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# Isolated Single-Cycle Attosecond Pulses

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Science  20 Oct 2006:
Vol. 314, Issue 5798, pp. 443-446
DOI: 10.1126/science.1132838

## Abstract

We generated single-cycle isolated attosecond pulses around ∼36 electron volts using phase-stabilized 5-femtosecond driving pulses with a modulated polarization state. Using a complete temporal characterization technique, we demonstrated the compression of the generated pulses for as low as 130 attoseconds, corresponding to less than 1.2 optical cycles. Numerical simulations of the generation process show that the carrier-envelope phase of the attosecond pulses is stable. The availability of single-cycle isolated attosecond pulses opens the way to a new regime in ultrafast physics, in which the strong-field electron dynamics in atoms and molecules is driven by the electric field of the attosecond pulses rather than by their intensity profile.

The past decade has seen remarkable advances in the field of femtosecond (1 fs = 10–15 s) light pulses with few optical cycles (1). The main achievements have been (i) the generation of ultrabroadband light pulses, directly from a laser oscillator or with the use of external spectral broadening mechanisms; (ii) the development of sophisticated techniques for dispersion compensation on ultrabroad bandwidths; (iii) the use of experimental methods for complete temporal characterization of ultrashort pulses, particularly frequency-resolved optical gating (FROG) (2) and spectral phase interferometry for direct electric field reconstruction (SPIDER) (3), in a number of different experimental implementations; and (iv) the generation of few-cycle light pulses with precisely controlled and reproducible electric field waveform [stabilized carrier-envelope phase (CEP)] (46). We show that these achievements can now be extended to the attosecond (1 as = 10–18 s) domain. We demonstrate the compression and the complete temporal characterization of isolated pulses with durations down to 130 as at 36-eV photon energy, which consist of less than 1.2 periods of the central frequency. This source of extreme ultraviolet (XUV) radiation lends itself as a tool to investigate basic electron processes in a spectral range approaching the energy level of the outermost electrons in atoms, molecules, and solid-state systems. The XUV source opens the way to a new regime in the applications of attosecond pulses in which a medium interacts with nearly single-cycle isolated attosecond pulses. Moreover, in this case it is appropriate to analyze the role of the CEP of the generated attosecond pulses. Using numerical simulations, we demonstrate that the carrier-envelope phase of the attosecond pulses is characterized by an excellent stability.

So far, isolated attosecond pulses with multiple optical cycles have been produced by selecting the high-energy (cut-off) harmonics (∼90 eV) generated in neon by few-cycle (<7 fs) linearly polarized fundamental pulses with stabilized CEP (79). In this case, the minimum pulse duration of the XUV pulses is limited by the bandwidth of the selected cut-off harmonics (∼10 eV), thus preventing the generation of single-cycle attosecond pulses. A different approach for the generation of broadband isolated attosecond pulses is based on the use of phase-stabilized few-cycle driving pulses in combination with the polarization gating technique (1013). Such a method uses the strong dependence of the harmonic generation process on the ellipticity of the driving pulses in order to obtain a temporal window of linear polarization for the fundamental pulses. XUV generation is possible only during this temporal polarization gate, which can be shorter than half an optical cycle of the fundamental radiation. In combination with the use of few-cycle driving pulses with stable CEP, this technique allows the generation of broadband isolated attosecond pulses. The advantages of this method are (i) the generation of broadband XUV pulses; (ii) the broad tunability of the attosecond pulses upon changing the generating gas medium; (iii) energy scalability; and (iv) the possibility to access the single-cycle regime.

The generation of broadband attosecond pulses is an important tool for photoelectron spectroscopy. Although they are not Fourier limited (chirped pulses), broadband attosecond pulses can be used to measure attosecond electron dynamics just as effectively as if the pulses were transform limited (14). However, in this case a complete temporal characterization of the attosecond pulses is required. On the other hand, for a number of applications in which the temporal structure of the attosecond pulses is important, dispersion compensation is required in order to obtain pulses with duration close to the transform-limited value. To completely characterize the attosecond pulses in terms of temporal intensity and phase, we experimentally applied the method of FROG for complete reconstruction of attosecond burst (FROG CRAB, hereafter called CRAB) (15), an extension to attosecond electron wavepackets of the FROG method. When an atom is ionized by an XUV attosecond electric field in the presence of a streaking infrared (IR) pulse, the IR electric field acts as an ultrafast phase modulator on the generated electron wavepacket. The corresponding photo-ionization spectrum can be written as a FROG spectrogram with a pure phase gate ϕ(t) (15): $Math$(1) where A(t) is the vector potential of the IR field and v is the final electron velocity. A number of iterative algorithms can then be used to reconstruct the electric field of both the attosecond pulse and of the streaking IR pulse from the measured CRAB trace.

We adjusted the CEP of the driving few-cycle light pulses [full-width at intensity half-maximum (FWHM): τD = 5 fs; central wavelength: λD = 750 nm] with controlled electric field in order to generate broadband and continuous XUV spectra in an Argon cell with static pressure, using the process of high-order harmonic generation (16, 17). The required temporal modulation of the driving IR pulse polarization was obtained with the use of two birefringent plates [for a detailed description of the experimental apparatus, see the supporting online material (SOM) text]. Upon changing the CEP of the driving pulses, a clear transition from two emission bursts to a single emission burst was observed in the spectral domain (13). Using a grazing incidence toroidal mirror, we focused the attosecond pulses into an Argon gas jet. The streaking IR beam was spatially overlapped with the XUV beam in the gas jet. The generated photoelectrons were collected within an acceptance angle of ±2° around θ = 0, where θ is the angle between v and the polarization direction of the IR field.

Figure 1A shows a portion of an experimental CRAB trace, which represents the evolution of the photoelectron spectra as a function of the temporal delay between the XUV and the streaking IR pulses. The measured trace follows the evolution of the vector potential, A(t), of the streaking pulse. The temporal structure of the attosecond pulses was retrieved using the principal-component generalized projection algorithm (PCGPA) (18). In the reconstructed temporal intensity profile and phase of the XUV pulses (Fig. 1B), the pulse duration was 280 as (the Fourier limit is ∼100 as), and the almost parabolic phase indicates the presence of a predominant second-order dispersion, corresponding to a positive linear chirp C≅ 42 fs–2. Such pulses correspond to only 2.5 optical cycles of the carrier frequency. The measured CRAB trace and the corresponding reconstruction of the XUV pulses clearly demonstrate the generation of isolated pulses, consistent with the measurement of a continuous XUV spectrum, with no clear evidences of harmonic peaks. The measured modulation of the width of the photoelectron spectrum was determined not only by the XUV pulse duration, but also by the chirp of the attosecond pulses (15). In our experimental conditions, the presence of positive chirp leads to a decrease of the electronic spectrum width (thus resulting in a spectral peak increase) in the temporal regions characterized by a negative slope of the vector potential, as clearly visible in Fig. 1A.

The measured positive chirp is intrinsic to the XUV generation process, because the harmonic emission time varies quasi-linearly with harmonic frequency (the spectral components at higher frequencies are emitted after those at lower frequencies) (19). As recently demonstrated in the case of trains of attosecond pulses (20), the positive chirp of the XUV radiation produced by high-order harmonic generation can be compensated for by the negative group delay dispersion of thin aluminum foils, which is almost constant on the bandwidth of the generated attosecond pulses. The CRAB trace reported in Fig. 1A was measured using a 100-nm-thick aluminum foil (on a nickel mesh) on the XUV beam, in order to filter out the fundamental radiation, thus reducing the intrinsic positive chirp of the attosecond pulses. To test the possibility of further compressing the XUV pulses, we used thicker aluminum foils. Figure 2A shows a complete CRAB trace measured with a 300-nm-thick aluminum foil. The retrieved CRAB trace (Fig. 3) reproduces the experimental trace: The CRAB error, evaluated as the root mean square error per element of the trace (21), is ∼10–3. In the intensity profile and the temporal phase of the retrieved attosecond pulses (Fig. 2B), the pulse duration (FWHM) is 130 as, close to the Fourier limit, thus indicating a good compensation of the intrinsic chirp. Such pulses correspond to fewer than 1.2 optical cycles of the carrier frequency (22).

The single-cycle nature of the generated isolated pulses has important implications for ultrafast science and adds another parameter to the study of attosecond phenomena: the carrier-envelope phase of the isolated attosecond pulses. To address this topic, we modeled the physical processes involved in the attosecond pulse generation using the nonadiabatic saddle-point method (23, 24). Such an approach is based on the concept of Feynman's path integrals (23, 25), which correspond to the complex trajectories (quantum paths) followed by the electrons from the ionization instant to the recombination with the parent ion in the process of high-order harmonic generation. We verified that the results of the numerical simulations were in agreement with the experimental data. In particular, they perfectly reproduce the effects of the CEP of the driving pulses on the spectral properties of the harmonic radiation. Moreover, the calculated temporal characteristics of the attosecond pulses (such as pulse duration, temporal and spectral phase, and chirp) turn out to be in very good agreement with the results of the experimental CRAB reconstruction procedure.

Figure 4 shows the electric field evolution calculated with the same driving pulse parameters that were used in the experiment and considering the contribution of the aluminum foil: The calculated pulse duration is 135 as (FWHM of the intensity profile), in agreement with the experimental result. The numerical simulations allow us to analyze the role of the experimental parameters on the CEP of the attosecond pulses. We calculated the temporal evolution of the XUV electric field upon changing the CEP of the driving pulses. We varied the driving CEP values in a range of ∼175 mrad, giving rise to an efficient generation of isolated attosecond pulses. As demonstrated in Fig. 4, which displays the calculated electric field evolution for two different values of the CEP of the driving pulses, the CEP of the isolated attosecond pulses is negligibly influenced by variation of the CEP of the driving pulses. The two pulses reported in Fig. 4 were temporally shifted to overlap their intensity envelopes; the same shift determines the overlap of the electric fields of the corresponding driving pulses (26). In the considered CEP range of the IR pulses, only one electron quantum path contributes in a relevant way to the XUV emission. Because the corresponding electron wavepacket is emitted around a stationary point of the intensity profile of the driving pulse (12), relative changes of the emission and recombination times with respect to the IR intensity envelope (due to different CEP values) do not significantly affect the phase accumulated by the electron wavepacket (27). This determines an intrinsic mechanism for stabilization of the electric field of the attosecond pulses against variations of the CEP of the driving pulses. We have analyzed the effects of fluctuations of the excitation intensity; in this case, the induced variation of the attosecond CEP is very small. Indeed, a 2% intensity fluctuation leads to a ∼140-mrad CEP shift. The most important conclusion is that the CEP of the generated attosecond pulses is markedly stable. The attosecond CEP could be finely tuned, for example, by using aluminum foils with variable thickness: At 36 eV, a π CEP variation is induced by the addition of ∼80 nm of aluminum (although in this case also the pulse duration is affected).

The intrinsic robustness of the stability of attosecond pulse CEP should lead to new applications in ultrafast physics. These results pave the way to theoretical and experimental studies for the determination of the exact electric field evolution of attosecond XUV pulses. As the energy of the generated attosecond pulses can be easily increased by increasing the energy of the IR driving pulses, we can envisage applications of the phase-stable single-cycle attosecond pulses to the study of strong-field electron dynamics in atoms and molecules, when processes are triggered and controlled by the electric field of the attosecond pulses, rather than by the intensity profile. As in the case of few-cycle IR pulses, we expect the possibility to influence and modify the ionization mechanisms of valence electrons upon changing the CEP of the attosecond pulses in the strong-field regime. In a lower intensity regime, as recently proposed in the case of few-cycle infrared pulses (28), the ultrafast dynamics of the population of bound and continuum states in atoms and molecules can be coherently influenced by the electric field temporal evolution of single-cycle attosecond pulses. The control of the CEP of such pulses provides an additional degree of freedom in the preparation and manipulation of atomic and molecular wavepackets. Another application is the investigation of photoionization processes in the presence of few-cycle XUV pulses and intense (>1013 W/cm2) synchronized IR fields. In this case, electron wavepackets can be emitted in the continuum following two different ionization channels: multiphoton above-threshold ionization associated to the IR field and absorption of single XUV photons. The coherent superposition of the two ionization probabilities determines an interference pattern in the photoelectron spectra, which should offer the possibility to measure the CEP of the attosecond pulses. Moreover, the availability of few-cycle isolated pulses in the photon energy range of about 30 eV is particularly important for the study of electron dynamics in chemistry and molecular and solid state physics, in which a number of fundamental processes are related to the outermost electrons, directly accessible by the generated attosecond pulses. On the other hand, the possibility of generating single-cycle pulses of less than 100 as at higher energy with the use of the polarization gating method in neon (13) should allow the study of the coherent dynamics of inner-shell electrons with unprecedented temporal resolution.

Supporting Online Material

SOM Text

References

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