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Using optical technology for current injection and electromagnetic emission simplifies the comparison between materials. Here, we inject current into monolayer graphene and bulk gallium arsenide (GaAs) using two-color quantum interference and detect the emitted electric field by electro-optic sampling. We find the amplitude of emitted terahertz (THz) radiation scales in the same way for both materials even though they differ in dimension, band gap, atomic composition, symmetry and lattice structure. In addition, we observe the same mapping of the current direction to the light characteristics. With no electrodes for injection or detection, our approach will allow electron scattering timescales to be directly measured. We envisage that it will enable exploration of new materials suitable for generating terahertz magnetic fields., Comment: 4 figures

The ability to manipulate the space-time structure of light waves diversifies light-matter interaction and light-driven applications. Conventionally, metasurfaces are employed to locally control the amplitude and phase of light fields by the material response and structure of small meta-atoms. However, the fixed spatial structures of metasurfaces offer limited opportunities. Here, using quantum control we introduce a new approach that enables the amplitude, sign, and even configuration of the generated light fields to be manipulated in an all-optical manner. Following this approach, we demonstrate the generation of flying doughnut terahertz (THz) pulses. We show that the single-cycle THz pulse radiated from the dynamic semiconductor ring current has an electric field structure that is azimuthally polarized and that the space- and time-resolved magnetic field has a strong, isolated longitudinal component. As a first application, we detect absorption features from ambient water vapor on the spatiotemporal structure of the measured electric fields and the calculated magnetic fields. Quantum control is a powerful and flexible route to generating any structured light pulse in the THz range, while pulse compression of cylindrical vector beams is available for very high-power magnetic-pulse generation from the mid-infrared to near UV spectral region. Pulses such as these will serve as unique probes for spectroscopy, imaging, telecommunications, and magnetic materials.

Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g., for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience., Comment: 110 pages, many figures

Measuring the field of visible light with high spatial resolution has been challenging, as many established methods only detect a focus-averaged signal. Here, we introduce a near-field method for optical field sampling that overcomes that limitation by employing the localization of the enhanced near-field of a nanometric needle tip. A probe field perturbs the photoemission from the tip, which is induced by a pump pulse, generating a field-dependent current modulation that can easily be captured with our electronic detection scheme. The approach provides reliable characterization of near-petahertz fields. We show that not only the spiral wave-front of visible femtosecond light pulses carrying orbital angular momentum (OAM) can be resolved, but also the field evolution with time in the focal plane. Additionally, our method is polarization sensitive, which makes it applicable to vectorial field reconstruction., Comment: 8 pages, 3 figures, supplemental information

We present a novel approach to single-shot characterization of the spectral phase of broadband laser pulses. Our method is inexpensive, insensitive to alignment and combines the simplicity and robustness of the dispersion scan technique, that does not require spatio-temporal pulse overlap, with the advantages of single-shot pulse characterization methods such as single-shot frequency-resolved optical gating at a real-time reconstruction rate of several Hz.

High-harmonic generation is the cornerstone of nonlinear optics. It has been demonstrated in a wide range of crystalline systems including dielectrics, semiconductors, and semi-metals, as well as in gases, leaving metals out due to their low damage threshold. Here, we report on the high-harmonic generation in metallic titanium nitride (TiN) films. TiN is a refractory plasmonic metal, known for its high melting temperature and laser damage threshold, with optical properties similar to those of gold. We show that TiN can withstand laser pulses with peak intensities as high as 13 TW/cm$^2$, one order of magnitude higher than gold, enabling the emission of intraband harmonics up to photon energies of 11 eV. These harmonics can pave the way for compact and efficient plasmonic devices producing vacuum ultraviolet (VUV) frequency combs. Through numerical calculations and experimental studies, we show that the intensity scaling and angular anisotropy of the emitted VUV radiation stem from the anisotropic conduction band structure of TiN, thus confirming its intraband origin.

Strong-field methods in solids enable new strategies for ultrafast nonlinear spectroscopy and provide all-optical insights into the electronic properties of condensed matter in reciprocal and real space. Additionally, solid-state media offers unprecedented possibilities to control high-harmonic generation using modified targets or tailored excitation fields. Here we merge these important points and demonstrate circularly-polarized high-harmonic generation with polarization-matched excitation fields for spectroscopy of chiral electronic properties at surfaces. The sensitivity of our approach is demonstrated for structural helicity and termination-mediated ferromagnetic order at the surface of silicon-dioxide and magnesium oxide, respectively. Circularly polarized radiation emanating from a solid sample now allows to add basic symmetry properties as chirality to the arsenal of strong-field spectroscopy in solids. Together with its inherent temporal (femtosecond) resolution and non-resonant broadband spectrum, the polarization control of high harmonics from condensed matter can illuminate ultrafast and strong field dynamics of surfaces, buried layers or thin films., Comment: 24 pages, 5 figures

Multiphoton-ionized electrons are born into a strong light field that will determine their short-term future. By controlling the infrared beam, we enable atoms or molecules to generate extreme ultraviolet (XUV) pulses and synthesize attosecond pulses - the shortest controlled events ever produced. Here we show that a weak obliquely incident beam imposes an optical grating on the fundamental beam, resulting in a spatially modulated attosecond pulse. We observe the modulation on a spectrally resolved near-field XUV image, encoding all information of the spectral phase of the recollision electron and, therefore, the attosecond pulse produced by structureless atoms. Near-field imaging is an efficient method for measuring the duration of attosecond pulses, especially important for soft X-ray pulses created in helium. For more complex systems, it includes auto ionization and giant plasmon resonances., Comment: 6 pages, 5 figures

A near-infrared laser generates gain on transitions between the $\text{B}^{\text{2}} \Sigma_{\text{u}}^{\text{+}}$ and $\text{X}^{\text{2}} \Sigma_{\text{g}}^{\text{+}}$ states of the nitrogen molecular cation in part by coupling the $\text{X}^{\text{2}} \Sigma_{\text{g}}^{\text{+}}$ and $\text{A}^{\text{2}} \Pi_{\text{u}}$ states in the V-system. Traditional time resolved pump-probe measurements rely on post-ionization coupling by the pump pulse to initialize dynamics in the $\text{A}^{\text{2}} \Pi_{\text{u}}$ state. Here we show that a weak second excitation pulse reduces ambiguity because it acts only on the ion independent of ionization. The additional control pulse can increase gain by moving population to the $\text{A}^{\text{2}} \Pi_{\text{u}}$ state, which modifies the lasing emission in two distinct ways. The presence of fast decoherence on $\text{X}^{\text{2}} \Sigma_{\text{g}}^{\text{+}}$ to $\text{A}^{\text{2}} \Pi_{\text{u}}$ transitions may prevent the formation of a coherent rotational wave packet in the ground state in our experiment, but the control pulse can reverse impulsive alignment by the pump pulse to remove rotational wave packets in the $\text{B}^{\text{2}} \Sigma_{\text{u}}^{\text{+}}$ state.

We demonstrate a novel method to measure the temporal evolution of electric fields with optical frequencies. Our technique is based on the detection of transient currents in air plasma. These directional currents result from sub-cycle ionization of air with a short pump pulse, and the steering of the released electrons with the pulse to be sampled. We assess the validity of our approach by comparing it with different state-of-the-art laser-pulse characterization techniques. Notably, our method works in ambient air and facilitates a direct measurement of the field waveform, which can be viewed in real time on an oscilloscope in the exact same way as a radio frequency signal.

Nonlinear absorption of femtosecond laser pulses provides a unique opportunity to confine energy deposition in any medium to a region that is below the focal diameter of a pulse. Illumination of a polymer film through a transparent high bandgap material such as glass, followed by nonlinear absorption of 800 nm light in polymers, allows us to further restrict absorption to a very thin layer along the propagation direction. We demonstrate this confinement by simulating femtosecond-laser-induced polymer modification by linear, two-photon and three-photon absorption, and discuss the control over energy absorption in polymers that multiphoton processes offer. Energy deposited behind a thin polymer film induces a protruding blister. We present experimental results of blister diameter and height scaling with pulse energy. Using 0.95 NA focussing, we obtained laser-induced blisters with diameters as small as 700 nm suggesting blister-based Laser-Induced Forward Transfer is possible on and below the single-micron scale. Sub-micrometer blister formation using femtosecond lasers also offers a novel method of direct, precise laser-writing of microstructures on films with single laser pulses. This method is a possible alternative to lithography, laser milling, and laser-based additive machining which leaves the surface composition unchanged., Comment: 19 pages, 8 figures, submitted to Physical Reviews Applied

The strong coupling between intense laser fields and valence electrons in molecules causes a distortion of the potential energy hypersurfaces which determine the motion of nuclei in a molecule and influences possible reaction pathways. The coupling strength varies with the angle between the light electric field and valence orbital, and thereby adds another dimension to the effective molecular potential energy surface, allowing for the emergence of light-induced conical intersections. Here, we demonstrate in theory and experiment that the full complexity of such light-induced potential energy surfaces can be uncovered. In H$_2^+$, the simplest of molecules, we observe a strongly modulated angular distribution of protons which has escaped prior observation. These modulations directly result from ultrafast dynamics on the light-induced molecular potentials and can be modified by varying the amplitude, duration and phase of the mid-infrared dressing field. This opens new opportunities for manipulating the dissociation of small molecules using strong laser fields.

We introduce a new technique for the generation of magnetic impulses. This technique is based on coherent control of electrical currents using cylindrical laser beams with azimuthal polarization. When used to ionize a medium, in this case atomic hydrogen is considered, an azimuthal current impulse is driven. The spatial distribution of this current bears close resemblance to that of a solenoid, and produces a magnetic field impulse. The excitation and relaxation dynamics of this current temporally confine the resulting magnetic field to a Tesla-scale, terahertz bandwidth impulse. Importantly, the magnetic fields are spatially isolated from electric fields. This all-optical approach will enable ultrafast time-domain spectroscopy of magnetic phenomena., Comment: 5 pages, 4 figures

The interplay between spin and orbital angular momentum in the up-conversion process allows us to control the macroscopic wave front of high harmonics by manipulating the microscopic polarizations of the driving field. We demonstrate control of orbital angular momentum in high harmonic generation from both solid and gas phase targets using the selection rules of spin angular momentum. The gas phase harmonics extend the control of angular momentum to extreme-ultraviolet wavelength. We also propose a bi-color scheme to produce spectrally separated extreme-ultraviolet radiation carrying orbital angular momentum.

A three step model for high harmonic generation from impurities in solids is developed. The process is found to be similar to high harmonic generation in atomic and molecular gases with the main difference coming from the non-parabolic nature of the bands. This opens a new avenue for strong field atomic and molecular physics in the condensed matter phase. As a first application, our conceptual study demonstrates the feasibility of tomographic measurement of impurity orbitals., Comment: 6 pages, 3 figures

Ionization of an atom or molecule by a strong laser field produces sub-optical cycle wave packets whose control has given rise to attosecond science. The final states of the wave packets depend on ionization and deflection by the laser field, which are convoluted in conventional experiments. Here, we demonstrate a technique enabling efficient electron deflection, separate from the field driving strong-field ionization. Using a mid-infrared deflection field permits one to distinguish electron wave packets generated at different field maxima of an intense few-cycle visible laser pulse. We utilize this capability to trace the scattering of low-energy electrons driven by the mid-infrared field. Our approach represents a general technique for studying and controlling strong-field ionization dynamics on the attosecond time scale., Comment: 5 Pages, 4 figures

A new amplification method based on the optical Kerr instability is suggested and theoretically analyzed, with emphasis on the near to mid-infrared wavelength regime. Our analysis for CaF2 and KBr crystals shows that one to two cycle pulse amplification by 3-4 orders of magnitude in the wavelength range from 1-14 microns is feasible with currently available laser sources. At 14 microns final output energies in the 0.05 mJ range are achievable corresponding to about 0.2-0.25% of the pump energy. The Kerr instability presents a promising process for the amplification of ultrashort mid-infrared pulses., Comment: 10 pages, 6 figures, supplementary section with a large table, summarizing all variables and parameters used in this work

We generate high-order harmonics of a mid-infrared laser from a silicon single crystal and find their origin in the recollision of coherently accelerated electrons with their holes, analogously to the atomic and molecular case, and to ZnO [Vampa et al., Nature 522, 462-464 (2015)], a direct bandgap material. Therefore indirect bandgap materials are shown to sustain the recollision process as well as direct bandgap materials. Furthermore, we find that the generation is perturbed with electric fields as low as 30 V/$\mu$m, equal to the DC damage threshold. Our results extend high-harmonic spectroscopy to the most technologically relevant material, and open the possibility to integrate high harmonics with conventional electronics.

We show that circularly polarized femtosecond laser pulses produce field-free alignment in linear and planar molecules. We study the rotational wavepacket evolution of O$_2$ and benzene created by circularly polarized light. For benzene, we align the molecular plane to the plane of polarization. For O$_2$, we demonstrate that circular polarization yields a net alignment along the laser propagation axis at certain phases of the evolution. Circular polarization gives us the ability to control alignment of linear molecules outside the plane of polarization, providing new capabilities for molecular imaging., Comment: 6 pages, 3 figures

We study theoretically and experimentally the electronic relaxation of NO2 molecules excited by absorption of one ~400 nm pump photon. Semi-classical simulations based on trajectory surface hopping calculations are performed. They predict fast oscillations of the electronic character around the intersection of the ground and first excited diabatic states. An experiment based on high-order harmonic transient grating spectroscopy reveals dynamics occuring on the same timescale. A systematic study of the detected transient is conducted to investigate the possible influence of the pump intensity, pump wavelength, and rotational temperature of the molecules. The quantitative agreement between measured and predicted dynamics shows that, in NO2, high harmonic transient grating spectroscopy encodes vibrational dynamics underlying the electronic relaxation., Comment: The following article has been accepted by Journal of Chemical Physics. After it is published, it will be found at http://jcp.aip.org/

The physics of high harmonics has led to the generation of attosecond pulses and to trains of attosecond pulses. Measurements that confirm the pulse duration are all performed in the far field. All pulse duration measurements tacitly assume that both the beam's wavefront and intensity profile are independent of frequency. However, if one or both are frequency dependent, then the retrieved pulse duration depends on the location where the measurement is made. We measure that each harmonic is very close to a Gaussian, but we also find that both the intensity profile and the beam wavefront depend significantly on the harmonic order. Thus, our findings mean that the pulse duration will depend on where the pulse is observed. Measurement of spectrally resolved wavefronts along with temporal characterization at one single point in the beam would enable complete space-time reconstruction of attosecond pulses. Future attosecond science experiments need not be restricted to spatially averaged observables.

We report measurements and theoretical simulations of high-order harmonic generation (HHG) in aligned N$_2$ molecules using a 1200-nm intense laser field when the generating pulse is perpendicular to the aligning one. With increasing laser intensity, the minimum in the HHG spectra first shifts its position and then disappears. Theoretical simulations including the macroscopic propagation effects in the medium reproduce these observations and the disappearance of the minimum is attributed to the additional contribution of HHG from inner orbitals. We also predict that the well-known shape resonance in the photoionization spectra of N$_2$ should exist in the HHG spectra. It is most clearly seen when the generating laser is parallel to the aligning one, and disappears gradually as the angle between the two lasers increases. No clear evidence of this shape resonance has been reported so far when using lasers with different wavelengths. Further experimentation is needed to draw conclusions., Comment: 8 pages, 4 figures

We present experimental results showing the appearance of a near-continuum in the high-order harmonic generation (HHG) spectra of atomic and molecular species as the driving laser intensity of an infrared pulse increases. Detailed macroscopic simulations reveal that these near-continuum spectra are capable of producing IAPs in the far field if a proper spatial filter is applied. Further, our simulations show that the near-continuum spectra and the IAPs are a product of strong temporal and spatial reshaping (blue shift and defocusing) of the driving field. This offers a possibility of producing IAPs with a broad range of photon energy, including plateau harmonics, by mid-IR laser pulses even without carrier-envelope phase stabilization., Comment: 7 pages, 5 figures, submitted to J.Phys. B (Oct 2011)

The balance of the linear photon momentum in multiphoton ionization is studied experimentally. In the experiment argon and neon atoms are singly ionized by circularly polarized laser pulses with a wavelength of 800 nm and 1400 nm in the intensity range of 10^{14} - 10^{15} W/cm^2. The photoelectrons are measured using velocity map imaging. We find that the photoelectrons carry linear momentum corresponding to the photons absorbed above the field free ionization threshold. Our finding has implications for concurrent models of the generation of terahertz radiation in filaments., Comment: 4 pages, 3 figures

We apply tomography, a general method for reconstructing 3-D distributions from multiple projections, to reconstruct the momentum distribution of electrons produced via strong field photoionization. The projections are obtained by rotating the electron distribution via the polarization of the ionizing laser beam and recording a momentum spectrum at each angle with a 2-D velocity map imaging spectrometer. For linearly polarized light the tomographic reconstruction agrees with the distribution obtained using an Abel inversion. Electron tomography, which can be applied to any polarization, will simplify the technology of electron imaging. The method can be directly generalized to other charged particles., Comment: Accepted by J. Phys. B

We present a new theoretical approach to attosecond laser-assisted photo- and Compton ionization. Attosecond x-ray absorption and scattering are described by $\hat{\mathrsfs{S}}^{(1,2)}$-matrices, which are coherent superpositions of "monochromatic" $\hat{S}^{(1,2)}$-matrices in a laser-modified Furry representation. Besides refining the existing theory of the soft x-ray photoelectron attosecond streak camera and spectral phase interferometry (ASC and ASPI), we formulate a theory of hard x-ray photoelectron and Compton ASC and ASPI. The resulting scheme has a simple structure and leads to closed-form expressions for ionization amplitudes. We investigate Compton electron interference in the separable Coulomb-Volkov continuum with both Coulomb and laser fields treated non-perturbatively. We find that at laser-field intensities below 10$^{13}$ Wcm$^{-2}$ normalized Compton lines almost coincide with the lines obtained in the laser-free regime. At higher intensities, attosecond interferences survive integration over electron momenta, and feature prominently in the Compton lines themselves. We define a regime where the electron ground-state density can be measured with controllable accuracy in an attosecond time interval. The new theory provides a firm basis for extracting photo- and Compton electron phases and atomic and molecular wavefunctions from experimental data., Comment: 15 pages, 5 figures