Showing papers on "High harmonic generation published in 2017"

High-harmonic generation in graphene enhanced by elliptically polarized light excitation

Abstract: The electronic properties of graphene can give rise to a range of nonlinear optical responses. One of the most desirable nonlinear optical processes is high-harmonic generation (HHG) originating from coherent electron motion induced by an intense light field. Here, we report on the observation of up to ninth-order harmonics in graphene excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced by an elliptically polarized laser excitation, and the resultant harmonic radiation has a particular polarization. The observed ellipticity dependence is reproduced by a fully quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique properties of HHG in graphene, and our findings open up the possibility of investigating strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.

High-harmonic generation from an atomically thin semiconductor

Abstract: Observations of high-harmonic generation from a single layer of a transition metal dichalcogenide opens the door to studying strong-field and attosecond phenomena in two-dimensional materials. High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales1,2,3,4,5,6. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands7,8,9,10,11,12,13,14. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process15,16, including different symmetries17,18,19, access to individual valleys20,21 and enhanced many-body interactions22,23,24,25. Here we demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

Anisotropic high-harmonic generation in bulk crystals

Abstract: High-harmonic generation in a solid turns out to be sensitive to the interatomic bonding — a very useful feature that could enable the all-optical imaging of the interatomic potential. The microscopic valence electron density determines the optical, electronic, structural and thermal properties of materials. However, current techniques for measuring this electron charge density are limited: for example, scanning tunnelling microscopy is confined to investigations at the surface, and electron diffraction requires very thin samples to avoid multiple scattering1. Therefore, an optical method is desirable for measuring the valence charge density of bulk materials. Since the discovery of high-harmonic generation (HHG) in solids2, there has been growing interest in using HHG to probe the electronic structure of solids3,4,5,6,7,8,9,10,11. Here, using single-crystal MgO, we demonstrate that high-harmonic generation in solids is sensitive to interatomic bonding. We find that harmonic efficiency is enhanced (diminished) for semi-classical electron trajectories that connect (avoid) neighbouring atomic sites in the crystal. These results indicate the possibility of using materials’ own electrons for retrieving the interatomic potential and thus the valence electron density, and perhaps even wavefunctions, in an all-optical setting.

53-attosecond X-ray pulses reach the carbon K-edge

Abstract: The motion of electrons in the microcosm occurs on a time scale set by the atomic unit of time—24 attoseconds. Attosecond pulses at photon energies corresponding to the fundamental absorption edges of matter, which lie in the soft X-ray regime above 200 eV, permit the probing of electronic excitation, chemical state, and atomic structure. Here we demonstrate a soft X-ray pulse duration of 53 as and single pulse streaking reaching the carbon K-absorption edge (284 eV) by utilizing intense two-cycle driving pulses near 1.8-μm center wavelength. Such pulses permit studies of electron dynamics in live biological samples and next-generation electronic materials such as diamond. Isolated attosecond pulses are produced using high harmonic generation and sources of these pulses often suffer from low photon flux in soft X-ray regime. Here the authors demonstrate efficient generation and characterization of 53 as pulses with photon energy near the water window.

Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids.

Abstract: Advanced first-principles calculations reveal that the generation of high harmonic spectra is enhanced by the inhomogeneity of the electron\penalty1000\-\allowhyphens{}-nuclei potential, which is obtained from the band structure.

Electric field-induced second-order nonlinear optical effects in silicon waveguides

Abstract: The symmetry of crystalline silicon inhibits a second-order optical nonlinear susceptibility, χ(2), in complementary metal–oxide–semiconductor-compatible silicon photonic platforms. However, χ(2) is required for important processes such as phase-only modulation, second-harmonic generation (SHG) and sum/difference frequency generation. Here, we break the crystalline symmetry by applying direct-current fields across p–i–n junctions in silicon ridge waveguides and induce a χ(2) proportional to the large χ(3) of silicon. The obtained χ(2) is first used to perturb the permittivity (the direct-current Kerr effect) and achieve phase-only modulation. Second, the spatial distribution of χ(2) is altered by periodically patterning p–i–n junctions to quasi-phase-match pump and second-harmonic modes and realize SHG. We measure a maximum SHG efficiency of P2ω/Pω2 = 13 ± 0.5% W−1 at λω = 2.29 µm and with field-induced χ(2) = 41 ± 1.5 pm V–1. We expect such field-induced χ(2) in silicon to lead to a new class of complex integrated devices such as carrier-envelope offset frequency stabilizers, terahertz generators, optical parametric oscillators and chirp-free modulators. The application of d.c. fields across p–i–n junctions in silicon ridge waveguides leads to crystal symmetry breaking. This induces a second-order optical nonlinear susceptibility that enables phase-only modulation and second-harmonic generation with an efficiency of ∼13% W–1 at 2.29 µm.

Plasmon-enhanced high-harmonic generation from silicon

Abstract: High-harmonic emission from crystalline silicon can be made ten times brighter by exploiting local plasmonic fields in arrays of nano-antennas. Plasmonic antennas can enhance the intensity of a nanojoule laser pulse by localizing the electric field in their proximity1. It has been proposed that the field can become strong enough to convert the fundamental laser frequency into high-order harmonics through an extremely nonlinear interaction with gas atoms that occupy the nanoscopic volume surrounding the antennas2,3,4. However, the small number of gas atoms that can occupy this volume limits the generation of high harmonics5,6,7. Here we use an array of monopole nano-antennas to demonstrate plasmon-assisted high-harmonic generation directly from the supporting crystalline silicon substrate. The high density of the substrate compared with a gas allows macroscopic buildup of harmonic emission. Despite the sparse coverage of antennas on the surface, harmonic emission is ten times brighter than without antennas. Imaging the high-harmonic radiation will allow nanometre and attosecond measurement of the plasmonic field8 thereby enabling more sensitive plasmon sensors9 while opening a new path to extreme-ultraviolet-frequency combs10.

Subwavelength coherent imaging of periodic samples using a 13.5 nm tabletop high-harmonic light source

Abstract: Coherent diffractive imaging of periodic samples is demonstrated with a tabletop, 13.5 nm high-harmonic source. With a novel image reconstruction technique, the record high spatial resolution of 12.6 nm is achieved in the extreme-ultraviolet region.

Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers.

Abstract: Nonlinear optical processes, such as harmonic generation, are of great interest for various applications, e.g., microscopy, therapy, and frequency conversion. However, high-order harmonic conversion is typically much less efficient than low-order, due to the weak intrinsic response of the higher-order nonlinear processes. Here we report ultra-strong optical nonlinearities in monolayer MoS2 (1L-MoS2): the third harmonic is 30 times stronger than the second, and the fourth is comparable to the second. The third harmonic generation efficiency for 1L-MoS2 is approximately three times higher than that for graphene, which was reported to have a large χ (3). We explain this by calculating the nonlinear response functions of 1L-MoS2 with a continuum-model Hamiltonian and quantum mechanical diagrammatic perturbation theory, highlighting the role of trigonal warping. A similar effect is expected in all other transition-metal dichalcogenides. Our results pave the way for efficient harmonic generation based on layered materials for applications such as microscopy and imaging. Harmonic generation is a nonlinear optical process occurring in a variety of materials; the higher orders generation is generally less efficient than lower orders. Here, the authors report that the third-harmonic is thirty times stronger than the second-harmonic in monolayer MoS2.

Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

Abstract: The strong ellipticity dependence of high-harmonic generation (HHG) in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to solids requires a fundamental understanding of the microscopic mechanism of HHG. Here we use first-principles simulations within a time-dependent density-functional framework and show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the high-harmonic plateau can be extended by as much as 30% using a finite ellipticity of the driving field. We furthermore demonstrate the possibility to generate, from single circularly polarized drivers, circularly polarized harmonics. Our work shows that ellipticity provides an additional knob to experimentally optimize HHG in solids. The mechanisms of high-order harmonic generation in bulk system and dilute gas are different. Here the authors use first-principle methods to explore the ellipticity dependence and control of the HHG in periodic solids by involving the interband and intraband dynamics in Si and MgO.

High-harmonic generation in amorphous solids

Abstract: High-harmonic generation in isolated atoms and molecules has been widely utilized in extreme ultraviolet photonics and attosecond pulse metrology. Recently, high-harmonic generation has been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruct electronic band structures, as well as compact extreme ultraviolet light sources. So far these studies are confined to crystalline solids; therefore, decoupling the respective roles of long-range periodicity and high density has been challenging. Here we report the observation of high-harmonic generation from amorphous fused silica. We decouple the role of long-range periodicity by comparing harmonics generated from fused silica and crystalline quartz, which contain the same atomic constituents but differ in long-range periodicity. Our results advance current understanding of the strong-field processes leading to high-harmonic generation in solids with implications for the development of robust and compact extreme ultraviolet light sources. Although higher harmonic generation from solids has become of interest in many fields, its observation is typically limited to crystalline solids. Here, the authors demonstrate that higher harmonics can be generated from amorphous solids.

Tunable orbital angular momentum in high-harmonic generation.

Abstract: Optical vortices are currently one of the most intensively studied topics in optics. These light beams, which carry orbital angular momentum (OAM), have been successfully utilized in the visible and infrared in a wide variety of applications. Moving to shorter wavelengths may open up completely new research directions in the areas of optical physics and material characterization. Here, we report on the generation of extreme-ultraviolet optical vortices with femtosecond duration carrying a controllable amount of OAM. From a basic physics viewpoint, our results help to resolve key questions such as the conservation of angular momentum in highly nonlinear light-matter interactions, and the disentanglement and independent control of the intrinsic and extrinsic components of the photon's angular momentum at short-wavelengths. The methods developed here will allow testing some of the recently proposed concepts such as OAM-induced dichroism, magnetic switching in organic molecules and violation of dipolar selection rules in atoms.

Giant Optical Second Harmonic Generation in Two-Dimensional Multiferroics

Abstract: Nonlinear optical properties of materials such as second and higher order harmonic generation and electro-optic effect play pivotal roles in lasers, frequency conversion, electro-optic modulators, switches, and so forth. The strength of nonlinear optical responses highly depends on intrinsic crystal symmetry, transition dipole moments, specific optical excitation, and local environment. Using first-principles electronic structure theory, here we predict giant second harmonic generation (SHG) in recently discovered two-dimensional (2D) ferroelectric–ferroelastic multiferroics–group IV monochalcogenides (i.e., GeSe, GeS, SnSe, and SnS). Remarkably, the strength of SHG susceptibility in GeSe and SnSe monolayers is more than 1 order of magnitude higher than that in monolayer MoS2, and 2 orders of magnitude higher than that in monolayer hexagonal BN. Their extraordinary SHG is dominated by the large residual of two opposite intraband contributions in the SHG susceptibility. More importantly, the SHG polarizati...

Ellipticity dependence of high-harmonic generation in solids: unraveling the interplay between intraband and interband dynamics

Abstract: The strong ellipticity dependence of high-harmonic generation in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to high-harmonic generation in solids requires a fundamental understanding of the microscopic mechanism of the high-harmonic generation. Here, using extensive first-principles simulations within a time-dependent density-functional framework, we show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the energy cutoff of the high-harmonic plateau can be increased by as much as 30\% using a finite ellipticity of the driving field, opening a new avenue for better understanding and control of HHG in solids based on ellipticity. Also, we demonstrate the possibility to generate, from a single circularly polarized driving field, circularly polarized harmonics with alternating helicity. Our work shows that ellipticity provides an additional knob to experimentally control high-order harmonic generation in solids.

Mapping the electron band structure by intraband high-harmonic generation in solids

Abstract: High-harmonic generation (HHG) has recently been extended to solids, enabling all-optical reconstruction of electron band structure. However, material absorption of above-the-bandgap interband harmonics used for this purpose in earlier work limits the applicability of this promising technique. Here, sub-100-fs mid-infrared pulses tunable within the range of wavelengths from 5.0 to 6.7 μm are used to study HHG in ZnSe. Below-the-bandgap high-order harmonics generated by such driver pulses fall within the transparency range of a solid material, thus removing absorption-related limitations on the depth of HHG. Such harmonics are shown to be ideally suited to probe the nonlinearities of electron bands, enabling an all-optical mapping of the electron band structure in bulk solids.

Plasmon-assisted high-harmonic generation in graphene.

Abstract: High-harmonic generation in condensed-matter systems is both a source of fundamental insight into quantum electron motion and a promising candidate to realize compact ultraviolet and ultrafast light sources. While graphene is anticipated to efficiently generate high-order harmonics due to its anharmonic charge-carrier dispersion, experiments performed on extended samples using THz illumination have revealed only a weak effect. The situation is further complicated by the enormous electromagnetic field intensities required by this highly nonperturbative nonlinear optical phenomenon. Here we argue that the large light intensity required for high-harmonic generation to occur can be reached by exploiting localized plasmons in doped graphene nanostructures. We demonstrate through rigorous time-domain simulations that the synergistic combination of strong plasmonic near-field enhancement and a pronounced intrinsic nonlinearity result in efficient broadband high-harmonic generation within a single material. Our results support the strong potential of nanostructured graphene as a robust, electrically tunable platform for high-harmonic generation.

Introduction to macroscopic power scaling principles for high-order harmonic generation

Abstract: This tutorial presents an introduction to power scaling concepts for high-order harmonic generation (HHG) and attosecond pulse production. We present an overview of state-of-the-art HHG-based extreme ultraviolet (XUV) sources, followed by a brief introduction to basic principles underlying HHG and a detailed discussion of macroscopic effects and scaling principles. Particular emphasis is put on a general scaling model that allows the invariant scaling of the HHG process both, to μJ-level driving laser pulses and thus to multi-MHz repetition rates as well as to 100 mJ-or even Joule-level laser pulses, allowing new intensity regimes with attosecond XUV pulses.

Symmetry-controlled temporal structure of high-harmonic carrier fields from a bulk crystal

Abstract: High-harmonic (HH) generation in crystalline solids1-6 marks an exciting development, with potential applications in high-efficiency attosecond sources7, all-optical bandstructure reconstruction8,9, and quasiparticle collisions10,11. Although the spectral1-4 and temporal shape5 of the HH intensity has been described microscopically1-6,12, the properties of the underlying HH carrier wave have remained elusive. Here we analyse the train of HH waveforms generated in a crystalline solid by consecutive half cycles of the same driving pulse. Extending the concept of frequency combs13-15 to optical clock rates, we show how the polarization and carrier-envelope phase (CEP) of HH pulses can be controlled by crystal symmetry. For some crystal directions, we can separate two orthogonally polarized HH combs mutually offset by the driving frequency to form a comb of even and odd harmonic orders. The corresponding CEP of successive pulses is constant or offset by π, depending on the polarization. In the context of a quantum description of solids, we identify novel capabilities for polarization- and phase-shaping of HH waveforms that cannot be accessed with gaseous sources.

Laser waveform control of extreme ultraviolet high harmonics from solids.

Abstract: 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.

Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.

Abstract: The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges o...

Next Generation Driver for Attosecond and Laser-plasma Physics

Abstract: The observation and manipulation of electron dynamics in matter call for attosecond light pulses, routinely available from high-order harmonic generation driven by few-femtosecond lasers. However, the energy limitation of these lasers supports only weak sources and correspondingly linear attosecond studies. Here we report on an optical parametric synthesizer designed for nonlinear attosecond optics and relativistic laser-plasma physics. This synthesizer uniquely combines ultra-relativistic focused intensities of about 1020 W/cm2 with a pulse duration of sub-two carrier-wave cycles. The coherent combination of two sequentially amplified and complementary spectral ranges yields sub-5-fs pulses with multi-TW peak power. The application of this source allows the generation of a broad spectral continuum at 100-eV photon energy in gases as well as high-order harmonics in relativistic plasmas. Unprecedented spatio-temporal confinement of light now permits the investigation of electric-field-driven electron phenomena in the relativistic regime and ultimately the rise of next-generation intense isolated attosecond sources.

Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy.

Abstract: We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajectories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in H_{2} and D_{2} are used simultaneously to retrieve the nuclear dynamics on the attosecond and angstrom scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.

Effect of transition dipole phase on high-order-harmonic generation in solid materials

Abstract: High-order harmonic spectra from solid materials driven by single-color multicycle laser fields sometimes contain even harmonics. In this work we attribute the appearance of even harmonics to the nonzero transition dipole phase (TDP) when the solid system has broken symmetry. By calculating the harmonic efficiency from graphene and gapped graphene by using the semiconductor Bloch equations under the tight-binding approximation, we demonstrate the role of the TDP, which has been ignored for a long time. When the crystal has inversion symmetry, or reflection symmetry with the symmetry plane perpendicular to the laser polarization direction, the TDP can be neglected. Without such symmetry, however, the TDP will lead to the appearance of even harmonics. We further show that the TDP is sensitive to the crystal geometry. To extract the structure information from the harmonic spectra of a solid the TDP cannot be ignored.

High harmonic imaging of ultrafast many-body dynamics in strongly correlated systems

Abstract: This Letter brings together two topics that, until now, have been the focus of intense but non-overlapping research efforts. The first concerns high harmonic generation in solids, which occurs when intense light field excites highly non-equilibrium electronic response in a semiconductor or a dielectric. The second concerns many-body dynamics in strongly correlated systems such as the Mott insulator. Here we show that high harmonic generation can be used to time-resolve ultrafast many-body dynamics associated with optically driven phase transition, with accuracy far exceeding one cycle of the driving light field. Our work paves the way for time-resolving highly non-equilibrium many body dynamics in strongly correlated systems, with few femtosecond accuracy.

Generation of microjoule pulses in the deep ultraviolet at megahertz repetition rates

Abstract: Although ultraviolet (UV) light is important in many areas of science and technology, there are very few if any lasers capable of delivering wavelength-tunable ultrashort UV pulses at high repetition rates. Here we report the generation of deep UV laser pulses at megahertz repetition rates and microjoule energies by means of dispersive wave (DW) emission from self-compressed solitons in gas-filled single-ring hollow-core photonic crystal fiber (SR-PCF). Pulses from an ytterbium fiber laser (∼300 fs) are first compressed to <25 fs in a SR-PCF-based nonlinear compression stage and subsequently used to pump a second SR-PCF stage for broadband DW generation in the deep UV. The UV wavelength is tunable by selecting the gas species and the pressure. Through rigorous optimization of the system, in particular employing a large-core fiber filled with light noble gases, we achieve 1 μJ pulse energies in the deep UV, which is more than 10 times higher, at average powers more than four orders of magnitude greater (reaching 1 W) than previously demonstrated, with only 20 μJ pulses from the pump laser.

Wannier-bloch approach to localization in high-harmonics generation in solids

Abstract: High harmonic generation can produce attosecond-long pulses of light, which are a useful probe of physical processes that require extremely high time resolution. A new mathematical analysis shows how electron delocalization contributes to this emission in a solid.

The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor

Abstract: High-harmonic generation from gases produces attosecond bursts and enables high-harmonic spectroscopy to explore electron dynamics in atoms and molecules. Recently, high-harmonic generation from solids has been reported, resulting in novel phenomena and unique control of the emission, absent in gas-phase media. Here we investigate high harmonics from semiconductors with controllable induced photo-carrier densities, as well as the driving wavelengths. We demonstrate that the dominant generation mechanism can be identified by monitoring the variation of the harmonic spectra with the carrier density. Moreover, the harmonic spectral dependence on the driving wavelength is reported and a different dependence from the well-known one in gas-phase media is observed. Our study provides distinct control of the harmonic process from semiconductors, sheds light on the underlying mechanism and helps optimize the harmonic properties for future solid-state attosecond light sources.

Coherent diffractive imaging of single helium nanodroplets with a high harmonic generation source

Abstract: Coherent diffractive imaging of individual free nanoparticles has opened routes for the in situ analysis of their transient structural, optical, and electronic properties. So far, single-shot single-particle diffraction was assumed to be feasible only at extreme ultraviolet and X-ray free-electron lasers, restricting this research field to large-scale facilities. Here we demonstrate single-shot imaging of isolated helium nanodroplets using extreme ultraviolet pulses from a femtosecond-laser-driven high harmonic source. We obtain bright wide-angle scattering patterns, that allow us to uniquely identify hitherto unresolved prolate shapes of superfluid helium droplets. Our results mark the advent of single-shot gas-phase nanoscopy with lab-based short-wavelength pulses and pave the way to ultrafast coherent diffractive imaging with phase-controlled multicolor fields and attosecond pulses.Diffraction imaging studies of free individual nanoparticles have so far been restricted to XUV and X-ray free - electron laser facilities. Here the authors demonstrate the possibility of using table-top XUV laser sources to image prolate shapes of superfluid helium droplets.

Large second harmonic generation enhancement in Si3N4 waveguides by all-optically induced quasi-phase-matching.

Abstract: Efficient second harmonic generation in integrated platforms is usually achieved by resonant structures, intermodal phase-matching or quasi-phase matching by periodically poling ferroelectric waveguides. However, in all these structures, it is impossible to reconfigure the phase-matching condition in an all-optical way. Here, we demonstrate that a Watt-level laser causes a periodic modification of the second-order susceptibility in a silicon nitride waveguide, allowing for quasi-phase-matching between the pump and second harmonic modes for arbitrary wavelengths inside the erbium band. The grating is long-term inscribed, and leads to a second harmonic generation enhancement of more than 30 dB. We estimate a χ (2) on the order of 0.3 pm/V, with a maximum conversion efficiency of 0.05% W−1. We explain the observed phenomenon with the coherent photogalvanic effect model, which correctly agrees with the retrieved experimental parameters. Phase-matching and quasi-phase-matching in periodically poled ferroelectrics ensure efficient harmonic generation, but only statically. Here, Billat et al. demonstrate all-optically reconfigurable second harmonic generation by inscribing a stable grating in CMOS-compatible nonlinear waveguides.

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids.

Abstract: We introduce a quasi-classical model in the k space combined with the energy band structure of solids to understand the mechanisms of high-order harmonic generation (HHG) process occurring in a subcycle timescale. This model interprets the multiple plateau structure in HHG spectra well and the linear dependence of cutoff energies on the amplitude of vector potential A0 of the laser fields. It also predicts the emission time of HHG, which agrees well with the results by solving the time-dependent Schrodinger equation (TDSE). It provides a scheme to reconstruct the energy dispersion relations in Brillouin zone and to control the trajectories of HHG by varying the shape of laser pulses. This model is instructive for experimental measurements.