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Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, as the result of a nonlinear perpendicular current akin to a Hall current. Here, we theoretically characterize the anomalous HHG mechanism, via development of an ab-initio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two key characteristics of the anomalous harmonic yields: an overall increase with laser wavelength; and pronounced minima at certain intensities or wavelengths around which the emission time profiles drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from the competing interband harmonics, and thus pave way for the experimental identification and time-domain control of pure anomalous harmonics., Comment: 7 pages, 4 figures

Extremely short, high-energy pulses are essential in modern ultrafast science. In a seminal paper in 19961, Nisoli and co-workers demonstrated the first intense pulse compression employing a gas-filled hollow-core fibre. Despite the huge body of scientific work on this technology stemming from ultrafast and attosecond research, here we identify an unexplored few-cycle visible-light generation mechanism, which relies on the nonlinear mixing of hollow-core fibre modes. Using a commercially available ytterbium laser, we generate 4.6 fs, 20 μJ pulses centred at around 600 nm (~2 cycles, ~4 GW peak power), ~40 times shorter than the input 175 fs, 1 mJ pulses at 1,035 nm. Our approach thus directly projects few-hundred-femtosecond-long infrared pulses into the single-cycle regime at visible frequencies, without the need for additional post-compression. As a powerful application of our findings, we present a compact, multicolour pump–probe set-up with a temporal resolution of a few optical cycles. Direct generation of few-cycle high-energy visible pulses is demonstrated via the nonlinear mixing of hollow-core fibre modes. Compression of near-infrared laser pulses by a factor of 40 with no additional dispersion compensation delivers 4.6 fs, 20 μJ pulses (~2 cycles, ~4 GW peak power) centred at around 600 nm.

We propose and study the manipulation of the macroscopic transient absorption of an ensemble of open two-level systems via temporal engineering. The key idea is to impose an ultrashort temporal gate on the polarization decay of the system by transient absorption spectroscopy, thus confining its free evolution and the natural reshaping of the excitation pulse. The numerical and analytical results demonstrate that even at moderate optical depths, the resonant absorption of light can be reduced or significantly enhanced by more than 5 orders of magnitude relative to that without laser manipulation. The achievement of the quasicomplete extinction of light at the resonant frequency, here referred to as resonant perfect absorption, arises from the full destructive interference between the excitation pulse and its subpulses developed and tailored during propagation, and is revealed to be connected with the formation of zero-area pulses in the time domain.

We develop and test a method that integrates many-electron weak-field asymptotic theory (ME-WFAT) [Phys. Rev. A 89, 013421 (2014)] in the integral representation (IR) into the density functional theory (DFT) framework. In particular, we present modifications of the integral formula in the IR ME-WFAT to incorporate the potential terms unique to DFT. By solving an adiabatic rate equation for the angle-resolved ionization yield in our DFT-based ME-WFAT method, we show that the results are in excellent agreement with those of real-time time-dependent density functional theory (RT-TDDFT) simulations for NO, OCS, CH$_3$Br, and CH$_3$Cl interacting with one- and two- color laser fields with a fundamental wavelength of $800$ nm. This agreement is significant because the WFAT calculations take only a small fraction of the time of full TDDFT calculations. These results suggest that in the wavelength region commonly used in strong-field experiments ($800$ nm and longer), our DFT-based WFAT treatment can be used to rapidly screen for the ionization properties of a large number of molecules as a function of alignment or orientation between the molecule and the strong field.

We present molecular-frame high-harmonic spectroscopic measurements of the spectral intensity and group delay of carbon dioxide. Using four different driving wavelengths and a range of intensities at each wavelength for high-harmonic generation, we observe a well-characterized minimum in the harmonic emission that exhibits both a wavelength and intensity dependence. Using the intensity dependence at each driving wavelength, we classify the minimum as due to either a structural two-center interference or dynamic multichannel interference, consistent with previous literature. By additionally measuring the group delay at each driving wavelength and intensity, we find that the sign of the group delay excursion across the interference is an acute probe of the interference mechanism. The experimental results are confirmed by ab initio time-dependent density functional theory calculations of both the spectral intensity and the phase of the harmonic emission.

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS$_2$, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. This observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multi-band recombination dipoles.

Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. To determine the relationship between a molecule's structure and the CM dynamics it exhibits, we perform systematic studies of para-functionalized bromobenzene molecules (X-C$_6$H$_4$-R) using real-time time-dependent density functional theory. We initiate valence-electron dynamics by emulating rapid strong-field ionization leading to a localized hole on the bromine atom. The resulting CM, which takes on the order of 1 fs, occurs via an X localized to C$_6$H$_4$ delocalized to R localized mechanism. Interestingly, the hole contrast on the acceptor functional group increases with increasing electron donating strength. This trend is well-described by the Hammett sigma value of the group, which is a commonly used metric for quantifying the effect of functionalization on the chemical reactivity of benzene derivatives. These results suggest that simple attochemistry principles and a density-based picture can be used to predict and understand CM., Comment: 5 pages, 3 figures

We perform ab initio calculations of high-harmonic spectroscopy (HHS) of two-center interference phenomena in oriented carbon-dichalcogen molecules, using time-dependent density functional theory (TDDFT). We show that by resolving the harmonic response into contributions from individual Kohn-Sham orbitals, we can extract target-specific characteristics for both the spectral amplitude and phase. We also discuss that this extraction is predicated on a careful analysis and normalization of the harmonic spectrum. Finally, we present field-free scattering calculations that mimic the recollision step in high-order-harmonic generation and allow the calculation of recombination dipole matrix elements without explicitly calculating the scattering states of a molecule. We show that the orbital-resolved TDDFT HHS results and results based on our field-free scattering calculations are in very good agreement with each other.

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{eV}$) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed ($\ensuremath{\sim}4\text{ }\text{ }\AA{}/\mathrm{fs}$) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

We theoretically investigate electron-hole recollisions in high-harmonic generation (HHG) in band-gap solids irradiated by linearly and elliptically polarized drivers. We find that in many cases the emitted harmonics do not originate in electron-hole pairs created at the minimum band gap, where the tunneling probability is maximized, but rather in pairs created across an extended region of the Brillouin zone (BZ). In these situations, the analogy to gas-phase HHG in terms of the short- and long-trajectory categorizations is inadequate. Our analysis methodology comprises three complementary levels of theory: the numerical solutions to the semiconductor Bloch equations, an extended semiclassical recollision model, and a quantum wave packet approach. We apply this methodology to two general material types with representative band structures: a bulk system and a hexagonal monolayer system. In the bulk, the interband harmonics generated using elliptically-polarized drivers are found to originate not from tunneling at the minimum band gap $\Gamma$, but from regions away from it. In the monolayer system driven by linearly-polarized pulses, tunneling regions near different symmetry points in the BZ lead to distinct harmonic energies and emission profiles. We show that the imperfect recollisions, where an electron-hole pair recollide while being spatially separated, are important in both bulk and monolayer materials. The excellent agreement between our three levels of theory highlights and characterizes the complexity behind the HHG emission dynamics in solids, and expands on the notion of interband HHG as always originating in trajectories tunnelled at the minimum band gap. Our work furthers the fundamental understanding of HHG in periodic systems and will benefit the future design of experiments., Comment: 18 pages, 13 figures

High harmonic generation (HHG) versus the crystal orientation of a monolayer MoS2 is investigated experimentally. It is found that the laser wavelength and the multiband electronic structure plays an important role in HHG process.

We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a 3D time-dependent Schr\"odinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level 1s-3p transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states $1s^{-1}3p$ and $2p^{-1}3p$ occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar $1s^{-1}-2p^{-1}$ response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources., Comment: 14 pages, 11 figures

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length-gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity-gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: a one-dimensional model of ZnO and the two-dimensional monolayer hexagonal boron nitride (hBN). The omittance of Berry connections or TDPs in the SBEs for hBN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process and are applicable to all strong-field matter simulations with SBEs.

The process of imperfect recollisions in solid-state high-harmonic generation is theoretically characterized: an electron and a hole recombine even when are spatially separated, leading to increased recollision energies of the interband harmonics.

We explore the implementation of weak field asymptotic theory using orbitals and potentials calculated via Density Functional Theory. This provides a way to calculate strong field ionization rates by assuming that the field is constant.

High power, broadband terahertz (THz) radiation from liquids, excited by intense, femtosecond 800 nm laser pulses has been demonstrated recently, overturning the long held belief that liquids would not give such emission due to their absorption in the THz region. Given the widespread interest in the use of THz radiation for several applications and the energy and bandwidth limitations of existing sources, liquids are expected to attract great attention in the future. While the emission at tens of microjoules from liquids is very promising, it is important to explore whether control of the THz flux and spectrum is achievable by manipulating the laser or liquid parameters. In this paper we present results on manipulating the spectrum of THz radiation from liquids by chirping the input laser pulse and optimizing the THz output energy by laser chirp as well as optimizing the focal position. We demonstrate tunability by varying the chirp of the laser pulse and show that the THz emission predominantly comes from the region near the end of the liquid path, consistent with the absorption of THz radiation by liquids. This control gives us an opportunity to tune the THz radiation to suit experimental needs. We present simulations that support the results.

We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.

The spatial phase and direction of extreme-ultraviolet light are controlled by an all-optical modulator based on argon gas. It works by using an infrared pulse to control the spatial and spectral phase of the free induction decay in the gas system.

Excitation of ionic solids with extreme ultraviolet pulses creates localized core-excitons, which in some cases couple strongly to the lattice. Here, core-excitonic states of magnesium oxide are studied in the time domain at the Mg $\text{L}_{2,3}$ edge with attosecond transient reflectivity spectroscopy. Attosecond pulses trigger the excitation of these short-lived quasiparticles, whose decay is perturbed by time-delayed near infrared optical pulses. Combined with a few-state theoretical model, this reveals that the optical pulse shifts the energy of bright core-exciton states as well as induces features arising from dark core-excitons. We report coherence lifetimes for the first two core-excitons of $2.3 \pm 0.2$ and $1.6 \pm 0.5$ femtoseconds and show that these short lifetimes are primarily a consequence of strong exciton-phonon coupling, disclosing the drastic influence of structural effects in this ultrafast relaxation process.

We study, experimentally and theoretically, the ionization probability of singly halogenated methane molecules, CH3Cl and CH3Br, in intense linearly polarized 800 nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within the molecules, which are then ionized by the second, stronger pulse. The angle-dependent ionization yields are extracted from fits of the measured delay-dependent ionization signal to a superposition of moments of the rotational wave packet’s angular distribution. Angle-dependent strong-field ionization (SFI) yields are also calculated using time-dependent density functional theory. Good agreement between measurements and theory is obtained. Interestingly, we find a marked difference between the angle-dependence of the ionization yields for these two halomethane species despite the similar structure of their highest occupied molecular orbitals. Calculations reveal that these differences are a result of multichannel (CH3Cl) vs single-channel (CH3Br) ionization and of increased hole localization on Br vs Cl. By adding calculations for CH3F, we can discern clear trends in the ionization dynamics with increasing halogen mass. These results are illustrative, as chemical functionalization and molecular alignment are likely to be important parameters for initiating and controlling charge migration dynamics via SFI.

We theoretically investigate high-harmonic generation in hexagonal boron nitride with linearly polarized laser pulses. We show that imperfect recollisions between electron-hole pairs in the crystal give rise to an electron-hole-pair polarization energy that leads to a double-peak structure in the subcycle emission profiles. An extended recollision model (ERM) is developed that allows for such imperfect recollisions, as well as effects related to Berry connections, Berry curvatures, and transition-dipole phases. The ERM illuminates the distinct spectrotemporal characteristics of harmonics emitted parallel and perpendicularly to the laser polarization direction. Imperfect recollisions are a general phenomenon and a manifestation of the spatially delocalized nature of the real-space wave packet, they arise naturally in systems with large Berry curvatures, or in any system driven by elliptically polarized light.

We investigate the nonlinear propagation of intense, two-cycle, carrier-envelope phase (CEP) stable laser pulses at 1.7 μm center wavelength in air. We observe CEP-dependent spectral interference in the visible part of the forward-propagating white light generated on propagation. The effect is robust against large fluctuations of the input pulse energy. This robustness is enabled by rigid clamping of both the peak optical field and the phase of the propagating waveform, which has been revealed by numerical simulations. The CEP locking can enhance the yield of the CEP-dependent strong-field processes in gaseous media with long-wavelength drivers, while the observed spectral interference enables single-shot, stand-off CEP metrology in the atmosphere.

We extend the recently developed technique of opto-optical modulation (OOM) to probe state-resolved ac-Stark-induced phase variations of a coherently excited ensemble of helium atoms. In a joint experimental and theoretical study, we find that the spatial redirection of the resonant emission from the OOM process is different for the low-lying 1s2p state as compared with the higher-lying Rydberg states, and that this redirection can be controlled through the spatial characteristics of the infrared (IR) probe beam. In particular, we observe that the intensity dependence of the IR-induced Stark phase on the 1s2p emission is nonlinear, and that the phase accumulation changes sign for moderate intensities. Our results suggest that OOM, combined with precise experimental shaping of the probe beam, could be used to measure the Stark-induced phase shifts of excited states., 5 pages, 4 figures. Updated version addressing referee comments and editorial changes. Reprinted with permission from [Phys. Rev. A 100, 023403 (2019)]. Copyright (2019) by the American Physical Society

We demonstrate high-harmonic spectroscopy in many-electron molecules using time-dependent density-functional theory. We show that a weak attosecond-pulse-train ionization seed that is properly synchronized with the strong driving mid-infrared laser field can produce experimentally relevant high-harmonic generation (HHG) signals, from which we extract both the spectral amplitude and the target-specific phase (group delay). We also show that further processing of the HHG signal can be used to achieve molecular-frame resolution, i.e., to resolve the contributions from rescattering on different sides of an oriented molecule. In this framework, we investigate transient two-center interference in CO2 and OCS, and how subcycle polarization effects shape the oriented/aligned angle-resolved spectra.

Nonlinear spectroscopies are utilized extensively for selective measurements of chemical dynamics in the optical, infrared, and radio-frequency regimes. The development of these techniques for extreme ultraviolet (XUV) light sources facilitates measurements of electronic dynamics on attosecond timescales. Here, we elucidate the temporal dynamics of nonlinear signal generation by utilizing a transient grating scheme with a subfemtosecond XUV pulse train and two few-cycle near-infrared pulses in atomic helium. Simultaneous detection of multiple diffraction orders reveals delays of ≥1.5 fs in higher-order XUV signal generation, which are reproduced theoretically by solving the coupled Maxwell–Schrödinger equations and with a phase grating model. The delays result in measurable order-dependent differences in the energies of transient light induced states. As nonlinear methods are extended into the attosecond regime, the observed higher-order signal generation delays will significantly impact and aid temporal and spectral measurements of dynamic processes., Ultrafast dynamics following light-matter interaction are governed by nonlinear processes. Here the authors show that initial nonlinear signal time-evolution is a consequence of phase grating accumulation using transient grating measurements with attosecond and near-infrared pulses.

Ultrafast processes in matter can be captured and even controlled by using sequences of few-cycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semiclassical three-step model for high-order harmonic generation., Comment: 17 pages, 8 figures, published on 16 January 2018

Strong-field laser excitation of solids can produce extremely nonlinear electronic and optical behaviour. As recently demonstrated, this includes the generation of high harmonics extending into the vacuum-ultraviolet and extreme-ultraviolet regions of the electromagnetic spectrum. High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases. How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate. Here we report a direct comparison of high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron-hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.

This review discusses recent experimental and theoretical analyses of high-harmonic spectroscopy in small molecules, with the aim of characterizing charge migration. We discuss the formulation of molecular high-harmonic spectra followed by methods to extract molecular-target-specific information, both in experiments and ab initio simulations. We present measured and simulated high-harmonic spectra from carbon dioxide and carbonyl sulfide to illustrate the necessity for multidimensional analyses for high-harmonic spectroscopies that include both the spectral amplitude and phase. Leveraging these results, we examine how such multidimensional analyses pave the way for the study of charge migration with high-harmonic spectroscopy and illustrate the beneficial role a static molecular feature can play when probing dynamics. Finally, we briefly expand our scope with an outlook on the critical role of integrating theoretical and experimental approaches, beyond just high-harmonic spectroscopy, for the development of versatile harmonic spectroscopic probes of charge migration.

The interaction of strong near-infrared (NIR) laser pulses with wide-bandgap dielectrics produces high harmonics in the extreme ultraviolet (XUV) wavelength range. These observations have opened up the possibility of attosecond metrology in solids, which would benefit from a precise measurement of the emission times of individual harmonics with respect to the NIR laser field. Here we show that, when high-harmonics are detected from the input surface of a magnesium oxide crystal, a bichromatic probing of the XUV emission shows a clear synchronization largely consistent with a semiclassical model of electron-hole recollisions in bulk solids. On the other hand, the bichromatic spectrogram of harmonics originating from the exit surface of the 200 $\mu$m-thick crystal is strongly modified, indicating the influence of laser field distortions during propagation. Our tracking of sub-cycle electron and hole re-collisions at XUV energies is relevant to the development of solid-state sources of attosecond pulses.

Synopsis There is a profound, almost symbiotic relation between electrons and photons. When light interacts with matter the electrons in the material will start to move and oscillate. When a charged particle, such as an electron, oscillates it will act as a dipole and emit light. We utilize this symbiotic relation and extend the control of light to the extreme ultraviolet (XUV) region using the newly developed XUV opto-optical modulator.

We study the macroscopic spatial and temporal properties of harmonic radiation generated by a model solid in the interaction with an intense, focused laser beam. We show that different temporal contributions to the harmonic yield can be separated in the spatial domain because they lead to radiation with different divergences, similar to what is observed in gas-phase harmonic generation. We show that applying a spatial filter in the far field results in a temporal separation of the two contributions upon refocusing, which yields spatially collimated harmonics, a spectrum with well-resolved peaks, and a subcycle time profile of the harmonic radiation with only one burst per half-cycle.

We have studied, experimentally and theoretically, the ionization probability of carbonyl sulfide (OCS) molecules in intense linearly polarized 800-nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within each molecule such that the ensemble exhibits preferential alignment in the laboratory frame at specific times. The second, stronger pulse induces ionization, and the variation in single and double ionization yields is measured as a function of the delay between the two pulses. The angular dependence of the ionization yield is extracted by fitting the delay-dependent yields to a sum of delay-dependent moments of the rotational wave packet's angular distribution. We compute these same angular-dependent strong-field ionization yields for OCS using time-dependent density-functional theory (TDDFT). For the single-ionization case, our measurements agree well with TDDFT calculations and with previous experiments. Furthermore, analysis of the simulated one-body density reveals that, when averaged over a laser cycle, the resulting hole is delocalized across the molecule for light polarized perpendicular to the molecular axis and mostly localized on the sulfur for parallel polarization. This suggests that preferential molecular alignment is a key parameter for controlling charge migration dynamics initiated by strong-field ionization. For double ionization, the agreement between experiment and theory is less compelling, reflecting the substantial challenges of computing double-ionization yields using TDDFT methods.

High-harmonic generation was used to probe the spectral intensity and phase of the recombination-dipole matrix element of methyl chloride (CH3Cl), revealing a Cooper minimum (CM) analogous to the 3p CM previously reported in argon. The CM structure altered the spectral response and group delay (GD) of the emitted harmonics, and was revealed only through careful removal of all additional contributors to the GD. In characterizing the GD dispersion, also known as the “attochirp” we additionally present the most complete validation to date of the commonly used strong-field approximation for calculating the GD, demonstrating the correct intensity scaling and extending its usefulness to simple molecules.

We present first-principles calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength regime, from $1-4$ $\mu$m. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility, and with measurements for the nonlinear susceptibility up to 2.4 $\mu$m. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow accurate calculations of the long-distance propagation of intense MIR laser pulses in air.

Using a model molecular system (${A}_{2}$) with two active electrons restricted to one dimension, we examine high-order harmonic generation (HHG) enhanced by rescattering. Our results show that even at intensities well below the single ionization saturation, harmonics generated from the cation (${A}_{2}{}^{+}$) can be significantly enhanced due to the rescattering of the electron that is initially ionized. This two-electron effect is manifested by the appearance of a secondary plateau and cutoff in the HHG spectrum, extending beyond the predicted cutoff in the single active electron approximation. We use our molecular model to investigate the wavelength dependence of rescattering enhanced HHG, which was first reported in a model atomic system [I. Tikhomirov, T. Sato, and K. L. Ishikawa, Phys. Rev. Lett. 118, 203202 (2017)]. We demonstrate that the HHG yield in the secondary cutoff is highly sensitive to the available electron rescattering energies as indicated by a dramatic scaling with respect to driving wavelength.

We present a theoretical investigation of charge migration following strong-field ionization in a multielectron system. We study a model homonuclear molecule with two electrons, each restricted to one dimension ($1+1D$), interacting with a strong, static electric field. We show that in this system charge migration results from the interplay between multiple ionization channels that overlap in space, creating a coherent electron-hole wave packet in the cation. We also find that, in our case, charge migration following the first ionization manifests as a modulation of the subsequent double-ionization signal. We derive a parametrized semiclassical model from the full multielectron system and we discuss the importance of the choice of cation electronic-structure basis for the efficacy of the semiclassical representation. We use the ab initio solution of the full $1+1D$ system as a reference for the qualitative and quantitative results of the parametrized semiclassical model. We discuss the extension of our model to long-wavelength time-dependent fields with full-dimension, many-electron targets.

We present a theoretical study of the role that resonant enhancement plays in the temporal and spectral properties of near-threshold harmonics in argon, driven by a moderately intense, near-infrared laser pulse. By studying how the temporal profile of the eleventh harmonic (H11) changes with peak intensity and pulse duration, we show that H11 is predominantly emitted when the instantaneous intensity of the laser pulse is such that a high-lying excited state is Stark-shifted into multiphoton resonance with the ground state. We demonstrate that if this resonant intensity is lower than the peak intensity, the harmonic pulse will in general exhibit two peaks in time, on the rising and falling edges of the laser pulse. The resonantly enhanced harmonic radiation exhibits strong characteristics of semi-classical long and short quantum paths, and in general both paths are enhanced by the resonance. We find that the resonant enhancement leads to the harmonic radiation being emitted between .5 and 1.1 optical cycles after the time of multiphoton resonance, indicating that the resonance introduces a delay as compared to non-resonant emission. We further demonstrate that the resonantly enhanced long-trajectory contribution to the harmonic radiation manifests in the spectral domain as red- and blueshifted features near the central harmonic frequency. Finally, we compare the single argon atom response to the macroscopic response of an argon gas and show that spectral and temporal effects of the resonance are still recognizable after propagation.

We extend the technique of attosecond transient absorption spectroscopy by incorporating tunable IR pulses from an OPA. This technique is used to control Autler-Townes splitting and drive XUV four-wave mixing processes in Helium.

We investigate the connection between crystal symmetry and temporal and spectral properties of high-order harmonics in solids. We calculate the orientation-dependent harmonic spectrum driven by an intense, linearly polarized infrared laser field, using a momentum-space description of the generation process in terms of strong-field-driven electron dynamics on the band structure. We show that the orientation dependence of both the spectral yield and the subcycle time profile of the harmonic radiation can be understood in terms of the coupling strengths and relative curvatures of the valence band and the low-lying conduction bands. In particular, we show that in some systems this gives rise to a rapid shift of a quarter optical cycle in the timing of harmonics in the secondary plateau as the crystal is rotated relative to the laser polarization. We address recent experimental results in MgO [Y. S. You et al., Nat. Phys. 13, 345 (2017).] and show that the observed change in orientation dependence for the highest harmonics can be interpreted in the momentum space picture in terms of the contributions of several different conduction bands.

Solid-state high-harmonic sources offer the possibility of compact, high-repetition-rate attosecond light emitters. However, the time structure of high harmonics must be characterized at the sub-cycle level. We use strong two-cycle laser pulses to directly control the time-dependent nonlinear current in single-crystal MgO, leading to the generation of extreme ultraviolet harmonics. We find that harmonics are delayed with respect to each other, yielding an atto-chirp, the value of which depends on the laser field strength. Our results provide the foundation for attosecond pulse metrology based on solid-state harmonics and a new approach to studying sub-cycle dynamics in solids.

We report a strong carrier-envelope-phase dependence of high-harmonics in bulk solids subjected to strong few-cycle laser fields. We discover that harmonics are delayed with respect to each other at the sub-cycle level, yielding an atto-chirp.

Results illustrating the nonlinear dynamics of ultrashort laser pulse filamentation in gases are presented, with particular emphasis on the filament properties useful for developing attosecond light sources. Two aspects of ultrashort pulse filaments are specifically discussed: (i) numerical simulation results on pulse self-compression by filamentation in a gas cell filled with noble gas. Measurements of high harmonics generated by the pulse extracted from the filament allows for the detection of intensity spikes and subcycle pulses generated within the filament. (ii) Simulation results on the spontaneous formation of conical wavepackets during filamentation in gases, which in turn can be used as efficient driving pulses for the generation of high harmonics and isolated attosecond pulses.