Publications

In this chapter, we introduce all-optical attosecond interferometry using high-harmonic generation (HHG). Interferometry provides an access to phase information, enabling the reconstruction of ultrafast electron dynamics with attosecond precision. We discuss two main pathways\u2014internal and external attosecond interferometry. In internal interferometry, the manipulation of quantum paths within the HHG mechanism enables phase-resolved studies of strong-field processes, such as field-induced tunneling. In external interferometry, the phase of the light emitted during the HHG process can be determined using optical interference in the extreme-ultraviolet regime. Both pathways have significantly progressed the state of the art of ultrafast spectroscopy, as evidenced by numerous examples described in this chapter. All-optical attosecond interferometry is applicable to a wide range of systems, such as atomic and molecular gases and condensed-matter systems. Combining the two pathways has the potential to access to hitherto elusive ultrafast multi-electron and chiral phenomena.

Strong laser pulses enable probing molecules with their own electrons. The oscillating electric field tears electrons off a molecule, accelerates them, and drives them back toward their parent ion within a few femtoseconds. The electrons are then diffracted by the molecular potential, encoding its structure and dynamics with angstrom and attosecond resolutions. Using elliptically polarized laser pulses, we show that laser-induced electron diffraction is sensitive to the chirality of the target. The field selectively ionizes molecules of a given orientation and drives the electrons along different sets of trajectories, leading them to recollide from different directions. Depending on the handedness of the molecule, the electrons are preferentially diffracted forward or backward along the light propagation axis. This asymmetry, reaching several percent, can be reversed for electrons recolliding from two ends of the molecule. The chiral sensitivity of laser-induced electron diffraction opens a new path to resolve ultrafast chiral dynamics.

Ever since its discovery ¹, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena ². However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.

Conferences are incredible opportunities to strengthen the inclusive outlook of our scientific community. The participation of female scientists, postdocs, and graduate students in the ATTO VIII conference was remarkable, with more than 40% of female invited speakers. The Local Organizing Committee seized this opportunity to promote an atmosphere that welcomes all. An entirely female evening panel, with experience across the attosecond science spectrum, was convened to explore the Future of Attosecond Science in the evening session of Wednesday, July 13. Furthermore, a booklet entitled Perspectives in Attosecond Science was compiled by Dr. Shima Gholam-Mirzaei of the University of Ottawa and ATTO co-chairs Luca Argenti and Michael Chini, in collaboration with members of the Local Organizing Committee and others, which included interviews with female scientists at all career levels and which was included in the conference materials. The text has been minimally edited to improve clarity and readability.

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

Strong-field imaging techniques such as laser-induced electron diffraction (LIED) provide unprecedented combined picometer spatial and attosecond temporal resolution by "self-imaging"a molecular target with its own rescattering electrons. Accessing the rich information contained in these experiments requires the ability to accurately manipulate the dynamics of these electrons-namely, their ionization amplitudes, and times of ionization and rescattering-with attosecond to femtosecond precision. The primary challenge is imposed by the multitude of quantum pathways of the photoelectron, reducing the effective measurement to a small range of energies and providing very limited spatial resolution. Here, we show how this ambiguity can be virtually eliminated by manipulating the rescattering pathways with a tailored laser field. Through combined experimental and theoretical approaches, a phase-controlled two-color laser waveformis shown to facilitate the selection of a specific quantum pathway, allowing a direct mapping between the electron's final momentum and the rescattering time. Integrating attosecond control with Ångstrom-scale resolution could advance ultrafast imaging of field-induced quantum phenomena.

Intense light\u2013matter interactions have revolutionized our ability to probe and manipulate quantum systems at sub-femtosecond timescales¹, opening routes to the all-optical control of electronic currents in solids at petahertz rates^2\u20137. Such control typically requires electric-field amplitudes in the range of almost volts per angstrom, when the voltage drop across a lattice site becomes comparable to the characteristic bandgap energies. In this regime, intense light\u2013matter interaction induces notable modifications to the electronic and optical properties^8\u201310, dramatically modifying the crystal band structure. Yet, identifying and characterizing such modifications remain an outstanding problem. As the oscillating electric field changes within the driving field\u2019s cycle, does the band structure follow and how can it be defined? Here we address this fundamental question, proposing all-optical spectroscopy to probe the laser-induced closing of the bandgap between adjacent conduction bands. Our work reveals the link between nonlinear light\u2013matter interactions in strongly driven crystals and the sub-cycle modifications in their effective band structure.

Interferometry has been at the heart of wave optics since its early stages, resolving the coherence of the light field and enabling the complete reconstruction of the optical information it encodes. Transferring this concept to the attosecond time domain shed new light on fundamental ultrafast electron phenomena. Here we introduce attosecond-gated interferometry and probe one of the most fundamental quantum mechanical phenomena, field-induced tunnelling. Our experiment probes the evolution of an electronic wavefunction under the tunnelling barrier and records the phase acquired by an electron as it propagates in a classically forbidden region. We identify the quantum nature of the electronic wavepacket and capture its evolution within the optical cycle. Attosecond-gated interferometry has the potential to reveal the underlying quantum dynamics of strong-field-driven atomic, molecular and solid-state systems.

We introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals. We then experimentally demonstrate this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of high-order harmonics.

Light-matter interaction based on strong laser fields enables probing the structure and dynamics of atomic and molecular systems with unprecedented resolutions, through high-order harmonic spectroscopy, laser-induced electron diffraction, and holography. All strong-field processes rely on a primary ionization mechanism where electrons tunnel through the target potential barrier lowered by the laser field. Tunnel ionization is, thus, of paramount importance in strong-field physics and attoscience. However, the tunneling dynamics and properties of the outgoing electronic wave packets often remain hidden beneath the influence of the subsequent scattering of the released electron onto the ionic potential. Here, we present a joint experimental-theoretical endeavor to characterize the influence of sub-barrier dynamics on the amplitude and phase of the wave packets emerging from the tunnel. We use chiral molecules, whose photoionization by circularly polarized light produces forward-backward asymmetric electron distributions with respect to the light propagation direction. These asymmetric patterns provide a background-free signature of the chiral potential in the ionization process. We first implement the attoclock technique, using bicircular two-color fields. We find that, in the tunnel-ionization process, molecular chirality induces a strong forward-backward asymmetry in the electron yield, while the subsequent scattering of the freed electron onto the chiral potential leads to an asymmetric angular streaking of the electron momentum distribution. In order to access the phase of the tunneling wave packets, we introduce subcycle gated chiral interferometry. We employ an orthogonally polarized two-color laser field whose optical chirality is manipulated on a sub-laser-cycle timescale. Numerical simulations are used to interpret the electron interference patterns inherent to this interaction scheme. They show that the combined action of the chiral potential and rotating laser field not only imprints asymmetric ionization amplitudes during the tunneling process, but also induces a forward-backward asymmetric phase profile onto the outgoing electron wave packets. Chiral light-matter interaction thus induces subtle angular-dependent shaping of both the amplitude and the phase of tunneling wave packets.

Strong-field light-matter interactions initiate a wide range of phenomena in which the quantum paths of electronic wavepackets can be manipulated by tailoring the laser field. Among the electrons released by a strong laser pulse from atomic and molecular targets, some are subsequently driven back to the vicinity of the ionic core by the oscillating laser field. The trajectories of these returning electrons are bent toward the core by the ionic potential, an effect known as Coulomb focusing. This process, studied over the past two decades, has been associated with the long range influence of the Coulomb potential. Here we explore the structural properties of the Coulomb focusing phenomenon. Specifically, we numerically study the sensitivity of the returning electron dynamics to the anisotropy of the ionic potential. We employ orthogonally polarized two-color strong fields and chiral molecules, whose asymmetric features lead to unambiguous fingerprints of the potential on the freed electrons. The Coulomb-focused electrons show an enhanced sensitivity to chirality, related to an asymmetric attoclock-like angular streaking stemming from field-assisted scattering of the electrons onto the chiral ionic potential. Anisotropic features of the ionic potential thus monitor the motion of Coulomb-focused electrons throughout their returning paths, shedding light on the structural properties of the interaction.

High harmonic generation (HHG) spectroscopy has emerged as an invaluable tool for studying electronic dynamics and structure in crystals. The primary challenges are imposed by the multiple degrees of freedom of the underlying dynamics as well as the low efficiency of the HHG process. Here we show that when the HHG process is driven by a synthesized bichromatic field, its efficiency can be significantly enhanced, increasing the photon flux by 1\u20132 orders of magnitude. The bichromatic field enhances the signal on a microscopic level by manipulating the tunnel ionization and subsequent electron dynamics driven by the synthesized laser waveform. We examine the scaling of the HHG yield on the field parameters, and observe a pronounced dependence on the HHG energy. Importantly, our study reveals that the different spectral regimes are dictated by different generation mechanisms as well as multiple bands in which the dynamics evolve. Our work demonstrates that shaped laser fields serve as a powerful approach to control multiband electron currents in solids, probe their origin, and enhance the efficiency of the HHG process.

Since 2001 and the first demonstrations of the feasibility of generating and measuring attosecond light pulses, attosecond science has developed into a very active and quickly evolving research field. Its ultimate goal is the real-time tracking of electron dynamics in all forms of matter, ranging from atoms and large molecules to the condensed phase and plasmas. The accomplishment of this goal has required and still calls for developments in ultrafast laser technology, ultrafast metrology, extreme ultra-violet (XUV) optics, pump-probe measurement schemes and non-linear laser-matter interaction. Moreover, the interpretation of the experimental results in attosecond experiments has stimulated and guided major developments in theoretical descriptions of ultrafast electronic processes in matter. Motivated by these two decades of development, several large-scale facilities, including extreme light infrastructure - attosecond light pulse source (ELI-ALPS) and several free electron laser facilities (the linac coherent light source (LCLS) at Stanford and the European XFEL in Hamburg) are now pushing the development of a new generation of attosecond sources. This considerable technological effort opens new and important perspectives in the field of ultrafast science with potential applications in photochemistry, photobiology and advanced electronics. In this context, the joint focus issue on Attosecond technology(/ies) and science of J. Phys. Photon. and J. Phys. B: At. Mol. Opt. Phys. aims to provide an overview of the state-of-the-art in attosecond science, from the basic science involved in the generation and in applications of attosecond pulses to the technologies that are required.

The Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

Using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics in multi-band solid-state systems. We identify the mapping of spectral caustics into the high-harmonic spectrum, and probe the structure of multiple unpopulated high conduction bands.

A single-molecule attosecond interferometry that can retrieve the spectral phase information associated with the structure of molecular orbitals, as well as the phase accumulated by an electron as it tunnels out, is demonstrated.Interferometry is a basic tool to resolve coherent properties in a wide range of light or matter wave phenomena. In the strong-field regime, interferometry serves as a fundamental building block in revealing ultrafast electron dynamics. In this work we manipulate strong-field-driven electron trajectories and probe the coherence of a molecular wavefunction by inducing an interferometer on a microscopic level. The two arms of the interferometer are controlled by a two-colour field, while the interference pattern is read via advanced, three-dimensional high-harmonic spectroscopy. This scheme recovers the spectral phase information associated with the structure of molecular orbitals, as well as the spatial properties of the interaction itself. Zooming into one of the most fundamental strong-field phenomena-field-induced tunnel ionization-we reconstruct the angle at which the electronic wavefunction tunnels through the barrier and follow its evolution with attosecond precision.

Low frequency Raman spectroscopy resolves the slow vibrations resulting from collective motions of molecular structures. This frequency region is extremely challenging to access via other multidimensional methods such as 2D-IR. In this paper, we describe a new scheme which measures 2D Raman spectra in the low frequency regime. We separate the pulse into a spectrally shaped pump and a transform-limited probe, which can be distinguished by their polarization states. Low frequency 2D Raman spectra in liquid tetrabromoethane are presented, revealing coupling dynamics at frequencies as low as 115 cm−1. The experimental results are supported by numerical simulations which replicate the key features of the measurement. This method opens the door for the deeper exploration of vibrational energy surfaces in complex molecular structures.

Strong-field-driven electric currents in condensed-matter systems are opening new frontiers in petahertz electronics. In this regime, new challenges are arising as the roles of band structure and coherent electron-hole dynamics have yet to be resolved. Here, by using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid-state systems. We demonstrate that when the electron-hole relative velocity approaches zero, enhanced constructive interference leads to the appearance of spectral caustics in the high-harmonic generation spectrum. We introduce the role of the dynamical joint density of states and identify its mapping into the spectrum, which exhibits singularities at the spectral caustics. By studying these singularities, we probe the structure of multiple unpopulated high conduction bands.

Solid-state high-harmonic generation (HHG) by an intense infra-red (IR) laser field offers a new route to generate coherent attosecond light pulses in the extreme ultraviolet regime. The propagation of the IR driving field in the dense solid medium is accompanied by non-linear processes which shape the generating waveform. In this work, we introduce a monolithic scheme in which we both exploit the non-linear propagation to manipulate a two color driving field, as well as generate high harmonics within a single crystal. We show that the resulting non-commensurate, bi-chromatic, generating field provides precise control over the periodicity of the HHG process. This control enables us to manipulate the spectral positions of the discrete harmonic peaks. Our method advances solid-state HHG spectroscopy, and offers a simple route towards tunable, robust XUV sources.

Controlling the polarization state of electromagnetic radiation enables the investigation of fundamental symmetry properties of matter through chiroptical processes. Over the past decades, many strategies have been developed to reveal structural or dynamical information about chiral molecules with high sensitivity, from the microwave to the extreme ultraviolet range. Most schemes employ circularly or elliptically polarized radiation, and more sophisticated configurations involve, for instance, light pulses with time-varying polarization states. All these schemes share a common property-the polarization state of light is always considered as constant over one optical cycle. In this study, we focus on the optical cycle in order to resolve and control a subcyle chiroptical process. We engineer an electric field whose instantaneous chirality can be controlled within the optical cycle, by combining two phase-locked orthogonally polarized fundamental and second harmonic fields. While the composite field has zero net ellipticity, it shows an instantaneous optical chirality which can be controlled via the two-color delay. We theoretically and experimentally investigate the photoionization of chiral molecules with this controlled chiral field. We find that electrons are preferentially ejected forward or backward relative to the laser propagation direction depending on the molecular handedness, similarly to the well-established photoelectron circular dichroism process. However, since the instantaneous chirality switches sign from one half-cycle to the next, electrons ionized from two consecutive half-cycles of the laser show opposite forward-backward asymmetries. This chiral signal, the enantiosensitive subcycle antisymmetric response gated by electric-field rotation, provides a unique insight into the influence of instantaneous chirality in the dynamical photoionization process. More generally, our results demonstrate the important role of subcycle polarization shaping of electric fields as a new route to study and manipulate chiroptical processes.

Probing vectorial properties of light-matter interactions requires control over the polarization state of light. The generation of extreme-ultraviolet (XUV) attosecond pulses opened new perspectives in measurements of chiral phenomena. Recently, new methods for polarization control in the XUV range, which are based on manipulation of the high harmonic generation (HHG) process were demonstrated [1-4]. However, the limited polarization control in this regime prevents the development of advanced measurement schemes for weak vectorial signals, which require polarization modulation.

Soft x-ray sources based on laser-driven high-harmonic generation (HHG) offer a tabletop alternative to sources generated at synchrotron and free-electron laser facilities [1,2]. In this work we demonstrate two orders of magnitude enhancement in conversion efficiency of HHG soft x-rays. The enhancement occurs on a single particle level and is based upon sub-optical-cycle control and enhancement of the tunnelling ionization rate [3]. Using a simple two-colour synthesizer to drive HHG, here we show that both high enhancement and high HHG flux can be achieved in the soft x-ray (SXR) region. In the presented results, the enhancement spans over a 250 eV bandwidth with pulse energies reaching the pJ level.

Photoelectron spectroscopy is a powerful method that provides insight into the quantum mechanical properties of a wide range of systems. The ionized electron wavefunction carries information on the structure of the bound orbital, the ionic potential as well as the photo-ionization dynamics itself. While photoelectron spectroscopy resolves the absolute amplitude of the wavefunction, retrieving the spectral phase information has been a long-standing challenge. Established photo-ionization spectroscopy methods, such as reconstruction of attosecond beating by interference of two-photon transitions (RABBITT), are able to access only the first derivative of the spectral phase, the group delay, due to their nonlinear nature [1,2]. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photo-ionization - photo-recombination - in high-harmonic generation (HHG). The extreme-ultraviolet attosecond pulses produced in HHG carry the full information of the light-matter interaction, including the electronic structure of the system under scrutiny. Their spectral phase directly encodes the photo-ionization dipole phase due to the final step of HHG - photo-recombination of a well-defined electron wavepacket into the ion. In this work, we access this phase using interferometry, which is highly challenging in the XUV spectral domain due to the absence of efficient optics.

We exploit high-order harmonic generation spectroscopy at the caustics of the recombining electron wave-packet as a method for directly comparing experimental spectra with ab-initio theories. Experimental results in xenon and comparison with ab-initio time-dependent configuration-interaction singles calculations allowed to assess the role of the wave-packet enhancement during the giant resonance. Results in argon show that this technique can also be applied to other targets.

Probing the vectorial properties of light-matter interactions inherently requires control over the polarization state of light. The generation of extreme-ultraviolet attosecond pulses has opened new perspectives in measurements of chiral phenomena. However, limited polarization control in this regime prevents the development of advanced vectorial measurement schemes. Here, we establish an extreme-ultraviolet lock-in detection scheme, allowing the isolation and amplification of extremely weak chiral signals, by achieving dynamical polarization control. We demonstrate a time-domain approach to control and modulate the polarization state, and perform its characterization via an in situ measurement. Our approach is based on the collinear superposition of two independent, phase-locked, orthogonally polarized extreme-ultraviolet sources and the control of their relative delay with sub-cycle accuracy. We achieve lock-in detection of magnetic circular dichroism, transferring weak amplitude variations into a phase modulation. This approach holds the potential to significantly extend the scope of vectorial measurements to the attosecond and nanometre frontiers.

High-harmonic generation spectroscopy is a powerful tool for ultrafast spectroscopy with intrinsic attosecond time resolution. Its major limitation-the fact that a strong infrared driving pulse is governing the entire generation process-is lifted by extreme ultraviolet (XUV)-initiated high-harmonic generation (HHG). Tunneling ionization is replaced by XUV photoionization, which decouples ionization from recollision. Here we probe the intensity dependence of XUV-initiated HHG and observe strong spectral frequency shifts of the high harmonics. We are able to tune the shift by controlling the instantaneous intensity of the infrared field. We directly access the reciprocal intensity parameter associated with the electron trajectories and identify short and long trajectories. Our findings are supported and analyzed by ab initio calculations and a semiclassical trajectory model. The ability to isolate and control long trajectories in XUV-initiated HHG increases the range of the intrinsic attosecond clock for spectroscopic applications.

Seven scientists share their views on some of the latest developments in attosecond science and X-ray free electron lasers (XFELs) and highlight exciting new directions.

A key challenge in attosecond science is the temporal characterization of attosecond pulses that are essential for understanding the evolution of electronic wavefunctions in atoms, molecules and solids(1-7). Current characterization methods, based on nonlinear light-matter interactions, are limited in terms of stability and waveform complexity. Here, we experimentally demonstrate a conceptually new linear and all-optical pulse characterization method, inspired by double-blind holography. Holography is realized by measuring the extreme ultraviolet (XUV) spectra of two unknown attosecond signals and their interference. Assuming a finite pulse duration constraint, we reconstruct the missing spectral phases and characterize the unknown signals in both isolated pulse and double pulse scenarios. This method can be implemented in a wide range of experimental realizations, enabling the study of complex electron dynamics via a single-shot and linear measurement.

In photoelectron spectroscopy, the ionized electron wavefunction carries information about the structure of the bound orbital and the ionic potential as well as about the photoionization dynamics. However, retrieving the quantum phase information has been a long-standing challenge. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photoionization-photo-recombination-in attosecond pulse generation. We demonstrate all-optical interferometry of two independent phase-locked attosecond light sources. This measurement enables us to directly determine the phase shift associated with electron scattering in simple quantum systems such as helium and neon, over a large energy range. Moreover, the strong-field nature of attosecond pulse generation resolves the dipole phase around the Cooper minimum in argon through a single scattering angle. This method may enable the probing of complex orbital phases in molecular systems as well as electron correlations through resonances subject to strong laser fields.

Ultrafast strong-field physics provides insight into quantum phenomena that evolve on an attosecond time scale, the most fundamental of which is quantum tunneling. The tunneling process initiates a range of strong field phenomena such as high harmonic generation (HHG), laser-induced electron diffraction, double ionization and photoelectron holography-all evolving during a fraction of the optical cycle. Here we apply attosecond photoelectron holography as a method to resolve the temporal properties of the tunneling process. Adding a weak second harmonic (SH) field to a strong fundamental laser field enables us to reconstruct the ionization times of photoelectrons that play a role in the formation of a photoelectron hologram with attosecond precision. We decouple the contributions of the two arms of the hologram and resolve the subtle differences in their ionization times, separated by only a few tens of attoseconds.

Spectral focusing of the recolliding electron in high-order harmonic generation driven by two-color fields is shown to be a powerful tool for isolating and enhancing hidden spectral features of the target under study. In previous works we used this technique for probing multi-electron effects in xenon and we compared our experimental results with time-dependent configuration-interaction singles calculations. We demonstrate here that this technique can be exploited for reconstructing the enhancement factor of the xenon giant dipole resonance and we discuss the sensitivity of this method to macroscopic effects. We then extend the technique to argon in order to test the applicability of this procedure to other targets.

High-harmonic generation (HHG) is a powerful tool to generate coherent attosecond light pulses in the extreme ultraviolet. However, the low conversion efficiency of HHG at the single atom level poses a significant practical limitation for many applications. Enhancing the efficiency of the process defines one of the primary challenges in the application of HHG as an advanced XUV source. In this work, we demonstrate a new mechanism, which in contrast to current methods, enhances the HHG conversion efficiency purely on a single particle level. We show that using a bichromatic driving field, sub-optical-cycle control and enhancement of the tunnelling ionization rate can be achieved, leading to enhancements in HHG efficiency by up to two orders of magnitude. Our method advances the perspectives of HHG spectroscopy, where isolating the single particle response is an essential component, and offers a simple route toward scalable, robust XUV sources. (c) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Chiral light-matter interactions have been investigated for two centuries, leading to the discovery of many chiroptical processes used for discrimination of enantiomers. Whereas most chiroptical effects result from a response of bound electrons, photoionization can produce much stronger chiral signals that manifest as asymmetries in the angular distribution of the photoelectrons along the light-propagation axis. We implemented self-referenced attosecond photoelectron interferometry to measure the temporal profile of the forward and backward electron wave packets emitted upon photoionization of camphor by circularly polarized laser pulses. We measured a delay between electrons ejected forward and backward, which depends on the ejection angle and reaches 24 attoseconds. The asymmetric temporal shape of electron wave packets emitted through an autoionizing state further reveals the chiral character of strongly correlated electronic dynamics.

Single-photon ionization is one of the most fundamental light matter interactions in nature, serving as a universal probe of the quantum state of matter. By probing the emitted electron, one can decode the full dynamics of the interaction. When photo-ionization is evolving in the presence of a strong laser field, the fundamental properties of the mechanism can be signicantly altered. Here we demonstrate how the liberated electron can perform a self-probing measurement of such interaction with attosecond precision. Extreme ultraviolet attosecond pulses initiate an electron wavepacket by photo-ionization, a strong infrared field controls its motion, and finally electron-ion collision maps it into re-emission of attosecond radiation bursts. Our measurements resolve the internal clock provided by the self-probing mechanism, obtaining a direct insight into the build-up of photo-ionization in the presence of the strong laser field.

Strong-field ionization followed by recollision provides a unique pump-probe measurement which reveals a range of electronic processes, combining sub-Angstrom spatial and attosecond temporal resolution. A major limitation of this approach is imposed by the coupling between the spatial and temporal degrees of freedom. In this paper we focus on the study of high harmonic generation and demonstrate the ability to isolate the internal dynamics - decoupling the temporal information from the spatial one. By applying an in situ approach we reveal the universality of the intrinsic pump-probe measurement and establish its validity in molecular systems. When several orbitals are involved we identify the fingerprint of the transition from the single-channel case into the multiple-channel dynamics, where complex multielectron phenomena are expected to be observed.

We investigated the giant resonance in xenon by high-order harmonic generation spectroscopy driven by a two-color field. The addition of a nonperturbative second harmonic component parallel to the driving field breaks the symmetry between neighboring subcycles resulting in the appearance of spectral caustics at two distinct cutoff energies. By controlling the phase delay between the two color components it is possible to tailor the harmonic emission in order to amplify and isolate the spectral feature of interest. In this Letter we demonstrate how this control scheme can be used to investigate the role of electron correlations that give birth to the giant resonance in xenon. The collective excitations of the giant dipole resonance in xenon combined with the spectral manipulation associated with the two-color driving field allow us to see features that are normally not accessible and to obtain a good agreement between the experimental results and the theoretical predictions.

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called â \u20ac diffraction before destructionâ \u20ac experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.

Probing electronic wave functions of polyatomic molecules is one of the major challenges in high-harmonic spectroscopy. The extremely nonlinear nature of the laser-molecule interaction couples the multiple degrees of freedom of the probed system. We combine two-dimensional control of the electron trajectories and vibrational control of the molecules to disentangle the two main steps in high-harmonic generation - ionization and recombination. We introduce a new measurement scheme, frequency-resolved optomolecular gating, which resolves the temporal amplitude and phase of the harmonic emission from excited molecules. Focusing on the study of vibrational motion in N2O4, we show that such advanced schemes provide a unique insight into the structural and dynamical properties of the underlying mechanism.

The phase retrieval problem arises in various fields ranging from physics and astronomy to biology and microscopy. Computational reconstruction of the Fourier phase from a single diffraction pattern is typically achieved using iterative alternating projections algorithms imposing a non-convex computational challenge. A different approach is holography, relying on a known reference field. Here we present a conceptually new approach for the reconstruction of two (or more) sufficiently separated objects. In our approach we combine the constraint the objects are finite as well as the information in the interference between them to construct an overdetermined set of linear equations. We show that this set of equations is guaranteed to yield the correct solution almost always and that it can be solved efficiently by standard numerical algebra tools. Essentially, our method combine commonly used constraint (that the object is finite) with a holographic approach (interference information). It differs from holographic methods in the fact that a known reference field is not required, instead the unknown objects serve as reference to one another (hence blind holography). Our method can be applied in a single-shot for two (or more) separated objects or with several measurements with a single object. It can benefit phase imaging techniques such as Fourier phytography microscopy, as well as coherent diffractive X-ray imaging in which the generation of a well-characterized, high resolution reference beam imposes a major challenge. We demonstrate our method experimentally both in the optical domain and in the X-ray domain using XFEL pulses.

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO₂ molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems.

Attosecond physics offers new insights into ultrafast quantum phenomena involving electron dynamics on the fastest measurable timescales. The rapid progress in this field enables us to re-visit one of the most fundamental strong-field phenomena: field-induced tunnel ionization. In this work, we employ high-harmonic generation to probe the electron wavefunction during field-induced tunnelling through a potential barrier. By using a combination of strong and weak driving laser fields, we modulate the atomic potential barrier on optical subcycle timescales. This induces a temporal interferometer between attosecond bursts originating from consecutive laser half-cycles. Our study provides direct insight into the basic properties of field-induced tunnelling, following the evolution of the electronic wavefunction within a temporal window of approximately 200 \u20ac\u2030attoseconds.

High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena.

We present a single-pulse two-dimensional Raman spectroscopy scheme. Our scheme offers not only a major simplification of the conventional setup but also an inherent favoring of the direct fifth-order signal over the cascaded signal, the latter being a signal that carries no coupling information.

Vibrational modes are often localized in certain regions of a molecule, and so the coupling between these modes is sensitive to the molecular structure. Two-dimensional vibrational spectroscopy can probe the strength of this coupling in a manner analogous to two-dimensional NMR spectroscopy, but on ultrafast timescales. Here, we demonstrate how two-dimensional Raman spectroscopy, based on fifth-order optical nonlinearity, can be performed with a single beam of shaped femtosecond optical pulses. Our spectroscopy scheme offers not only a major simplification of the conventional set-up, but also an inherent elimination of a competing nonlinear signal, which overwhelms the desired signal in other schemes and carries no coupling information.

High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF₆ as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20-26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected.

Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy. While in some scenarios the phase is resolved by an interferometric measurement, in others it is reconstructed via numerical optimization, based on some a-priori knowledge about the signal. The latter commonly use iterative algorithms, and thus have to deal with their convergence, stagnation, and robustness to noise. Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear equations. We present and experimentally demonstrate our approach for the case of lens-less imaging.

High-harmonic generation spectroscopy is a promising tool for resolving electron dynamics and structure in atomic and molecular systems. This scheme, commonly described by the strong field approximation, requires a deep insight into the basic mechanism that leads to the harmonic generation. Recently, we have demonstrated the ability to resolve the first stage of the process-field induced tunnel ionization-by adding a weak perturbation to the strong fundamental field. Here we generalize this approach and show that the assumptions behind the strong field approximation are valid over a wide range of tunnel ionization conditions. Performing a systematic study-modifying the fundamental wavelength, intensity and atomic system-we observed a good agreement with quantum path analysis over a range of Keldysh parameters. The generality of this scheme opens new perspectives in high harmonics spectroscopy, holding the potential of probing large, complex molecular systems.

Strong field transient grating spectroscopy has shown to be a very versatile tool in time-resolved molecular spectroscopy. Here we use this technique to investigate the high-order harmonic generation from SF₆ molecules vibrationally excited by impulsive stimulated Raman scattering. Transient grating spectroscopy enables us to reveal clear modulations of the harmonic emission. This heterodyne detection shows that the harmonic emission generated between 14 and 26eV is mainly sensitive to two among the three active Raman modes in SF₆, i.e. the strongest and fully symmetric υ_1-A_1g mode (774cm^-1, 43 fs) and the slowest mode υ_5-T_2g (524cm^-1, 63 fs). A time-frequency analysis of the harmonic emission reveals additional dynamics: the strength and central frequency of the υ₁ mode oscillate with a frequency of 52cm^-1 (640 fs). This could be a signature of the vibration of dimers in the generating medium. Harmonic 11 shows a remarkable behaviour, oscillating in the opposite phase, both on the fast (774cm ^-1) and slow (52cm^-1) timescales, which indicates a strong modulation of the recombination matrix element as a function of the nuclear geometry. These results demonstrate that the high sensitivity of high-order harmonic generation to molecular vibrations, associated to the high sensitivity of transient grating spectroscopy, make their combination a unique tool to probe vibrational dynamics.

The frequency and intensity of attosecond light pulses can be increased by optimizing the optical pulses that drive a high-harmonic generation process.

In strong-field light-matter interactions, the strong laser field dominates the dynamics. However, recent experiments indicate that the Coulomb force can play an important role as well. In this Letter, we have studied the photoelectron momentum distributions produced from noble gases in elliptically polarized, 800 nm laser light. By performing a complete mapping of the three-dimensional electron momentum, we find that Coulomb focusing significantly narrows the lateral momentum spread. We find a surprisingly sensitive dependence of Coulomb focusing on the initial transverse momentum distribution, i.e., the momentum at the moment of birth of the photoelectron. We also observe a strong signature of the low-energy structure in the above threshold ionization spectrum.

Recollision experiments have been very successful in resolving attosecond scale dynamics. However, such schemes rely on the single atom response, neglecting the macroscopic properties of the interaction and the effects of using multi-cycle laser fields. In this paper we perform a complete spatio-spectral analysis of the high harmonic generation process and resolve the distribution of the subcycle dynamics of the recolliding electron. Specifically, we focus on the measurement of ionization times. Recently, we have demonstrated that the addition of a weak, crossed polarized second harmonic field allows us to resolve the moment of ionization (Shafir, 2012) [1]. In this paper we extend this measurement and perform a complete spatio-spectral analysis. We apply this analysis to reconstruct the ionization times of both short and long trajectories showing good agreement with the quantum path analysis.

Reconstruction of signals from measurements of their spectral intensities, also known as the phase retrieval problem, is of fundamental importance in many scientific fields. In this paper we present a novel framework, denoted as vectorial phase retrieval, for reconstruction of pairs of signals from spectral intensity measurements of the two signals and of their interference. We show that this new framework can alleviate some of the theoretical and computational challenges associated with classical phase retrieval from a single signal. First, we prove that for compactly supported signals, in the absence of measurement noise, this new setup admits a unique solution. Next, we present a statistical analysis of vectorial phase retrieval and derive a computationally efficient algorithm to solve it. Finally, we illustrate via simulations, that our algorithm can accurately reconstruct signals even at considerable noise levels.

Tunneling of a particle through a barrier is one of the most fundamental and ubiquitous quantum processes. When induced by an intense laser field, electron tunneling from atoms and molecules initiates a broad range of processes that evolve on the attosecond time-scale^1,2. As the liberated electron is driven by the laser field, it can return to the parent ion and recombine to the initial (ground) state, releasing its energy in an attosecond burst of light. This process, known as High Harmonic Generation (HHG) provides an excellent spatio-temporal filter for the electron motion. The angstrom-scale spatial resolution is determined by the size of the atomic ground state to which the electron must recombine. The attosecond temporal resolution arises from the mapping between the photon energy (harmonic order) and the return time of the corresponding electron trajectory.

The tunnelling of a particle through a barrier is one of the most fundamental and ubiquitous quantum processes. When induced by an intense laser field, electron tunnelling from atoms and molecules initiates a broad range of phenomena such as the generation of attosecond pulses, laser-induced electron diffraction and holography. These processes evolve on the attosecond timescale (1attosecond 1as = 10^-18 seconds) and are well suited to the investigation of a general issue much debated since the early days of quantum mechanics-the link between the tunnelling of an electron through a barrier and its dynamics outside the barrier. Previous experiments have measured tunnelling rates with attosecond time resolution and tunnelling delay times. Here we study laser-induced tunnelling by using a weak probe field to steer the tunnelled electron in the lateral direction and then monitor the effect on the attosecond light bursts emitted when the liberated electron re-encounters the parent ion. We show that this approach allows us to measure the time at which the electron exits from the tunnelling barrier. We demonstrate the high sensitivity of the measurement by detecting subtle delays in ionization times from two orbitals of a carbon dioxide molecule. Measurement of the tunnelling process is essential for all attosecond experiments where strong-field ionization initiates ultrafast dynamics. Our approach provides a general tool for time-resolving multi-electron rearrangements in atoms and molecules-one of the key challenges in ultrafast science.

Recollision processes provide direct insight into the structure and dynamics of electronic wave functions. However, the strength of the process sets its basic limitations-the interaction couples numerous degrees of freedom. In this Letter we decouple the basic steps of the process and resolve the role of the ionic potential which is at the heart of a broad range of strong field phenomena. Specifically, we measure high harmonic generation from argon atoms. By manipulating the polarization of the laser field we resolve the vectorial properties of the interaction. Our study shows that the ionic core plays a significant role in all steps of the interaction. In particular, Coulomb focusing induces an angular deflection of the electrons before recombination. A complete spatiospectral analysis reveals the influence of the potential on the spatiotemporal properties of the emitted light.

Many intriguing phenomena in nature - from phase transitions to black holes - occur at singularities. A unique type of singularity common in wave phenomena, known as caustics^1,2, links processes observed in many different branches of physics^3,4. Here, we investigate the role of caustics in attosecond science and in particular the physical process behind high harmonic generation⁵. We experimentally demonstrate spectral focusing in high harmonic generation, showing a robust intensity enhancement of an order of magnitude over a spectral width of several harmonics. This new level of control holds promises in both scientific and technological aspects of attosecond science^6,7. Moreover, our study provides a deeper insight into the basic mechanism underlying the high harmonic generation process, revealing its quantum nature⁸ and universal properties.

The waveforms of attosecond pulses produced by high-harmonic generation carry information on the electronic structure and dynamics in atomic and molecular systems. Current methods for the temporal characterization of such pulses have limited sensitivity and impose significant experimental complexity. We propose a new linear and all-optical method inspired by widely used multidimensional phase retrieval algorithms. Our new scheme is based on the spectral measurement of two attosecond sources and their interference. As an example, we focus on the case of spectral polarization measurements of attosecond pulses, relying on their most fundamental property-being well confined in time. We demonstrate this method numerically by reconstructing the temporal profiles of attosecond pulses generated from aligned CO₂ molecules.

Ultrafast science is inherently, due to the lack of fast enough detectors and electronics, based on nonlinear interactions. Typically, however, nonlinear measurements require significant powers and often operate in a limited spectral range. Here we overcome the difficulties of ultraweak ultrafast measurements by precision time-domain localization of spectral components. We utilize this for linear self-referenced characterization of pulse trains having ∼ 1 photon per pulse, a regime in which nonlinear techniques are impractical, at a temporal resolution of ∼ 10 fs. This technique does not only set a new scale of sensitivity in ultrashort pulse characterization, but is also applicable in any spectral range from the near-infrared to the deep UV.

Over the last five decades laser technology has been able to compress optical pulse duration by several orders of magnitudes. During the past decade it has been established that the interaction of intense laser pulses with atoms or molecules can lead to the generation of XUV pulses and energetic electron pulses with attosecond duration¹ (1 attosecond10¹⁸ second). This discovery has opened a window into a new time regime previously inaccessible. The advent of this new technology enables the investigation of new fields of time resolved studies in which the observation of fast electronic dynamics can be attained. The study of new areas of science, such as time resolved measurements of multi-electron dynamics and imaging molecular and nuclear dynamics, has consequently become accessible.

A linear self-referenced technique for temporal characterization of ultraweak pulse trains is presented. Shot-noise limited time-resolved single photon detection enables temporal resolution down to 10fs for pulse trains with ∼ 1 photon per pulse.

We propose a new linear and all-optical method for attosecond pulses characteri-zation. Our scheme is based only on spectral and polarization measurements. We demonstrate this method numerically on attosecond pulses generated from aligned CO₂ molecules.

We study high-order harmonic generation in aligned molecules close to the ionization threshold. Two distinct contributions to the harmonic signal are observed, which show very different responses to molecular alignment and ellipticity of the driving field. We perform a classical electron trajectory analysis, taking into account the significant influence of the Coulomb potential on the strong-field-driven electron dynamics. The two contributions are related to primary ionization and excitation processes, offering a deeper understanding of the origin of high harmonics near the ionization threshold. This Letter shows that high-harmonic spectroscopy can be extended to the near-threshold spectral range, which is in general spectroscopically rich.

We have measured high-order harmonic generation spectra of D2, N2, and CO2 by mixing orthogonally polarized 800 and 400 nm laser fields. The intensity of the high-harmonic spectrum is modulated as we change the relative phase of the two pulses. For randomly orientated molecules, the phase of the intensity modulation depends on the symmetry of the molecular orbitals from which the high harmonics are emitted. This allows us to identify the symmetry of any orbital that contributes to high-harmonic generation, even without aligning the molecule. Our approach can be a route to imaging dynamical changes in three-dimensional molecular orbitals on a time scale as short as a few hundred attoseconds.

In this paper, we analyze a new approach that was first presented by Shafir et al (2009 Nat. Phys. 5 412-6) to probe the symmetry of atomic wavefunctions via the high harmonic generation process. In this scheme, we control the two-dimensional (2D) motion of a free electron using a two-color field to probe the atoms from different angles. We present a new theoretical analysis that focuses on the spherical symmetry of atomic potentials. We analyze previously presented experimental results (Shafir et al 2009 Nat. Phys. 5 412-6) and demonstrate the ability to distinguish between spherically symmetric (s state) and non-spherically symmetric (p state) orbitais. Finally, we discuss the limitations of our approach and compare it with alternative methods.

We perform high harmonic generation spectroscopy of aligned nitrogen molecules to characterize the attosecond dynamics of multielectron rearrangement during strong-field ionization. We use the spectrum and ellipticity of the harmonic light to reconstruct the relative phase between different ionization continua participating in the ionization, and thus determine the shape and location of the hole left in the molecule by strong-field ionization. Our interferometric technique uses transitions between the ionic states, induced by the laser field on the subcycle time scale.

We study the spatial profile of high order harmonics generated by a transient grating of rotational excitation. We show that the phase modulation of the harmonic emission as a function of molecular alignment is encoded in the diffraction pattern. In molecular nitrogen, the phase difference between aligned and isotropic molecules decreases from 1.6 rad for harmonic 19 to less than 0.3 rad for harmonic 27. In CO₂ we observe a strong phase jump for the highest harmonics. The position of this phase jump in the harmonic spectrum depends on the laser intensity, reflecting the contribution from multiple molecular orbitals to the harmonic emission.

Molecular structures, dynamics and chemical properties are determined by shared electrons in valence shells. We show how one can selectively remove a valence electron from either Π vs. Σ or bonding vs. nonbonding orbital by applying an intense infrared laser field to an ensemble of aligned molecules. In molecules, such ionization often induces multielectron dynamics on the attosecond time scale. Ionizing laser field also allows one to record and reconstruct these dynamics with attosecond temporal and sub-Ångstrom spatial resolution. Reconstruction relies on monitoring and controlling high-frequency emission produced when the liberated electron recombines with the valence shell hole created by ionization.

We present a method for controlling the spatial properties of a high-order harmonic beam on a subcycle time scale. By adding a second-harmonic field to the driving laser field, we modify the spatiotemporal structure of the harmonic beam and manipulate it with attosecond resolution. Such a manipulation maps the subcycle dynamics of a recolliding electron to the spatial domain.

High harmonic emission occurs when an electron, liberated from a molecule by an incident intense laser field, gains energy from the field and recombines with the parent molecular ion. The emission provides a snapshot of the structure and dynamics of the recombining system, encoded in the amplitudes, phases and polarization of the harmonic light. Here we show with CO 2 molecules that high harmonic interferometry can retrieve this structural and dynamic information: by measuring the phases and amplitudes of the harmonic emission, we reveal fingerprints' of multiple molecular orbitals participating in the process and decode the underlying attosecond multi-electron dynamics, including the dynamics of electron rearrangement upon ionization. These findings establish high harmonic interferometry as an effective approach to resolving multi-electron dynamics with sub-ngström spatial resolution arising from the de Broglie wavelength of the recombining electron, and attosecond temporal resolution arising from the timescale of the recombination event.

Strong-field light-matter interactions can encode the spatial properties of the electronic wavefunctions that contribute to the process. In particular, the broadband harmonic spectra, measured for a series of molecular alignments, can be used to create a tomographic reconstruction of molecular orbitals. Here, we present an extension of the tomography approach to systems that cannot be naturally aligned. We demonstrate this ability by probing the two-dimensional properties of atomic wavefunctions. By manipulating an electron-ion recollision process, we are able to resolve the symmetry of the atomic wavefunction with high contrast.

We describe the roles of multiple electronic continua in high-harmonic generation from aligned molecules. First, we show how the circularity of emitted harmonics tracks the interplay of different electronic continua participating in the nonlinear response. Second, we show that the interplay of different continua can lead to large variations of harmonic phases. Finally, we show how multiple electronic continua allow one to shape the polarization of high harmonics and attosecond pulses.

While high harmonic generation from atoms is relatively well understood, the ability to align gas-phase molecules opens an opportunity to more deeply understand the underlying physics. Many assumptions, such as the single active electron approximation, neglect of the Coulomb potential, the strong field approximation, and the assumption of plane waves, are being challenged by new experimental observations. We study high harmonic emission from aligned molecules such as N2, O2 and CO2. We present experimental measurements of the amplitude of the emission as a function of molecular angle, as well as the polarization state.

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.

We study experimentally and theoretically the high harmonic emission from aligned samples of nitrogen and carbon dioxide, in an elliptically polarized laser field. The ellipticity induces a lateral shift of the recombining electron wavepacket in the generation process. We show that this effect, which is well known from high harmonic generation (HHG) in atoms, can be useful to maintain the plane wave approximation in the case of HHG from molecules whose orbitals contain nodal planes. The study of the harmonic signal as a function of molecular alignment also reveals the role of the ellipticity on the recollision angle of the electron wavepacket, which can be used to accurately track the position of resonances in harmonic spectra.

High harmonic emission in isotropic gases is polarized in the same direction as the incident laser polarization. Laser-induced molecular alignment allows us to break the symmetry of the gas medium. By using aligned molecules in high harmonic generation experiments, we show that the polarization of the extreme ultraviolet emission depends strongly on the molecular alignment and the orbital structure. Polarization measurements give insight into the molecular orbital symmetry. Furthermore, molecular alignment will allow us to produce attosecond pulses with time-dependent polarization.

We present a method for controlling the spatial properties of high-harmonic beams with high efficiency. The high nonlinearity of harmonic generation allows weak control beams to induce a phase mask for the extreme UV light as it is formed. We fabricate a phase grating and demonstrate efficient diffraction in the far field. Diffractive elements formed in this way are transient. Since they are induced by the subcycle interaction of the medium with the fundamental and control fields, they can be extended to the attosecond time scale.

Temporal gating allows high accuracy time-resolved measurements of a broad range of ultrafast processes. By manipulating the interaction between an atom and an intense laser field, we extend gating into the nonlinear medium in which attosecond optical and electron pulses are generated. Our gate is an amplitude gate induced by ellipticity of the fundamental pulse. The gate modulates the spectrum of the high harmonic emission and we use the measured modulation to characterize the sub-laser-cycle dynamics of the recollision electron wave packet.

Generating attosecond pulses has required a radically different approach from previous ultrafast optical methods. The technology of attosecond measurement, however, is built on established methods of characterizing femtosecond pulses: the pulse is measured after it has left the region where it was produced. We offer a completely different approach: in situ measurement. That is, we integrate attosecond-pulse production and measurement in a manner that can be applied to many high-order nonlinear interactions. To demonstrate this approach, we combine a low-intensity (

Polarization gating of high-order harmonic generation takes advantage of the significant reduction of harmonic generation efficiency for elliptically polarized excitation fields, in order to generate short bursts of harmonic radiation from relatively long pulses. We show that the currently used method for generation of polarization gated pulses using wave-plate combinations is inefficient, and propose an alternative method based on polarization pulse shaping techniques. This method is shown to be significantly more efficient and to enable significant shortening of the gate duration. Using this scheme, isolated attosecond pulses should be achievable with excitation pulses of a duration as long as 20 fs.

Coherent-control schemes to manipulate weak-field interactions are generally invalid at stronger fields, since strong-field interactions are accompanied by level power broadenings and level shifts that usually elude simple analytical treatments. Here we show that a broad subgroup of weak-field solutions (those with real fields, i.e., fields with only one quadrature in the complex plane) can be extended to the strong-field regime while retaining their properties. The salient feature of these fields is a symmetry that cancels out power broadening effects. Such fields can be generated from ultrashort coherent pulses or from incoherent broadband down-converted light. Weak-field coherent-control approaches based on these solutions can therefore be extended to the strong-field regime as we demonstrate in a two-photon absorption experiment in atomic cesium.

All-optical processing of the entire vibrational spectrum was investigated by using a more complex and carefully designed probe pulse. The probe pulse was constructed containing contributions from several narrow spectral bands with controllable intensities and phases. Strong interference effcts were observed in the coherent anti-Stokes Raman spectroscopy (CARS) which resulted from the presence of several spectrally separated probe frequencies. A scheme for nonlinear spectroscopy was also suggested, where the information from the entire spectrum could be collected into a single coherent entity through coherent control of the nonlinear process.

The polarization pulse shaping was applied to the control of two-photon absorption in atomic rubidium. It was shown that the technique enables the manipulation of the transient vector properties of a light matter interaction. It was established that control can be exerted on the angular distribution of the final state. The ability to control the final state population of a nearly degenerate system and to perform M-state resolved spectroscopy were demonstrated.

Single-pulse vibrational spectroscopy was readily achieved using coherent control techniques. By tailoring the spectral phase of an ultrashort pulse, the interference between quantum processes induced by the various spectral components of the pulse was controlled, leading either to selective population of given Raman levels or to the generation of narrow features in the CARS spectrum by all the populated Raman levels. By applying this principle, high-resolution spectroscopy was demonstrated in the vibrational energy range 700-1400 cm^-1. By measuring a complex Raman spectrum of a molecule in this spectral region, the method was found to be robust and practical.

Phase-and-polarization coherent control is applied to control the nonlinear response of a quantum system. We use it to obtain high-resolution background-free single-pulse coherent anti-Stokes Raman spectra. The ability to control both the spectral phase and the spectral polarization enables measurement of a specific off-diagonal susceptibility tensor element while exploiting the different spectral response of the resonant Raman signal and the nonresonant background to achieve maximal background suppression.

Molecular vibrations have oscillation periods that reflect the molecular structure, and are hence being used as a spectroscopic fingerprint for detection and identification. At present, all nonlinear spectroscopy schemes use two or more laser beams to measure such vibrations. The availability of ultrashort (femtosecond) optical pulses with durations shorter than typical molecular vibration periods has enabled the coherent excitation of molecular vibrations using a single pulse. Here we perform single-pulse vibrational spectroscopy on several molecules in the liquid phase, where both the excitation and the readout processes are performed by the same pulse. The main difficulty with single-pulse spectroscopy is that all vibrational levels with energies within the pulse bandwidth are excited. We achieve high spectral resolution, nearly two orders of magnitude better than the pulse bandwidth, by using quantum coherent control techniques. By appropriately modulating the spectral phase of the pulse we are able to exploit the quantum interference between multiple paths to selectively populate a given vibrational level, and to probe this population using the same pulse. This scheme, using a single broadband laser source, is particularly attractive for nonlinear microscopy applications, as we demonstrate by constructing a coherent anti-Stokes Raman (CARS) microscope operating with a single laser beam.

Quantum control of coherent anti-Stokes Raman spectroscopy (CARS) was demonstrated. Raman spectra was measured with a resolution of the order of 5 cm^-1 using shaped pulses with a bandwidth of about 120 cm^-1. Nearly complete suppression of the nonresonant background signal was also demonstrated. Selective population of only one of the two Raman levels of pyridine, lying within the bandwidth of excitation pulses, was achieved. Simple modeling was used to derive the required spectral phases and the measured signals were found in agreement with the model predictions.

The coherent transient enhancement of optically induced resonant transitions was discussed. Using pulse shaping techniques, the total transient population was enhanced by inducing constructive interference, and for 100 fs pulses, an enhancement by a factor of about 2.5 was demonstrated. The results showed that the population transient peak remains nearly constant, even when the absorption coefficient was increased by over three order of magnitude.

A narrow-band coherent anti-Stokes Raman spectroscopy (CARS) signal was generated from a broad-band probe pulse through simple spectral phase manipulation of the probe pulse. The spectral resolution increased by an order of magnitude. The signal at a given wavelength was enhanced by almost a factor of 2 relative to the maximal signal obtained at this frequency by a transform limited pulse.

High spectral resolution nonlinear vibrational spectroscopy with a single ultrashort pulse is demonstrated on a variety of samples. The spectral data are obtained by shaping the excitation pulse in order to control the relative phase between the weak resonant signal and the strong nonresonant background, in analogy with phase-contrast microscopy techniques. This is unlike the more conventional approach to nonlinear spectroscopy, in which the nonresonant background is reduced to a minimum. By measuring the spectrum of the coherent anti-Stokes Raman signal, it is possible to infer the vibrational energy levels in a band spanning almost an entire octave.

Under certain conditions, a high-finesse resonance phenomenon can occur in a grating waveguide structure (GWS). By varying these conditions, a shift in the resonance wavelength can be achieved. Specifically, utilizing the high finesse property of the GWS, small changes in the refractive index can result in a tuning range larger than the resonance bandwidth. Here, we consider different electric-field and charge carrier mechanisms that can affect the refractive index in semiconductor materials, and exploit them in order to control the refractive index change and, therefore, the resonance wavelength in the GWS. The predicted results are verified experimentally with an active GWS formed with semiconductor materials and operated in a reverse voltage configuration.

Resonant multiphoton transitions were enhanced by exploiting the general spectral response of the interaction around resonance. Large enhancements of resonant two-photon absorption (TPA) were achieved by properly designing the spectral amplitude and phase of the exciting pulse.