The goal of attoscience is to observe and control electronic dynamics occurring on atomic time and length scales in matter. One key enabling technology is the production of attosecond pulse trains or isolated attosecond pulses in the XUV or soft-X-ray spectral region. These attosecond pulses can then be used, often in combination with the driver pulses that produce them, in various time-resolved spectroscopy experiments (attosecond ponderomotive streaking, transient absorption, attosecond-pump/attosecond-probe etc.) to investigate ultrafast processes in atoms, molecules, plasmas, solids and nanostructures: prominent examples include ultrafast relaxation dynamics and multi-electron correlation effects in atoms and molecules,ultrafast correlation-driven charge migration in molecules, charge transfer reactions in molecules and on solid surfaces, sub-cycle ballistic electron transport in solids. Other attoscience techniques such as HHG-based orbital tomography, laser-induced electron diffraction and holography use the laser-driven returning electron wavepackets liberated from small molecules by tunneling ionization to determine the molecular orbital structure. Ultimately this might allow making the molecular movie of ongoing chemical reactions, albeit in atoms and small molecules.
The various attoscience projects in the Ultrafast Optics and X-Rays group aim to push the technological and methodological frontiers of attoscience further.
High-harmonic generation (HHG) and its wavelength scaling
When high-power femtosecond laser pulses are focused into noble gases, such as Ar, Ne, and He, at an intensity of ~1014 W/cm2, an extreme nonlinear optical phenomenon called high-harmonic generation (HHG) is observed. HHG is a coherent strong-field process, where the electrons are tunnel ionized and accelerated by the intense femtosecond laser pulse, and then they recombine into the parent atom (or molecule) in the next half cycle of the laser pulse. The recombination process forms electron dipoles at every half cycle of driving laser pulses and generates harmonic pulses. The nonperturbative coherent behavior of ionized electrons enables to reach a typical harmonic order of 20-500 or the XUV and soft X-ray ranges in wavelength. The dipole radiation happening within sub-cycle of driving laser pulses enables the generation of attosecond pulses.
HHG has been mostly driven by Ti:sapphire laser amplifiers with a fixed wavelength of 800 nm, but the driving wavelength has been found to be very important for scaling the HHG process in terms of the cutoff photon-energy (wavelength) of high-harmonic photons and the conversion efficiency. A longer wavelength driver significantly increases the harmonic photon energy (proportional to λ2 as the ionized electrons are accelerated by the field for a longer time before they combine with a parent atom. On the other hand, the stronger quantum diffusion of the electron wavepacket due to a longer excursion time can dramatically decrease the recombination probability and thereby the conversion efficiency (proportional to λ-(5-8) depending on definition). The driving wavelength also affects the phase-matching condition of HHG. These issues are important not only for the optimization of HHG but also the practical application of HHG sources, such as attosecond science, FEL seeding, and soft-X-ray imaging.
Our group has made a great effort on the study of wavelength scaling of HHG theoretically and experimentally. For example, we developed a semi-analytic expression of HHG conversion efficiency and a 3D pulse propagation code to investigate the macroscopic features of HHG. The OPCPA and OPA systems developed in our group provide high-power femtosecond laser pulses at various wavelengths for the experimental studies. The HHG research in our group has been focused on (1) long-wavelength-driven HHG for soft-X-ray harmonic radiation via cutoff extension and (2) short-wavelength-driven HHG for efficient XUV harmonic radiation.
(1) Long-wavelength-driven HHG: water-window soft X-ray source
One of the most important current tasks is the development of sources of attosecond pulses with higher photon flux and at higher photon energies. High-flux tabletop HHG sources in the water window (284-543 eV) would open up unprecedented capabilities for in-vivo studies of biological specimens. Another important photon energy region is near 1 keV, where many inner-shell absorption edges in catalytic, magnetic, and strongly correlated-electron materials are situated. Ongoing research of the Ultrafast Optics and X-Rays group aims to extend attoscience into these important energy regions.
Our early study based on single-atom calculations revealed that a 1.5-3 µm driver pulses can extend the HHG cutoff into the keV range . Further investigation considering macroscopic effects confirmed that the water-window range can be covered by a 2-µm-driven HHG . Motivated by the theoretical prediction, we developed femtosecond 2-µm light source based on optical parametric chirped-pulse amplification (OPCPA) technology  and a 1.6-µm light source based on OPA technology .
For the long-wavelength-driven HHG, we generated mJ-level 2-µm pulses at kHz repetition rate by using the cryo-cooled Yb:YAG CPA system as the main pump laser, as shown in Fig. 1. The 2-µm OPCPA is composed of 3 stages, delivering CEP-stable 35-fs pulses at 0.85 mJ of maximum energy before compression .
We used the 2-µm pulses for driving HHG in noble gases for cutoff extension with high efficiencies . The actual photo of the HHG vacuum chamber is shown in Fig. 2. The measured HHG spectra from Xe, Kr, and Ar are shown in Figs. 2(a)-(c), where the estimated laser intensities at the focus are (0.7±0.1)x1014 W/cm2 for Xe, (1.1±0.1)x1014 W/cm2 for Kr and (1.7±0.2)x1014 W/cm2 for Ar. They clearly show the cutoff extension from each gas compared to the conventional 800-nm-driven HHG. The cutoff energies in Xe, Kr, and Ar are at ~85 eV (~14 nm, ~149th harmonic), ~120 eV (~10 nm, ~211th harmonic) and ~160 eV (~7.8 nm, ~269th harmonic), respectively. The HHG peak efficiencies per harmonic near cutoff were measured to be ~1x10-9 for Xe at ~70 eV, ~0.8x10-9 for Kr at ~110 eV, ~2x10-9 for Ar at ~130 eV, respectively. In terms of photon flux, the number of photons per second over 1% bandwidth (BW) at 130 eV for Ar is as high as 0.8x108.
The water-window range can be reached by using Ne and He gases with high pressures (~1 bar for Ne and a few bars for He) as well as using higher driving energy with a loose-focusing geometry to achieve a good phase matching condition. To achieve this goal, recently, we first developed a high-pressure gas cell system that supports up to 10 bars of He in our vacuum chamber and then upgraded the cryo-Yb:YAG OPCPA pump laser and thereby the 2-µm OPCPA to a multi-mJ system at a kHz repetition rate. We expect to generate high-flux HHG with ~109 photons/s/1% BW in the water-window soft-X-ray range.
(2) Short-wavelength-driven HHG: efficient XUV source
Our studies on the wavelength scaling of HHG efficiency, as confirmed by other groups, have shown that the conversion efficiency is proportional to λ-(5-6)) (definition with a fixed number of cycles into one harmonic), where λ is the driving wavelength. If the HHG is driven by a short-wavelength driver in the visible, the efficiency can be as high as 10-4 although the cutoff energy is in the XUV range (10-100 eV). Since there are still many applications in this region for attoscience, XUV lithography and molecular spectroscopy, we carefully investigated the wavelength scaling of short-wavelength-driven HHG.
We experimentally studied the HHG efficiency and cutoff  using a Ti:sapphire laser at 800 nm and its second harmonic pulse at 400 nm. The results show that an optimal driving wavelength for 90 eV is 500-600 nm in He, which is accessible by the OP(CP)A technology. Also, it can be predicted that the efficiency can reach >10-3 at <30 eV, if the driving wavelength further goes down to the UV region. This study provided a quantitative guideline of the wavelength-scaling of HHG efficiency.
To further study the wavelength scaling of HHG in the visible wavelength, we recently developed a tunable OPA in the visible range  and systematically performed HHG experiments in various gases. In fact, the HHG with visible driver wavelengths is in the transition between the tunneling and the multi-photon ionization regimes where the Keldysh parameter is around unity. With careful controls of the macroscopic factors including the driver pulse intensities and phase matching, our experiment (Fig. 4(a)) shows a less dramatic wavelength scaling of the single atom efficiency (~λ-4.7) than the calculation of the conventional three-step model (TSM) (Fig. 4(b)) that works well for near- and mid-IR driver wavelengths.
The discrepancy is well explained by a modified TSM for increased Keldysh parameters that employs complex ionization times in addition to the non-adiabatic ionization (Fig. 4(c)). The modified TSM is also in good agreement with the calculation result of time-dependent Schrödinger equation (Fig. (d)). The complex ionization time is critical to avoid the divergence when replacing the quasi-static ionization model by the more general non-adiabatic ionization model. Together, the two modifications present a consistent description of the influence of the atomic potential on the rescattering process in the intermediate Keldysh regime . The extension of the wavelength scaling study to the UV range will give a clear answer for the HHG in the near-threshold regime.
(3) High-harmonic spectroscopy (HHS)
The three-step model that includes tunnel ionization of electrons by the strong field, acceleration, and recombination with the parent atom provides an excellent understanding of the physics underlying the single-atom response. The tunnel ionization and acceleration are mostly determined by the driving electric field while recombination depends on the orbital structure of the parent atom. The emitted XUV photon spectrum is directly related to the dipole moment due to the coherence between the returning electron wave packet and the ionic ground state. The ad hoc factorization of the three-step model has been found to be very useful in the understanding of high-order harmonic (HH) spectra . The harmonic spectrum, S, can be described as follows:
where ω is the photon energy of the emitted XUV radiation, E is the kinetic energy of the returning electron, d is the transition dipole element in the length form, W is the electron wave packet (EWP), and σr is the photorecombination cross section (PRCS) that is related to the photoionization cross section (PICS). The essence of HHS is that we can get the transient dipole information or the imaging of atomic or molecular orbitals from HH spectra.
Besides the development of high-flux XUV sources, long-wavelength-driven HHG is crucial for HH spectroscopy because the extended cutoff and broad plateau give additional information on the single-atom response in the high-photon-energy region, revealing the atomic and molecular orbital structure more clearly. High-energy electrons can excite inner-shell dynamics and multi-electron effects.
We performed HHS under the presence of macroscopic effects. Accurate 3D simulations of the pulse propagation make it possible to calculate the EWP and remove the distortion of HH spectra by the EWP. The accurate PRCS can still be extracted in this way. Fig. 5 shows how to extract the PRCS of the outermost 4p shell in Kr from the measured HH spectrum and 3D wavepacket calculation with propagation (macroscopic WP). We observed a Cooper minimum of Kr, which has been observed at 60-70 eV in our measurement, shifted from a known value of 80 eV, attributed to the propagation effect during HHG. After the correction we see a good agreement between the extracted PRCS curve and a known curve on the bottom. We will extend our precision HHS to various molecules as well as to the range of >300 eV to study inner-shell dynamics.
Novel schemes to generate isolated attosecond pulses
The generation of intense isolated attosecond pulses is of utmost importance for time-resolved spectroscopy. We are pursuing novel schemes such as HHG driven by multi-color sub-cycle waveforms [10,11,12]. Recently, by combining two-color waveform synthesis and an energy-scaling method of HHG, the generation of intense isolated attosecond pulses with 500-as duration, 1.3-µJ energy and 2.6-GW peak power was demonstrated, that are sufficiently strong for attosecond-pump/attosecond-probe spectroscopy [13,14,15].
Characterization of attosecond pulses
The development of attosecond sources has necessitated the codevelopment of attosecond pulse retrieval methods. Fortunately, cutting-edge concepts developed for characterizing femtosecond pulses, such as FROG, can also be applied to attosecond pulse characterization. However, for attosecond pulse characterization using FROG-CRAB, the crystal is replaced by an atomic gas, and the outgoing photon by an electron. During photoionization, the attosecond pulse spectrum and phase is mapped directly onto photoelectrons, which are subsequently probed by a strong IR pulse. The acquisition of photoelectron energy spectra as function of delay between the attosecond and IR pulses contains all the temporal information about the XUV pulse.
In order to perform such a characterization, we have developed and tested a complete, in-vacuum XUV + IR streaking apparatus. Attosecond timing precision over hours of operation is provided by active stabilization, and the design allows for the use of separate IR streak and drive pulses (for instance, the use of an 800-nm pulse to drive the attosecond pulse generation, and a 2-µm pulse to streak the photoelectrons). The figure below shows a typical spectrogram collected with our setup, along with the corresponding XUV pulse train extracted using a FROG-CRAB algorithm. Beyond pulse characterization, it is possible to perform a variety of attosecond XUV pump/IR probe experiments, as the interaction chamber is housed with an XUV spectrometer, ion time-of-flight spectrometer, and electron time-of-flight spectrometer, allowing to collect all three spectra simultaneously.
Few-body molecular dissociation dynamics
The response of small molecules to strong fields depends critically on wavelength. Using a combination of photoelectron and photoion spectroscopy, we are exploring this dependence using coordinated sequences of XUV and IR pulses, and gauging the possibility of using attosecond and IR pulses to control molecular dissociation dynamics. Isolated attosecond pulses offer a unique capability: in contrast to few-cycle IR pulses and XUV pulse trains, they can ionize a molecule on a timescale confined to a femtosecond or shorter, i.e., well within the period of vibration of even the fastest molecular vibrations. A sequence of attosecond and IR pulses thus offers a way to separate a controlled interaction with a molecule on its electronic and vibrational timescales. This study incorporates a number of the laser and vacuum technologies we have developed for attosecond science at MIT, including ion time-of-flight, electron time-of-flight, and XUV spectrometers (see figure below), our coherent wavelength synthesizer based on OPCPA technology, and the attosecond streaking technology described above. (Senior Researcher: Jeff Moses).
Plasmonics and nano-photonics
Plasmonics has great potential for realizing ultrafast electron sources. Due to a strong intensity enhancement at well defined regions just nanometers in diameter, localized electron emission can be achieved through multiphoton processes, such as direct photo-ionization and strong-field tunneling. The emitted electrons can then be injected into compact accelerators and free-electron X-ray sources. Our group has recently performed experiments for investigating different electron sources based on field emitters with and without plasmonic field enhancement and various emission mechanisms. We have observed a transition from multiphoton to the tunneling regime of electron emission across large scale arrays of tips, which had previously only been demonstrated in the context of single tip emission. Furthermore, by monitoring emitted electron energy spectra, strong-field effects, such as a high-energy plateau of rescattered electrons from the tip surface (see Fig. 8), have been observed .
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