High harmonic generation (HHG) in solids could enable attosecond and ultraviolet light sources with high compactness, great controllability and rich functions. However, the HHG process is accompanied by a quite large wavevector mismatch that is uncompensated by any traditional phase-matching method, directly limiting its energy conversion efficiency. Here, we propose an effective strategy for phase-matching of HHG with arbitrary harmonic orders in solids. Two flakes of solids with an interlayer twist induce a nonlinear optical phase that depends on the crystal symmetry, twist angle and harmonic order, which can be accurately designed to compensate for the phase mismatch in HHG. Guided by the twist-phase-matching theory, we achieved a record-high conversion efficiency of $~1.5\times10^{-5}$ for the fifth HHG in twisted hexagonal boron nitride crystals with a total thickness of only 1 $μm$. Our work establishes a foundation for developing ultrashort-wavelength and ultrafast-pulse laser sources in compact solid-state tabletop systems for fundamental and applied sciences.
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…
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…
Bicircular twisted Laguerre-Gaussian beams possess a definite torus knot angular momentum (TKAM) as a new form of angular momentum. TKAM is conserved in nonlinear atomic processes such as high harmonic generation and can be classified by a time delay parameter $τ$ and a coordination parameter $γ$. These parameters are defined by the respective projected orbital angular momentum and the energy of the two superimposed Laguerre-Gaussian beams. We derive a consistent geometric method to determine $τ$ and $γ$ from the driving beam as well as from the high harmonic radiation. This method relates bot…
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…
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…
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 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 classif…
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…
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…
Mechanisms of high-harmonic generation from crystals are described by treating the electric field of a laser as a quasi-static strong field. Under the quasi-static electric field, electrons in periodic potentials form dressed states, known as Wannier-Stark states. The energy differences between the dressed states determine the frequencies of the radiation. The radiation yield is determined by the magnitudes of the inter-band and intra-band current matrix elements between the dressed states. The generation of attosecond pulses from solids is predicted. Ramifications for strong-field physics are…
We extend the semi-classical trajectory description for the high-order harmonic generation~(HHG) from solids by integrating the effect of electron-scattering. Comparing the extended semi-classical trajectory model with a one-dimensional quantum mechanical simulation, we find that the multi-plateau feature of the HHG spectrum is formed by Umklapp scattering under the electron-hole acceleration dynamics by laser fields. Furthermore, by tracing the scattered trajectories in real-space, the model fairly describes the emitted photon energy and the emission timing of the HHG even in the higher plate…
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.
Probing lattice fluctuations using solid-state high-harmonic spectroscopy
Purdue University（普渡大学）；Louisiana State University（路易斯安那州立大学）；Columbia University（哥伦比亚大学）；Argonne National Laboratory（阿贡国家实验室）；Binghamton University（宾厄姆顿大学）
We theoretically investigated the dependence of higher-order harmonic generation (HHG) in solid-state materials on the ellipticity of the electric field. We found that in the multiphoton absorption and ac Zener regimes, the intensity of HHG monotonically decreases with increasing ellipticity of the incident electric field, while in the semimetal regime, the intensity reaches a maximum for finite values of ellipticity. Moreover, the characteristics of the polarization of the emitted HHG change depending on the field intensity; only parallel emissions with respect to the major axis exist in the …
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 …
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…
We establish time-resolved high harmonic generation (tr-HHG) as a powerful spectroscopy for photoinduced dynamics in strongly correlated materials through a detailed investigation of the insulator-to-metal transitions in vanadium dioxide. We benchmark our technique by comparing our measurements to established momentum-resolved ultrafast electron diffraction, and theoretical density functional calculations. Tr-HHG allows distinguishing of individual dynamic channels, including a transition to a thermodynamically hidden phase. In addition, the HHG yield is shown to be modulated at a frequency ch…
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…
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）
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…
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.
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.
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 theoretically demonstrate for the first time that a single free electron in circular/spiral motion emits twisted photons carrying well defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of l-th harmonic carry lhbar total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and more ubiquitous in laboratories and in nature than ever been thought.
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…
Real-space picture of electron recollision with the parent ion guides our understanding of the highly nonlinear response of atoms and molecules to intense low-frequency laser fields. It is also among several leading contestants for the dominant mechanism of high harmonic generation (HHG) in solids, where it is typically viewed in the momentum space, as the recombination of the conduction band electron with the valence band hole, competing with another HHG mechanism, the strong-field driven Bloch oscillations. In this work, we use numerical simulations to directly test and confirm the real-spac…
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）
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…
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…
We investigate high-order harmonic generation in a solid, modeled as a multi-level 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 [Ndabashimiye {\it et al.}, Nature 534, 520 (2016)]. We also sho…
The polarization matrix ($2\times2$) obtained from two component eigen-spinors of spherical harmonics help us to evaluate the differential matrix $N$ of the anisotropic optical medium. The geometric phase is realized through {\it helicity} of photon, assuming the transmission of polarized light through the crystal which has been twisted about the normal to its surface over a closed path.
Focusing on the twist angle for the minimal commensurate structure, we perform nonperturbative calculations of electron dynamics in the twisted bilayer graphene (TBG) under intense laser fields. We show that the TBG exhibits enriched high-harmonic generation that cannot occur in monolayer or conventional bilayers. We elucidate the mechanism of these nonlinear responses by analyzing dynamical symmetries, momentum-resolved dynamics, and roles of interlayer coupling. Our results imply nonlinear "optotwistronics," or controlling optical properties of layered materials by artificial twists.
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 …
