Showing papers on "High harmonic generation published in 2016"

Solid-state harmonics beyond the atomic limit

Abstract: 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.

High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure

Abstract: Plasmonic high-harmonic generation (HHG) drew attention as a means of producing coherent extreme ultraviolet (EUV) radiation by taking advantage of field enhancement occurring in metallic nanostructures. Here a metal-sapphire nanostructure is devised to provide a solid tip as the HHG emitter, replacing commonly used gaseous atoms. The fabricated solid tip is made of monocrystalline sapphire surrounded by a gold thin-film layer, and intended to produce EUV harmonics by the inter- and intra-band oscillations of electrons driven by the incident laser. The metal-sapphire nanostructure enhances the incident laser field by means of surface plasmon polaritons, triggering HHG directly from moderate femtosecond pulses of ∼0.1 TW cm−2 intensities. The measured EUV spectra exhibit odd-order harmonics up to ∼60 nm wavelengths without the plasma atomic lines typically seen when using gaseous atoms as the HHG emitter. This experimental outcome confirms that the plasmonic HHG approach is a promising way to realize coherent EUV sources for nano-scale near-field applications in spectroscopy, microscopy, lithography and atto-second physics. It has been suggested that strong field enhancement for high harmonic generation may be achievable with nano-antennas. Here, the authors show relevant field enhancement using a metal-sapphire nanostructure that provides a solid tip as the high harmonic emitter, replacing commonly used gaseous atoms.

7 μm, ultrafast, sub-millijoule-level mid-infrared optical parametric chirped pulse amplifier pumped at 2 μm

Abstract: We present a novel all-fiber pumped optical parametric chirped pulse amplifier (OPCPA) architecture to generate self-carrier-to-envelope-phase stable, sub-eight-optical-cycle duration pulses at 7 μm wavelength approaching millijoule-level pulse energy at 100 Hz repetition rate. The system yields a peak power of 1.1 GW and, if focused to the diffraction limit, would reach a peak intensity of 7×1014 W/cm2. The OPCPA is pumped by a 2 μm Ho:YLF chirped pulse amplifier to leverage the highly efficient and broadband response of the nonlinear crystal ZGP. The 7 μm seed at 100 MHz is generated via difference frequency generation from an Er:Tm:Ho multi-arm fiber frequency comb, and a fraction of its output optically injects the Ho:YLF amplifier. While the pulse bandwidth at 7 μm is perfectly suited for nonlinear and spectroscopic applications, current parameters offer, for the first time, to the best of our knowledge, the possibility to explore strong-field physics in an entirely new wavelength range with a ponderomotive force 77 times larger than from an 800 nm source. The overall OPCPA system is very compact and provides a new tool for investigations directly in the molecular fingerprint region of the electro-magnetic spectrum or to drive high harmonic generation to produce fully coherent x-rays in the multi-kiloelectron-volt range and possibly zeptosecond temporal waveforms.

Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator.

Abstract: Electrons with a linear energy/momentum dispersion are called massless Dirac electrons and represent the low-energy excitations in exotic materials such as graphene and topological insulators. Dirac electrons are characterized by notable properties such as a high mobility, a tunable density and, in topological insulators, a protection against backscattering through the spin-momentum locking mechanism. All those properties make graphene and topological insulators appealing for plasmonics applications. However, Dirac electrons are expected to present also a strong nonlinear optical behaviour. This should mirror in phenomena such as electromagnetic-induced transparency and harmonic generation. Here we demonstrate that in Bi2Se3 topological insulator, an electromagnetic-induced transparency is achieved under the application of a strong terahertz electric field. This effect, concomitantly determined by harmonic generation and charge-mobility reduction, is exclusively related to the presence of Dirac electron at the surface of Bi2Se3, and opens the road towards tunable terahertz nonlinear optical devices based on topological insulator materials.

Ultra-strong nonlinear optical processes and trigonal warping in MoS$_2$ layers

Abstract: We report ultra-strong high-order nonlinear multiphoton processes in monolayer MoS$_2$ (1L-MoS$_2$): the third harmonic is thirty times stronger than the second harmonic, and the fourth harmonic is comparable to the second harmonic. We find that second and third harmonic processes are strongly dependent on elliptical polarization, which can be used to selectively tune harmonic generation with different orders. We explain this by calculating the nonlinear response functions of 1L-MoS$_2$ with a continuum-model Hamiltonian and quantum-mechanical diagrammatic perturbation theory, highlighting the crucial role of trigonal warping. A similar effect is expected for all other transition-metal dichalcogenides. Our results pave the way for efficient and tunable harmonic generation based on layered materials for various applications, including microscopy and imaging

Energetic sub-2-cycle laser with 216 W average power

Abstract: Few-cycle lasers are essential for many research areas such as attosecond physics that promise to address fundamental questions in science and technology. Therefore, further advancements are connected to significant progress in the underlying laser technology. Here, two-stage nonlinear compression of a 660 W femtosecond fiber laser system is utilized to achieve unprecedented average power levels of energetic ultrashort or even few-cycle laser pulses. In a first compression step, 408 W, 320 μJ, 30 fs pulses are achieved, which can be further compressed to 216 W, 170 μJ, 6.3 fs pulses in a second compression stage. To the best of our knowledge, this is the highest average power few-cycle laser system presented so far. It is expected to significantly advance the fields of high harmonic generation and attosecond science.

High-order harmonic generation in solids: A unifying approach

Abstract: There have been several experimental reports showing high-order harmonic generation from solids, but there has been no unifying theory presented as of yet for all these experiments. Here we report on the systematic investigation of high-order harmonic generation within the semiconductor Bloch equations, taking into account multiple bands and relaxation processes phenomenologically. In addition to reproducing key experiments, we show the following: (i) Electronic excitations, direct-indirect excitation pathways, and relaxation processes are responsible for high-order harmonic generation and control using midinfrared drivers in zinc oxide. We describe an intuitive picture explaining a two-color experiment involving noninversion symmetric crystals. (ii) High-order harmonic generation can be considered as a general feature of ultrafast strong-field-driven electronic dynamics in solids. We demonstrate this statement by predicting high-order harmonic spectra of solids that have not been studied yet.

Observation of High-Harmonic Generation from an Atomically Thin Semiconductor

Abstract: We report the observation of nonperturbative high-harmonic generation from monolayer MoS2. The yield is higher in monolayer compared to a single layer of the bulk, an effect attributed to strong electron-hole interactions in the monolayer.

Diabatic Mechanisms of Higher-Order Harmonic Generation in Solid-State Materials under High-Intensity Electric Fields.

Abstract: We theoretically investigate mechanisms of higher-order harmonic generation in solid-state materials under a high-intensity ac electric field. A new theoretical framework presented in this Letter holds the legitimacy of Bloch's theorem even under the influence of the high-intensity electric field and provides an exact treatment of the diabatic processes of Bloch electrons. Utilizing this framework, we first discovered that the diabatic processes, namely, ac Zener tunneling and semimetallization of semiconductors, are key factors for nonperturbative mechanisms of HHG. These mechanisms are classified by the field intensity and could be understood by an extended simple man model based on an analogy between tunnel ionization in gaseous media and Zener tunneling in semiconductors. These conclusions would stimulate the universal understanding of HHG mechanisms in both atomic and solid cases.

Scale-invariant nonlinear optics in gases

Abstract: Nonlinear optical methods have become ubiquitous in many scientific areas, from fundamental studies of time-resolved electron dynamics to microscopy and spectroscopy applications. They are, however, often limited to a certain range of parameters such as pulse energy and average power. Restrictions arise from, for example, the required field intensity as well as from parasitic nonlinear effects and saturation mechanisms. Here, we identify a fundamental principle of nonlinear light–matter interaction in gases and show that paraxial nonlinear wave equations are scale-invariant if spatial dimensions, gas density, and laser pulse energy are scaled appropriately. As an example, we apply this principle to high-order harmonic generation and provide a general method for increasing peak and average power of attosecond sources. In addition, we experimentally demonstrate the implications for the compression of short laser pulses. Our scaling principle extends well beyond those examples and includes many nonlinear processes with applications in different areas of science.

Shaping the Radiation Pattern of Second-Harmonic Generation from AlGaAs Dielectric Nanoantennas

Abstract: We study the manipulation of the radiation pattern of second-harmonic generation from AlGaAs all-dielectric nanoantennas exhibiting electric and magnetic resonances. We show the importance of the interference of different higher order multipoles in the nonlinear response of dielectric antennas for shaping of their second-harmonic radiation pattern. In particular, we show how such multipolar interference can be engineered in AlGaAs nanodisks by manipulating the pump beam polarization, incidence angle, and disk geometry. In this way we demonstrate the shaping of the radiation pattern in order to increase the second-harmonic power by a factor of 8 when measured in experiment through a finite numerical aperture microscope objective.

Multilevel perspective on high-order harmonic generation in solids

Abstract: We investigate high-order harmonic generation in a solid, modeled as a multilevel system dressed by a strong infrared laser field. We show that the cutoff energies and the relative strengths of the multiple plateaus that emerge in the harmonic spectrum can be understood both qualitatively and quantitatively by considering a combination of adiabatic and diabatic processes driven by the strong field. Such a model was recently used to interpret the multiple plateaus exhibited in harmonic spectra generated by solid argon and krypton [G. Ndabashimiye et al., Nature 534, 520 (2016)]. We also show that when the multilevel system originates from the Bloch state at the $\mathrm{\ensuremath{\Gamma}}$ point of the band structure, the laser-dressed states are equivalent to the Houston states [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)] and will therefore map out the band structure away from the $\mathrm{\ensuremath{\Gamma}}$ point as the laser field increases. This leads to a semiclassical three-step picture in momentum space that describes the high-order harmonic generation process in a solid.

Rotational Doppler effect in nonlinear optics

Abstract: The change in pitch of a passing car engine is a classic example of the translational Doppler effect, but rotational Doppler shifts can also arise, as shown for circularly polarized light passing through a spinning nonlinear optical crystal. The translational Doppler effect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies1,2,3,4,5,6,7,8, and for the Global Positioning System. The Doppler effect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms9 and has benefited cooling and trapping of atoms with laser light10,11,12. Despite numerous successful applications of the translational Doppler effect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves13—the so-called rotational Doppler effect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.

Nonlocality-driven supercontinuum white light generation in plasmonic nanostructures

Abstract: Structured plasmonic metals are widely employed for achieving nonlinear functionalities at the nanoscale due to their ability to confine and enhance electromagnetic fields and strong, inherent nonlinearity. Optical nonlinearities in centrosymmetric metals are dominated by conduction electron dynamics, which at the nanoscale can be significantly affected by the nonlocal effects. Here we show that nonlocal corrections, being usually small in the linear optical response, define nonlinear properties of plasmonic nanostructures. Using a full non-perturbative time-domain hydrodynamic description of electron plasma under femtosecond excitation, we numerically investigate harmonic generation in metallic Archimedean nanospirals, revealing the interplay between geometric and nonlocal effects. The quantum pressure term in the nonlinear hydrodynamic model results in the emergence of fractional nonlinear harmonics leading to broadband coherent white-light generation. The described effects present a novel class of nonlinear phenomena in metallic nanostructures determined by nonlocality of the electron response.

Stoner versus Heisenberg: Ultrafast exchange reduction and magnon generation during laser-induced demagnetization

Abstract: The excitation of a ferromagnetic film by a femtosecond laser pulse causes an unexpectedly fast quenching of the film's magnetization on subpicosecond time scales. The microscopic physical mechanisms responsible for this remain a scientific puzzle. The authors employ femtosecond extreme ultraviolet pulses produced by high harmonic generation to follow how the magnetization of a thin cobalt film evolves after the excitation by a 40-fs laser pulse. By measuring the time-, energy-, and angle-resolved magneto-optical response of the Co films across the ${M}_{2,3}$ absorption edge, they obtain a set of time-lapsed magnetic asymmetry spectra, which contain a wealth of information about the different mechanisms at work. When combined with advanced ab initio magneto-optical calculations, they identify two dominant contributions: first, a transient reduction of exchange splitting, and second, magnon excitation. This work thus distinguishes between two fundamental models of magnetism, the Stoner and Heisenberg models, which ascribe magnetization dynamics to an exchange splitting reduction and spin wave excitations, respectively.

High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses

Abstract: We investigate the high-order-harmonic generation (HHG) from solids by simulating the dynamics of a single active electron in periodic potentials. The corresponding time-dependent Schr\"odinger equations (TDSEs) are solved numerically by using $B$-spline basis sets in coordinate space. The energy-band structure and wave vectors can be directly retrieved from the eigenfunctions. The harmonic spectra obtained agree well with the results simulated by TDSE in $k$-space using Bloch states and show a two-plateau structure. Both of the cutoff energies of the two plateaus in the harmonic spectrum scale linearly with the field strength. We also study HHG driven by intense few-cycle laser pulses and find that the cutoff energy of the harmonic spectrum is sensitive to the changes of the carrier envelope phase.

Time-dependent complete-active-space self-consistent-field method for atoms: Application to high-order harmonic generation

Abstract: We present a numerical implementation of the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method [Phys. Rev. A 88, 023402 (2013)] for atoms driven by a strong linearly polarized laser pulse. The present implementation treats the problem in its full dimensionality and introduces a gauge-invariant frozen-core approximation, an efficient evaluation of the Coulomb mean field scaling linearly with the number of basis functions, and a split-operator method specifically designed for stable propagation of stiff spatial derivative operators. We apply this method to high-harmonic generation in helium, beryllium, and neon and explore the role of electron correlations.

Development of high harmonic generation spectroscopy of organic molecules and biomolecules

Abstract: In this review we will discuss the topic of high order harmonic generation (HHG) from samples of organic and bio-molecules. The possibility to extract useful dynamical and structural information from the measurement of the HHG emission, a technique termed high harmonic generation spectroscopy (HHGS), will be the special focus of our discussions. We will begin by introducing the salient facts of HHG from atoms and simple molecules and explaining the principles behind HHGS. Next the technical difficulties associated with HHG from samples of organic molecules and biomolecules, principally the low sample density and the low ionization potential, will be examined. Then we will present some recent experiments where HHG spectra from samples of these molecules have been measured and discuss what has been learned from these measurements. Finally we will look at the future prospects for HHG spectroscopy of organic molecules, discussing some of the technical and in principle limits of the technique and methods that may ameliorate these limits.

Improved strong-field approximation and quantum-orbit theory: Application to ionization by a bicircular laser field

Abstract: A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

Selection rules of high-order-harmonic generation: Symmetries of molecules and laser fields

Abstract: The selection rules of high harmonic generation (HHG) are investigated using three-dimensional time-dependent density functional theory (TDDFT). From the harmonic spectra obtained with various real molecules and different forms of laser fields, several factors that contribute to selection rules are revealed. Extending the targets to stereoscopic molecules, it is shown that the allowed harmonics are dependent on the symmetries of the projections of molecules. For laser fields, the symmetries contributing to the selection rules are discussed according to Lissajous figures and their dynamical directivities. All the phenomena are explained by the symmetry of the full time-dependent Hamiltonian under a combined transformation. We present a systematic study on the selection rules and propose an intuitive method for the judgment of allowed harmonic orders, which can be extended to more complex molecules and various forms of laser pulses.

High-harmonic generation at 250 MHz with photon energies exceeding 100 eV

Abstract: Ultrafast spectroscopy in the extreme ultraviolet demands for ever-higher pulse repetition rates and photon energies. Here, we drive cavity-enhanced high-order harmonic generation (HHG) at a repetition rate of 250 MHz, with 30 fs pulses and an average power of 10 kW. Employing an optimized cavity geometry and a high-pressure gas target, we couple out nanowatt-level harmonics at photon energies around 100 eV. This constitutes an improvement of more than two orders of magnitude over previous megahertz-repetition-rate HHG experiments and paves the way toward high-photon-energy frequency-comb spectroscopy and toward pump-probe photoelectron microscopy and spectroscopy at unprecedented repetition rates.

Laser material processing with tightly focused cylindrical vector beams

Abstract: We demonstrate a comprehensive modification study of silica glass, crystalline silicon, and amorphous silicon film, irradiated by tightly focused cylindrical vector beams with azimuthal and radial polarizations. The evidence of the longitudinal field associated with radial polarization is revealed by second harmonic generation in z-cut lithium niobate crystal. Despite the lower threshold of ring-shaped modification of silicon materials, the modification in the center of single pulse radially polarized beam is not observed. The phenomenon is interpreted in terms of the enhanced reflection of longitudinal component at the interface with high-index contrast, demonstrating that the longitudinal component is inefficient for the flat surface modification. Enhanced interaction of the longitudinal light field with silicon nanopillar structures produced by the first pulse of double-pulse irradiation is also demonstrated.

Multipolar Third-Harmonic Generation Driven by Optically Induced Magnetic Resonances

Abstract: We analyze third-harmonic generation from high-index dielectric nanoparticles and discuss the basic features and multipolar nature of the parametrically generated electromagnetic fields near the Mie-type optical resonances. By combining both analytical and numerical methods, we study the nonlinear scattering from simple nanoparticle geometries such as spheres and disks in the vicinity of the magnetic dipole resonance. We reveal the approaches for manipulating and directing the resonantly enhanced nonlinear emission with subwavelength all-dielectric structures that can be of particular interest for novel designs of nonlinear optical antennas and engineering the magnetic optical nonlinear response at nanoscale.

Echo-enabled harmonics up to the 75th order from precisely tailored electron beams

Abstract: Echo-enabled harmonic generation has been used to seed a free-electron laser and has been demonstrated up to the 75th harmonic, producing 32 nm light from a 2,400 nm laser.

Ptychographic coherent diffractive imaging with orthogonal probe relaxation.

Abstract: Ptychography is a scanning coherent diffractive imaging (CDI) technique that relies upon a high level of stability of the illumination during the course of an experiment. This is particularly an issue for coherent short wavelength sources, where the beam intensity is usually tightly focused on the sample in order to maximize the photon flux density on the illuminated region of the sample and thus a small change in the beam position results in a significant change in illumination of the sample. We present an improved ptychographic method that allows for limited stability of the illumination wavefront and thus significantly improve the reconstruction quality without additional prior knowledge. We have tested our reconstruction method in a proof of concept experiment, where the beam instability of a visible light source was emulated using a piezo driven mirror, and also in a short wavelength microscopy CDI setup using a high harmonic generation source in the extreme ultraviolet range. Our work shows a natural extension of the ptychography method that paves the way to use ptychographic imaging with any limited pointing stability coherent source such as free electron or soft X-ray lasers and improve reconstruction quality of long duration synchrotron experiments.

Role of Excited States In High-order Harmonic Generation.

Abstract: We investigate the role of excited states in high-order harmonic generation by studying the spectral, spatial, and temporal characteristics of the radiation produced near the ionization threshold of argon by few-cycle laser pulses. We show that the population of excited states can lead either to direct extreme ultraviolet emission through free induction decay or to the generation of high-order harmonics through ionization from these states and recombination to the ground state. By using the attosecond lighthouse technique, we demonstrate that the high-harmonic emission from excited states is temporally delayed by a few femtoseconds compared to the usual harmonics, leading to a strong nonadiabatic spectral redshift.

Dependence of high-order-harmonic generation on dipole moment in Si O 2 crystals

Abstract: High-order-harmonic generation in \ensuremath{\alpha}-quartz $\mathrm{Si}{\mathrm{O}}_{2}$ is theoretically investigated under a strong laser field by solving the extended semiconductor Bloch equations. The accurate band structures as well as dipole moments between different bands are obtained from state-of-the-art first-principles calculations. We find that the shapes of $k$-space-dependent dipole moments play an important role in harmonic generation. The calculated results show that harmonic conversion efficiency is significantly enhanced and the cutoff energy is distinctly increased when the dipole moments change greatly along a valley in the $k$ direction in the solid. Based on that dependence on the dipole moment, we also show that symmetry groups greatly affect the harmonic spectra from the solid materials. Moreover, a two-color synthesized field is used to achieve a supercontinuum harmonic spectrum near the cutoff region, and isolated attosecond pulses can be obtained directly by filtering out the harmonic radiation. We hope the contribution presented in this work provides a useful reference for future studies on laser-crystal interactions.

Circularly polarized molecular high harmonic generation using a bicircular laser

Abstract: We investigate the process of circularly polarized high harmonic generation in molecules using a bicircular laser field. In this context, we show that molecules offer a very robust framework for the production of circularly polarized harmonics, provided their symmetry is compatible with that of the laser field. Using a discrete time-dependent symmetry analysis, we show how all the features (harmonic order and polarization) of spectra can be explained and predicted. The symmetry analysis is generic and can easily be applied to other target and/or field configurations.