will induce a CEP jitter. A more robust approach is based on an intra-pulse scheme, in which DFG is achieved between long and short wavelength components of a single ultrabroadband pulse [17, 18]; in this case the two pulses undergoing the DFG process are automatically synchronized and delay-induced CEP jitter is suppressed. In a first implementation of this idea, pulses generated by DFG from an ultrabroadband Ti:sapphire oscillator have been stretched and used to seed an optical parametric chirped pulse amplifier pumped by an electronically synchronized 30 ps Nd:YLF laser [19]; the system produces 20-fs, 80-µJ phase stable pulses at 2.1 µm. We recently proposed an alternative scheme [20], which is driven by a CPA Ti:sapphire system: the seed, generated by DFG of a hollow-fiber-broadened supercontinuum, is amplified by an OPA pumped by the FF of Ti:sapphire and operated around degeneracy. The advantages of our approach are the following: (i) generation of energetic seed pulses, minimizing background superfluorescence in the OPA stages; (ii) use of a single laser system for generating DFG and pumping the OPAs, simplifying synchronization issues; (iii) use of short pump pulses avoiding the need to stretch the seed pulses and thus simplifying (or avoiding) the compressor. In a preliminary experiment we generated 20-µJ phase stable pulses at 1.4 µm; here we increase the energy by an order of magnitude and demonstrate a nearly transform-limited (TL) 15-fs duration.

3. Experimental setup

The experimental setup is shown in Fig. 1. The source is a CPA Ti:sapphire laser system producing 1.5 mJ, 50 fs, p-polarized pulses at a 1 kHz repetition rate and 800 nm wavelength. A fraction of the energy (≈250 µJ) is coupled in a 60-cm long, 300-µm inner diameter hollow fiber filled with krypton (0.7 bar pressure) to generate a broadband supercontinuum by self-phase-modulation [21, 22]. The outcoupled pulses, with 200-µJ energy and spectrum extending from 650 to 1000 nm, are compressed by 14 bounces on ultrabroadband chirped mirrors, in order to acquire a slightly negative chirp and optimize the subsequent DFG process. The pulses are then focused by a 1500 mm radius spherical mirror onto a 200 µm thick β-barium borate (BBO) crystal cut for DFG with type II [e+o(DFG)→e] phase matching (θ=32°, ϕ=30°, Shandong Newphotons, China): DFG takes place between different frequency components of the supercontinuum, which is sent into the crystal with extraordinary polarization. For a given crystal orientation, different pairs of frequencies can be phase-matched simultaneously, giving rise to a broad DF spectrum even for a relatively thick crystal. For an intensity of 100 GW/cm ², just below the onset of third-order nonlinear processes in the crystal, s-polarized DF pulses with energy up to 20 nJ are produced. The bandwidth and central wavelength of the DF pulses can be controlled by acting on the crystal phase-matching angle and the pulse chirp, finely tuned by a pair of thin glass wedges; a typical spectrum, shown in Fig. 2 as a black solid line, corresponds to a TL pulse duration of 6 fs. A thin film polarizer is used to suppress the residual supercontinuum collinear with the DF pulses, without introducing any significant amount of dispersion; also, to prevent chirping of the DF pulses, they are handled exclusively by reflective optics. The DF pulses are used to seed a two-stage OPA pumped by the residual 800-nm light; use of a quasi-monochromatic pump, with respect to the broadband one employed in the previous experiment, optimizes the OPA performance. The first stage is pumped by 250 µJ and uses a 2 mm thick BBO crystal cut for type I phase matching (θ=21°, ϕ=0°); it produces pulse energies up to 3.5 µJ with a spectrum (blue dashed line in Fig. 2) almost as broad as that of the DF pulses. A type I OPA operated around degeneracy displays in fact a broad phase-matching bandwidth, due to the group-velocity matching between signal and idler [23]. By tilting both the crystals for DF generation and amplification it is possible to tune the central frequency of the pulses after the first stage as shown in Fig. 3. In both OPA stages we used a non-collinear geometry with a small angle (≈ 1.5°) between pump and seed to facilitate combination and separation of the beams and to prevent signal-idler interference. The second OPA stage was pumped by 1 mJ and used a 3 mm thick BBO cut for type II phase matching (θ=28.5°, ϕ=30°); this configuration was chosen because, due to its narrower gain bandwidth, it allows to control the amplified pulse spectrum and generate pulses with TL duration. When driven into saturation, the second OPA stage generates pulses with 200-µJ energy and spectrum shown as red dotted line in Fig. 2; note that, since the OPA is operated at degeneracy, this corresponds to a 40% pump conversion efficiency. Both OPA stages work in a regime in which parametric superfluorescence, once the DF seed is blocked, is negligible; this is important because any superfluorescence background would not be phase-stabilized and would thus degrade the CEP stability of the system.

 

Fig. 1. Experimental setup for the generation of high-energy self-phase-stabilized pulses; Ti:Sa, CPA Ti:sapphire laser; DFG, 200 µm thick BBO crystal; POL, thin film polarizer.

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Fig. 2. Normalized spectra of the DF pulses (black solid line) and of the pulses after the first (blue dashed line) and second (red dotted line) OPA stages.

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Fig. 3. Normalized spectra of the amplified pulses after the first OPA stage.

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Fig. 4. Beam profile after the second OPA stage.

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4. Pulse characterization

Thanks to the saturation of the second OPA stage, the amplified pulses display a good energy stability, with peak-to-peak fluctuations <5%. They also show an excellent spatial beam quality, with a clean beam profile as reported in Fig. 4. The amplified pulses are expected to be close to a TL duration without the need of any compression. In fact the DF pulses are generated by a ≈12 fs pulse and thus have a comparable duration. The contribution to dispersion due to the propagation in the BBO crystals used for the NOPA stages can be minimized by tuning the central wavelength of the amplified pulses around 1.55 µm, where BBO exhibits zero second-order dispersion. The amplified pulse width is measured by an unbalanced collinear second-harmonic autocorrelator using a 100-µm-thick BBO crystal. The resulting interferometric autocorrelation is shown in Fig. 5 (thick solid line), together with a calculated trace (thin solid line) starting from the corresponding measured spectrum (see inset of Fig. 5) and assuming a flat spectral phase. The results indicate that the pulses are nearly TL and have a FWHM duration of 15 fs, which corresponds to ≈3 optical cycles at the carrier wavelength. The CEP stability of the amplified pulses was verified and characterized by an f -to-2f interferometer [24]. A suitably attenuated fraction of the pulse energy is first focused in a 2 mm thick sapphire plate, to generate a white light continuum, and then frequency doubled in a 100 µm thick BBO crystal. The spatially overlapped FF and SH are sent to a spectrometer through a polarizer. In the 700–800 nm wavelength range, the spectrally broadened FF and the SH are overlapped; by adjusting their relative intensities with the polarizer, an interference pattern is observed. Fig. 6(a) shows, as a black solid line, an interferogram acquired by averaging over 200 shots; the appearance of a high-contrast fringe pattern is a clear demonstration of CEP stabilization. To prove that the fringes stem from FF-SH interference and do not have any spurious origin, we inserted a 5.9 mm thick BK7 plate before the SH crystal. The plate is expected to increase, due to dispersion, the delay between the 750 and 1500 nm components, and thus decrease the fringe period, as observed in Fig. 6(b). By taking the inverse Fourier transforms of the oscillatory components of the interferograms (see inset of Fig. 6) one finds an increase in delay by 206.2 fs, in excellent agreement with the calculated 204.3 fs group delay introduced by the plate. Finally, Fig. 7 displays a sequence of interferograms acquired over a 6 seconds observation time, indicating that the CEP has some residual fluctuations. They are attributed mainly to environmental noise of the system (mechanical vibrations, air turbulence...), which will have to be accurately reduced in order to optimize this source for applications.

 

Fig. 5. Measured interferometric autocorrelation of the high-energy pulses (red thick solid line) and calculated autocorrelation (black thin solid line) starting from the pulse spectrum (shown in the inset) and assuming flat spectral phase.

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Fig. 6. Spectral interference patterns between FF and SH as generated (a) and with a 5.9 mm thick BK7 plate on the beam path (b). The inset shows the Fourier transforms of the oscillatory components of the interferograms.

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Fig. 7. Sequence of interferograms acquired over successive laser shots. Each interferogram corresponds to 10 pulses.

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5. Conclusions

In this work we have presented a source of high-energy, self phase stabilized few-optical-cycle pulses in the IR, based on DFG between different spectral components of a high-energy ultra-broadband pulse followed by parametric amplification. The main advantages of our approach can be summarized as follows: (i) it is based on the widespread and reliable CPA Ti:sapphire technology; (ii) it uses a passive, all-optical CEP stabilization method; (iii) thanks to the low material dispersion in the IR, it directly generates short pulses without need of any compression. We demonstrate 200-µJ, 15-fs phase-stable pulses at 1.5 µm; the duration and energy of these pulses make them ideally suited to be used as drivers for attosecond pulse generation through HHG. The system has the potential of generating shorter pulses by using also in the second amplification stage a type I configuration, characterized by a broader bandwidth acceptance; the availability of a suitable compressor will allow generating near single-cycle CEP-stable pulses. Higher-energy pulses can be produced by use of more efficient nonlinear crystals such as lithium niobate; however, even more intriguing is the possibility of using this system as a front-end for a high-energy OPA, pumped by a 100-mJ, 10-Hz Ti:sapphire system, enabling TW-level self CEP-stabilized pulses.