High harmonic generation (HHG) from crystals in strong laser fields has been understood by the band theory of solid, which is based on the periodic boundary condition (PBC) of translational invariant. For systems having PBC of rotational invariant, in principles an analogous Bloch theorem can be developed and applied. Taking a ring-type cluster of cyclo[18]carbon as a representative, we theoretically suggest a quasi-band model and study its HHG by solving time-dependent Liouville-von Neumann equation. Under the irradiation of circularly polarized laser, explicit selection rules for left-handed and right-handed harmonics are observed, while in linearly polarized laser field, cyclo[18]carbon exhibits solid-like HHG originated from intra-band oscillations and inter-band transitions, which in turn is promising to optically detect the symmetry and geometry of controversial structures. In a sense, this work presents a connection linking the high harmonics of gases and solids.
High harmonic generation in solids is becoming an important method for strong field solid state physics research. The power scale relationship between high harmonics and the driving laser is investigated both experimentally and theoretically. Results of the power scale dependence clearly divided the interaction into two regimes. The modification of the bandgap by intense laser proved to be very important for theoretically reproducing the experimental result. Combining with the Keldysh theory analysis, the harmonic generation process is found to be transitioned from multiphoton excitations to t…
High harmonic generation in solids provides us compact and coherent UV sources. Our simulations illustrate abnormal harmonic yield dependence on the intensity of driving or pre-excitation pulses. A multielectron interference model is proposed to reveal the mechanism of the extreme nonlinear optical phenomena. We find that the $k$-resolved intraband harmonic demonstrates different symmetry, phase, and amplitude, which can be observed by using a resonant pre-excitation pulse. The position of the interference minimum obtained by solving the semiconductor Bloch equations agrees well with that obta…
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. Th…
We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectrum in the second or higher plateau is redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase, suggesting the step-by-step excitation process of higher conduction bands in the HHG process. Even order harmonics in the higher plateaus of HHG are present due to the break of symmetry in the k space. It may stimulate related experimental work.
We demonstrate that high-harmonic generation (HHG) in solids dominantly originates from strongly localized surface states through non-perturbative processes. Measurements reveal that HHG from bulk states is suppressed by at least 1-2 orders of magnitude due to the lack of phase matching, when generated perturbatively, or by at least 3-4 orders of magnitude, when generated non-perturbatively. We derive a theory that fully supports this observation and quantitatively describes the generation of harmonics from the surface states as well as from interfaces between solids; it also predicts a much w…
Recent studies have demonstrated that the polarization states of high harmonics from solids can differ from those of the driving pulses. To gain insights on the microscopic origin of this behavior, we perform one-particle intraband-only calculations and reproduce some of the most striking observations. For instance, our calculations yield circularly polarized harmonics from elliptically polarized pulses that sensitively depend on the driving conditions. Furthermore, we perform experiments on ZnS and find partly similar characteristics as reported from silicon. Comparison to our intraband-only …
We report on the realization of a solid-state-based vacuum ultraviolet frequency comb, using multi-harmonic generation in an external enhancement cavity. Optical conversions in such arrangements were so-far reported only using gaseous media. We present a theory that allows selecting the most suited solid generation medium for specific target harmonics by adapting the bandgap of the material. Consequently, we experimentally use a thin AlN film grown on a sapphire substrate to realize a compact frequency comb multi-harmonic source in the DUV/VUV spectral range. Extending our earlier VUV source […
Symmetry breaking by quantum light in solid-state high-harmonic generation
ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科技研究院）；Atominstitut, Technische Universität Wien（原子物理研究所，维也纳工业大学）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文系）；Department of Materials Science and Engineering, Pohang University of Science and Technology（浦项科技大学材料科学与工程系）；Departamento de Física, Área de Física, Universidad de Panamá（巴拿马大学物理系）；Sistema Nacional de Investigación de Panamá（巴拿马国家研究系统）；Centro de Investigación con Técnicas Nucleares, Universidad de Panamá（巴拿马大学核技术研究中心）；Parque Científico y Tecnológico, Universidad Autónoma de Chiriquí（奇里基自治大学科技园）；Eastern Institute of Technology（东方理工学院）
We study numerically the Bloch electron wavepacket dynamics in periodic potentials to simulate laser-solid interactions. We introduce a new perspective in the coordinate space combined with the motion of the Bloch electron wavepackets moving at group and phase velocities under the laser fields. This model interprets the origins of the two contributions (intra- and interband transitions) of the high-order harmonic generation (HHG) by investigating the local and global behavior of the wavepackets. It also elucidates the underlying physical picture of the HHG intensity enhancement by means of car…
High-order harmonic generation (HHG) in isolated atoms and molecules has been widely utilized in extreme ultraviolet (XUV) photonics and attosecond pulse metrology. Recently, HHG has also been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruction of electronic band structures, as well as compact XUV light sources. Previous HHG studies are confined on crystalline solids; therefore decoupling the respective roles of long-range periodicity and high density has been challenging. Here, we report the first observ…
High harmonic generation (HHG) in solid and gaseous targets has been proven to be a powerful avenue for the generation of attosecond pulses, whereas the influence of electron-phonon scattering on HHG is a critical outstanding problem. Here we first introduce a temperature dependent lattice vibration model by characterizing the spacing fluctuation. Our results reveal that (i) structural disorder induced by lattice vibration does not lead to generation of even-order harmonics; (ii) dephasing of HHG occurs as the lattice temperature is growing; (iii) an open-trajectory picture predicts the maxima…
Twisting harmonics: Transfer of orbital angular momentum in solid-state high-harmonic generation
ELI-ALPS, ELI-Hu Non-Profit Ltd.（极端光基础设施激光平台，匈牙利非营利有限公司）；Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学理论物理研究所）；Laboratoire Photonique Numérique et Nanosciences (LP2N), UMR 5298, CNRS-IOGS-Université Bordeaux（数字光子学与纳米科学实验室（LP2N），UMR 5298，法国国家科学研究中心-高等光学学院-波尔多大学）；Centro de Investigaciones en Óptica, A.C.（光学研究中心）；School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology（上海理工大学光电信息与计算机工程学院）；Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic and Information Engineering, School of Engineering, Westlake University（西湖大学工学院电子与信息工程系三维微纳制造与表征浙江省重点实验室）；International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University（广岛大学结型手性超材料可持续国际研究所（WPI-SKCM2））；Helmholtz-Institut Jena（耶拿亥姆霍兹研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（德国重离子研究中心亥姆霍兹有限公司）
High-harmonic generation by a highly non-linear interaction of infrared laser fields with matter allows for the generation of attosecond pulses in the XUV spectral regime. This process, well established for atoms, has been recently extended to the condensed phase. Remarkably well pronounced harmonics up to order ~30 have been observed for dielectrics. We present the first ab-initio multi-scale simulation of solid-state high-harmonic generation. We find that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the…
We investigate the high harmonic generation (HHG) in solids driven by laser fields with different ellipticities. The HHG spectra show a two-plateau structure within the energy gap between the valence band and the first conduction band. These two plateaus depend distinctly on the laser ellipticity. The first plateau is decreased while the second plateau is enhanced with increasing the laser ellipticity. To understand these phenomena, we develop an intuitive Reciprocal-Space- Trajectory (RST) method, with which HHG in solids is explained by a trajectory-ensemble from different initial states and…
Using one-dimensional semiconductor Bloch equations, we investigate the multiband dynamics of electrons in a cutoff extension scheme employing an infrared pulse with additional UV injection. An extended three-step model is firstly validated to play a dominant role in emitting harmonics in the second plateau. Surprisingly, further analysis employing the acceleration theorem shows that though harmonics in both the primary and secondary present positive and negative chirps, the positive (negative) chirp in the first region is related to the so-called short (long) trajectory, while that in the sec…
We revisit the mechanism of high harmonic generation (HHG) from solids by comparing HHG in laser fields with different ellipticities but constant maximum amplitude. It is shown that the cutoff of HHG is strongly extended in a circularly polarized field. Moreover, the harmonic yield with large ellipticity is comparable to or even higher than that in the linearly polarized field. To understand the underlying physics, we develop a reciprocal-space-trajectory method, which explains HHG in solids by a trajectory ensemble from different ionization times and different initial states in the reciprocal…
Field-driven helicity in solid-state high-harmonic generation
Universidad de Panamá（巴拿马大学）；Pohang University of Science and Technology（浦项科技大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；Eastern Institute of Technology（东方理工学院）；Sistema Nacional de Investigación de Panamá（巴拿马国家研究系统）；Centro de Investigación con Técnicas Nucleares, Universidad de Panamá（巴拿马大学核技术研究中心）；Universidad Autónoma de Chiriquí（奇里基自治大学）
We study the role of transition rule in high-order harmonic generation from solids driven by linearly polarized laser elds. The orientation-dependent transition dipoles can regulate the emergence of the multi-plateau structure. In the multi-plateau zone, however, di erent from the mechanisms of step-by-step excitation reported previously, we nd that the emission time and orientationdependent yields exhibit synchronization and more ne patterns, respectively. And the orientationdependent yields and its ne patterns can be attributed to the collective contribution of the transition rule and quantu…
Sculpting ultrafast mid-infrared light for solid-state high harmonic generation
Eastern Institute of Technology（东方理工学院）；ELI-ALPS, ELI-Hu Non-Profit Ltd.（极强光激光科学研究所有限公司）；Laboratoire Photonique Numérique et Nanosciences (LP2N), UMR 5298, CNRS-IOGS-Université Bordeaux（波尔多大学光子学与纳米科学实验室）；Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena（耶拿大学理论物理研究所）；Centro de Investigaciones en Óptica, A.C.（光学研究中心）；School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology（上海理工大学光电信息与计算机工程学院）；Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic and Information Engineering, School of Engineering, Westlake University（西湖大学工学院电子与信息工程系三维微纳加工与表征浙江省重点实验室）；Helmholtz-Institut Jena（耶拿亥姆霍兹研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（达姆施塔特重离子研究中心）
Programmable high-harmonic emission in solids through photon pathways
Advanced Research Center for Nanolithography（先进纳米光刻研究中心）；Max-Born-Institute for Nonlinear Optics and Short Pulse Spectroscopy（马克斯·玻恩非线性光学与超短脉冲光谱研究所）；Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas（马德里材料科学研究所，西班牙高等科学研究委员会）；Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit（自由大学物理与天文系及激光实验室）
Attosecond metrology sensitive to sub-optical-cycle electronic and structural dynamics is opening up new avenues for ultrafast spectroscopy of condensed matter. Using intense lightwaves to precisely control the extremely fast carrier dynamics in crystals holds great promise for next-generation electronics and devices operating at petahertz bandwidth. The carrier dynamics can produce high-order harmonics of the driving light field extending up into the extreme-ultraviolet region. Here, we introduce polarization-state-resolved high-harmonic spectroscopy of solids, which provides deeper insights …
The generation of high-order harmonics in a medium of chiral molecules driven by intense bi-elliptical laser fields can lead to strong chiroptical response in a broad range of harmonic numbers and ellipticities [D. Ayuso et al, J. Phys. B 51, 06LT01 (2018)]. Here we present a comprehensive analytical model that can describe the most relevant features arising in the high-order harmonic spectra of chiral molecules driven by strong bi-elliptical fields. Our model recovers the physical picture underlying chiral high-order harmonic generation based on ultrafast chiral hole motion and identifies the…
Kerr-type nonlinearities form the basis for our physical understanding of nonlinear optical phenomena in condensed matter, such as self-focusing, solitary waves, and wave mixing. In strong fields, they are complemented by higher-order nonlinearities that enable high harmonic generation, which is currently understood as the interplay of light-driven intraband charge dynamics and interband recombination. Remarkably, the nonlinear response emerging from the associated sub-cycle injection dynamics of electrons into the conduction band has been almost completely overlooked in solids and only partia…
State-of-the-art experiments employ strong ultrafast optical fields to study the nonlinear response of electrons in solids on an attosecond time-scale. Notably, a recent experiment retrieved a 3rd order nonlinear susceptibility by comparing the nonlinear response induced by a strong laser field to a linear response induced by the otherwise identical weak field. In parallel, experiments have demonstrated high harmonic generation (HHG) in solids, a highly nonlinear process that until recently had only been observed in gases. The highly nonlinear nature of HHG has the potential to extract even hi…
Transient High-Harmonic Generation from Solids: From Spectroscopy and Control to Programmable Emission
Advanced Research Center for Nanolithography（先进纳米光刻研究中心）；Imaging Physics, Faculty of Applied Sciences, Technische Universiteit Delft（代尔夫特理工大学应用科学学院成像物理）；Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit（阿姆斯特丹自由大学物理与天文学系及激光实验室）
Non-perturbative and phase-sensitive light-matter interactions have led to the generation of attosecond pulses of light and the control electrical currents on the same timescale. Traditionally, probing these effects via high harmonic generation has involved complicated lasers and apparatuses to generate the few-cycle and high peak power pulses needed to obtain and measure spectra that are sensitive to the phase of the light wave. Instead, we show that nonlinear effects dependent on the carrier-envelope phase can be accessed in solid state crystals with simple low-energy frequency combs that we…
Structural chirality plays an important role in solid state physics and leads to a variety of novel physics. The feasibility of probing structural chirality of crystals using high harmonic generation in solids is explored in this work. Through first-principles calculations based on the time-dependent density functional theory framework, we demonstrate that evident circular dichroism (CD) effects can be induced in the high harmonic spectra from a chiral crystal -- bulk tellurium. The CD signal reverses for crystals with opposite structural chirality. Besides, the high harmonic spectroscopy also…
Various interference effects are known to exist in the process of high harmonic generation (HHG) both at the single atom and macroscopic levels. In particular, the quantum path difference between the long and short trajectories of electron excursion causes the HHG yield to experience interference-based temporal and spectral modulations. In solids, due to additional phenomena such as multi-band superposition and crystal symmetry dependency, the HHG mechanism appears to be more complicated than in gaseous atoms in identifying accompanying interference phenomena. Here, we first report experimenta…
We theoretically investigate the spectral caustics of high-order harmonics in solids. We analyze the 1-dimension model of solids HHG and find that, apart from the caustics originated from the van Hove singularities in the energy-band structure, another kind of catastrophe singularities also emerge when the different branches of electron-hole trajectories generating high-order harmonics coalesce into a single branch. We solve time-dependent Schrödinger equation in periodic potential and demonstrate the control of this kind of singularities in HHG with the aids of two-color laser fields. The dif…
Sensing coherent phonon dynamics in solids with delayed even harmonics
Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；School of Nuclear Science and Technology, Lanzhou University（兰州大学核科学与技术学院）；School of Physics, Ningxia University（宁夏大学物理学院）
The long standing issue of separating resonant from non-resonant processes in extreme nonlinear optics is resolved. The theoretical formalism is applied to high harmonic generation (HHG) in solids and reveals a deeper view into the dominant laser and material dependent mechanisms. Mid-infrared driven HHG in semiconductors is dominated by the resonant interband current. As a result of the dynamic Stark shift, virtual processes gain in importance in near-infrared driven HHG in dielectrics. Finally, our analysis identifies limitations of microscopic one-electron-hole theories.
We studied the high-order harmonic generation (HHG) from 2D solid materials in circularly and bichromatic circularly polarized laser fields numerically by simulating the dynamics of single-active-electron processes in 2D periodic potentials. Contrary to the absence of HHG in the atomic case, circular HHGs below the bandgap with different helicities are produced from intraband transitions in solids with $C_4$ symmetry driven by circularly polarized lasers. Harmonics above the bandgap are elliptically polarized due to the interband transitions. High-order elliptically polarized harmonics can be …
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…
An accurate analytic model describing high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that: (i) the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals, (ii) the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential, the yield is increased for heavier atoms, and (iii) the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possibl…
The present work discusses the impact of vacancy defects in solid high-order harmonic generation. The total energy cutoff of the high-order harmonic spectrum increases as a function of concentration of vacancy defects, and the total spectrum gradually turns into a single slanted spectrum without having an abrupt transition between primary and secondary plateaus. The spectral intensity of the below-band-gap harmonics in a solid with vacancy defects is enhanced significantly in comparison to the harmonics in a pristine solid. The changes in the harmonic spectra are understood in terms of their e…
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.
Generation of high-order harmonics in gases enabled to probe the attosecond electron dynamics in atoms and molecules with unprecedented resolution. Extending the techniques developed originally for atomic and molecular gases to solid state materials requires a fundamental understanding of the physics that has been partially addressed theoretically. Here we employ time-dependent density-functional theory to investigate how the electron dynamics resulting in high-harmonic emission in monolayer hexagonal boron nitride is affected by the presence of vacancies. We show how these realistic spin-pola…
