Solid-state High-harmonic Generation Research Articles

Ultrafast dephasing in solid-state high harmonic generation: macroscopic origin revealed by real-space dynamics [Invited

Using a fully real-space perspective on high harmonic generation (HHG) in solids, we examine the relationship between microscopic response, macroscopic propagation of this response to the far-field, and the extremely short dephasing times routinely used in the theoretical simulations of experimentally measured solid-state HHG spectra. We find that far-field propagation naturally reduces the contribution to the observed HHG emission from electrons that do not return to the lattice site where they have been injected into the conduction band. We then show that extremely short dephasing times routinely used in microscopic simulations suppress many electron trajectories that contribute to the far-field spectra, leading to significant distortions of the true high harmonic response. We show that a real-space based dephasing mechanism, which preferentially suppresses trajectories that veer too far away from their original lattice site, yields HHG spectra that faithfully retain those trajectories that contribute to the far-field spectra while filtering out those that do not, already at the microscopic level. Our findings emphasize the similarities between atomic and solid-state HHG by highlighting the importance of the intensity-dependent phase of HHG emission and address the longstanding issue regarding the origin of extremely short dephasing times in solid-state HHG.

Sample-orientation effects in solid-state high-harmonic generation: computational study of GaAs

We report on a large-scale simulation study of the sample-orientation effects in solid-state high-harmonic generation, utilizing a fully three-dimensional GaAs model in conjunction with a solver for semiconductor Bloch equations that faithfully reflects the material symmetry and accounts for the optical response from the entire Brillouin zone. The simulations, qualitatively compared to two sets of independent measurements, demonstrate that the orientation-resolved high-harmonic spectra represent an effective tool for rigorous testing of material models. The results are relevant for the future development of all-optical reconstruction of electronic band-structure from the solid-state high-harmonic generation measurements.

A solid-state high harmonic generation spectrometer with cryogenic cooling.

Solid-state high harmonic generation (sHHG) spectroscopy is a promising technique for studying electronic structure, symmetry, and dynamics in condensed matter systems. Here, we report on the implementation of an advanced sHHG spectrometer based on a vacuum chamber and closed-cycle helium cryostat. Using an in situ temperature probe, it is demonstrated that the sample interaction region retains cryogenic temperature during the application of high-intensity femtosecond laser pulses that generate high harmonics. The presented implementation opens the door for temperature-dependent sHHG measurements down to a few Kelvin, which makes sHHG spectroscopy a new tool for studying phases of matter that emerge at low temperatures, which is particularly interesting for highly correlated materials.

Solid-state high harmonic spectroscopy for all-optical band structure probing of high-pressure quantum states

High pressure has triggered various novel states/properties in condensed matter, as the most representative and dramatic example being near-room-temperature superconductivity in highly pressured hydrides (~200 GPa). However, the mechanism of superconductivity is not confirmed, due to the lacking of effective approach to probe the electronic band structure under such high pressures. Here, we theoretically propose that the band structure and electron-phonon coupling (EPC) of high-pressure quantum states can be probed by solid-state high harmonic generation (sHHG). This strategy is investigated in high-pressure Im-3m H3S by the state-of-the-art first-principles time-dependent density-functional theory simulations, where the sHHG is revealed to be strongly dependent on the electronic structures and EPC. The dispersion of multiple bands near the Fermi level is effectively retrieved along different momentum directions. Our study provides unique insights into the potential all-optical route for band structure and EPC probing of high-pressure quantum states, which is expected to be helpful for the experimental exploration of high-pressure superconductivity in the future.

Transient High-Harmonic Spectroscopy in an Inorganic-Organic Lead Halide Perovskite.

High-harmonic generation is the frequency upconversion of an intense femtosecond infrared laser in a material. In condensed-phase high-harmonic generation, laser-driven currents of coherently excited charge carriers map the electronic structure onto the emitted light. This promises a thus far scarcely explored potential of condensed-phase time-resolved high-harmonic spectroscopy for probing carrier dynamics. Here, we realize this potential and use time-resolved solid-state high-harmonic spectroscopy from a laser-excited methylammonium lead bromide (MAPbBr3) thin film, a key material in perovskite solar cells, for measuring carrier cooling and relaxation on femto- and picosecond time scales. Through comparison with transient absorption, we show the links between carrier dynamics and experimental observables of generated harmonics. By highlighting and understanding the interplay of these dynamics, we demonstrate transient optical control over the emission of solid-state high-harmonic generation in MAPbBr3.

Revealing the nonadiabatic tunneling dynamics in solid-state high harmonic generation

Revealing the nonadiabatic tunneling dynamics in solid-state high harmonic generation

Control of the electron dynamics in solid-state high harmonic generation on ultrafast time scales by a polarization-skewed laser pulse.

Since high-order harmonic generation (HHG) from atoms depends sensitively on the polarization of the driving laser field, the polarization gating (PG) technique was developed and applied successfully to generate isolated attosecond pulses from atomic gases. The situation is, however, different in solid-state systems as it has been demonstrated that due to collisions with neighboring atomic cores of the crystal lattice strong HHG can be generated even by elliptically- and circularly-polarized laser fields. Here we apply PG to solid-state systems and find that the conventional PG technique is inefficient for the generation of isolated ultrashort harmonic pulse bursts. In contrast, we demonstrate that a polarization-skewed laser pulse is able to confine the harmonic emission to a time window of less than one-tenth of the laser cycle. This method provides a novel way to control HHG and to generate isolated attosecond pulses in solids.

High-sensitivity frequency comb carrier-envelope-phase metrology in solid state high harmonic generation

Non-perturbative and phase-sensitive light–matter interactions have led to the generation of attosecond pulses of light and the control of electrical currents on the same time scale. 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 pulse energy frequency combs that we combine with high-sensitivity demodulation techniques to measure harmonic spectral modulations. Central to this advance is the use of a scalable 100 MHz erbium-fiber frequency comb at 1550 nm to produce 12 nJ, 20 fs pulses that are focused to the T W / c m 2 level. In a single pass through a 500 µm ZnO crystal, this yields harmonic spectra extending down to 200 nm. With this system, we introduce a technique of carrier-envelope amplitude modulation spectroscopy (CAMS) and use it to characterize the phase-sensitive modulation of the ultraviolet harmonics with an 85 dB signal-to-noise ratio. We further verify the non-perturbative nature of the harmonic generation through polarization gating of the driving pulse to increase the effects of the carrier-envelope phase. This work demonstrates robust and ultra-sensitive methods for generating and characterizing harmonic generation at 100 MHz rates that should provide advantages in the study of attosecond nonlinear processes in solid state systems. Additionally, as a simple and low-noise frequency comb, this broadband source will be useful for precision dual-comb spectroscopy of a range of physical systems across the ultraviolet and visible spectral regions (200–650 nm).

Extended high-harmonic spectra through a cascade resonance in confined quantum systems

The study of high-harmonic generation in confined quantum systems is vital to establishing a complete physical picture of harmonic generation from atoms and molecules to bulk solids. Based on a multilevel approach, we demonstrate how intraband resonances significantly influence the harmonic spectra via charge pumping to the higher subbands and, thus, redefine the cutoff laws. As a proof of principle, we consider the interaction of graphene nanoribbons, with zigzag as well as armchair terminations, and resonant fields polarized along the cross-ribbon direction. Here, this effect is particularly prominent due to many nearly equi-separated energy levels. In such a scenario, a cascade resonance effect can take place in high-harmonic generation when the field strength is above a critical threshold, which is completely different from the harmonic generation mechanism of atoms, molecules and bulk solids. We further discuss the implications not only for other systems in a nanoribbon geometry, but also systems where only a few subbands (energy levels) meet this frequency-matching condition by considering a generalized multilevel Hamiltonian. Our study highlights that cascade resonance bears fundamentally distinct influence on the laws of harmonic generation, specifically the cutoff laws based on laser duration, field strength, and wavelength, thus unraveling new insights in solid-state high-harmonic generation.

Efficient attosecond pulse generation from WS2 semiconductor by tailoring the driving laser pulse

High harmonic generation in semiconductor materials with ultra-short pulses of the femtosecond order provides a promising approach to generate attosecond pulses and control the electron dynamics. In this study, an accurate time dependent density functional theory model describing high-order harmonic generation in WS2 bulk is investigated. The effect of driving laser specifications such as ellipticity and chirp rate on producing attosecond pulse is studied. The results show that using a nonlinearly chirped laser can lead to generation of harmonics up to 50 eV, and consequently, production of an attosecond pulse with duration of 440 as. Moreover, a two-color chirped driving laser is proposed which is capable of increasing harmonics up to 63 eV with a slight decrease in the intensity, and reducing the output attosecond pulse duration to 310 as. Our results offer a valuable route towards development of solid-state high harmonic generation spectroscopy and high-performance attosecond source applications.

Control of high-order harmonic emission in solids via the tailored intraband current

Delocalized Bloch electrons in solids are usually regarded as a kind of representative quantum Fermi gas. To unravel the real-space dynamics of Bloch electrons under a tailoring intraband current, we introduced a quasiparticle picture of a wave packet via superposing the multiple Bloch states within a given crystal-momentum region. We find that temporal characteristics and yield modulation in solid-state high-harmonic generation (HHG) depend sensitively on the crystal-momentum region of generating electron-hole pair. Its mechanism could be clarified by the gradual symmetrization of the time-dependent carrier distribution with the growing tunneling-momentum range. Manipulation of tunneling-momentum range is experimentally feasible via photon-carrier doping of appropriate preexcitation pulse. Finally, we elucidate the role of dephasing in the process of HHG. The scheme of customizing intraband current provides an alternative way to regulate the high-harmonic generation of solids.

Highly efficient ultraviolet high-harmonic generation from epsilon-near-zero indium tin oxide films

High-harmonic generation in the ultraviolet region is promising for wireless technology used for communications and sensing. However, small high-order nonlinear coefficients prevent us from obtaining high conversion efficiency and functional photonic devices. Here, we show highly efficient ultraviolet harmonic generation extending to the fifth order directly from an epsilon-near-zero indium tin oxide (ITO) film. The real part of the annealed ITO films was designed to reach zero around 1050 nm, matching with the central wavelength of an Yb-based fiber laser, and the internal driving electric field was extremely enhanced. A high energy conversion efficiency of 10 − 4 and 10 − 6 for 257.5 nm (fourth-order) and 206 nm (fifth-order) ultraviolet harmonic generation was obtained, which is at least 2 orders of magnitude higher than early reports. Our results demonstrate a new route for overcoming the inefficiency problem and open up the possibilities of compact solid-state high-harmonic generation sources at nanoscale.

Neighboring Atom Collisions in Solid-State High Harmonic Generation

High harmonic generation (HHG) from solids shows great application prospects in compact short-wavelength light sources and as a tool for imaging the dynamics in crystals with subnanometer spatial and attosecond temporal resolution. However, the underlying collision dynamics behind solid HHG is still intensively debated and no direct mapping relationship between the collision dynamics with band structure has been built. Here, we show that the electron and its associated hole can be elastically scattered by neighboring atoms when their wavelength approaches the atomic size. We reveal that the elastic scattering of electron/hole from neighboring atoms can dramatically influence the electron recombination with its left-behind hole, which turns out to be the fundamental reason for the anisotropic interband HHG observed recently in bulk crystals. Our findings link the electron/hole backward scattering with Van Hove singularities and forward scattering with critical lines in the band structure and thus build a clear mapping between the band structure and the harmonic spectrum. Our work provides a unifying picture for several seemingly unrelated experimental observations and theoretical predictions, including the anisotropic harmonic emission in MgO, the atomic-like recollision mechanism of solid HHG, and the delocalization of HHG in ZnO. This strongly improved understanding will pave the way for controlling the solid-state HHG and visualizing the structure-dependent electron dynamics in solids.

Enhanced harmonic generation in gases using an all-dielectric metasurface

Abstract Strong field confinement, long-lifetime resonances, and slow-light effects suggest that metasurfaces are a promising tool for nonlinear optical applications. These nanostructured devices have been utilized for relatively high efficiency solid-state high-harmonic generation platforms, four-wave mixing, and Raman scattering experiments, among others. Here, we report the first all-dielectric metasurface to enhance harmonic generation from a surrounding gas, achieving as much as a factor of 45 increase in the overall yield for Argon atoms. When compared to metal nanostructures, dielectrics are more robust against damage for high power applications such as those using atomic gases. We employ dimerized high-contrast gratings fabricated in silicon-on-insulator that support bound states in the continuum, a resonance feature accessible in broken-symmetry planar devices. Our 1D gratings maintain large mode volumes, overcoming one of the more severe limitations of earlier device designs and greatly contributing to enhanced third- and fifth-harmonic generation. The interaction lengths that can be achieved are also significantly greater than the 10’s of nm to which earlier solid-state designs were restricted. We perform finite-difference time-domain simulations to fully characterize the wavelength, linewidth, mode profile, and polarization dependence of the resonances. Our experiments confirm these predictions and are consistent with other nonlinear optical properties. The tunable wavelength dependence and quality factor control we demonstrate in these devices make them an attractive tool for the next generation of high-harmonic sources, which are anticipated to be pumped at longer wavelengths and with lower peak power, higher repetition rate lasers.

Strong-field-driven dynamics and high-harmonic generation in interacting one dimensional systems

This work explores the interplay of electronic band structure, Coulomb interactions, and optical resonances that triggers high-harmonic generation in condensed matter systems driven by intense and ultrashort optical pulses. The authors results are in qualitative agreement with atomistic simulations of quasi one dimensional carbon nanotubes and provide a roadmap to identify material platforms for solid-state high-harmonic generation

Attosecond spectral singularities in solid-state high-harmonic generation

Strong-field-driven electric currents in condensed-matter systems are opening new frontiers in petahertz electronics. In this regime, new challenges are arising as the roles of band structure and coherent electron–hole dynamics have yet to be resolved. Here, by using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid-state systems. We demonstrate that when the electron–hole relative velocity approaches zero, enhanced constructive interference leads to the appearance of spectral caustics in the high-harmonic generation spectrum. We introduce the role of the dynamical joint density of states and identify its mapping into the spectrum, which exhibits singularities at the spectral caustics. By studying these singularities, we probe the structure of multiple unpopulated high conduction bands. High-harmonic waves are generated from a MgO crystal under experimental conditions where the simple semi-classical analysis fails. High-harmonic generation spectroscopy directly probes the strong-field attosecond dynamics over multiple bands.

固体高次高調波発生の理論と第一原理計算

固体高次高調波発生の理論と第一原理計算

Shaping electron-hole trajectories for solid-state high harmonic generation control.

Solid-state high-harmonic generation (HHG) by an intense infra-red (IR) laser field offers a new route to generate coherent attosecond light pulses in the extreme ultraviolet regime. The propagation of the IR driving field in the dense solid medium is accompanied by non-linear processes which shape the generating waveform. In this work, we introduce a monolithic scheme in which we both exploit the non-linear propagation to manipulate a two color driving field, as well as generate high harmonics within a single crystal. We show that the resulting non-commensurate, bi-chromatic, generating field provides precise control over the periodicity of the HHG process. This control enables us to manipulate the spectral positions of the discrete harmonic peaks. Our method advances solid-state HHG spectroscopy, and offers a simple route towards tunable, robust XUV sources.

Probing the dephasing time of crystals via spectral properties of high-order harmonic generation

Coherent time is a characteristic time in the extreme nonlinear optics regime and thus generally introduced as the dephasing time in the simulations of the solid-state high-harmonic generation. This characteristic time linked with the coherent decay of quantum trajectory controls the emergence of the spectral splittings in the high harmonic spectroscopy, which can been attributed to the temporal interference between two adjacent harmonic emission channels. To reproduce the harmonic peaks and spectral splittings, a temporal two-slit interference model in the momentum space is introduced. In addition, mechanisms of spectral splitting provide a state-of-the-art avenue to probe the characteristic elapse between electron and hole. Based on the subfemtosecond resolution of the spectral interference opening and closing zones in the wavelength-dependent high-order harmonic spectra, we also propose an alternative scheme to probe the dephasing time of crystals by the feasible laser pulses in present experimental setups.

Fiber-amplifier-pumped, 1-MHz, 1-µJ, 2.1-µm, femtosecond OPA with chirped-pulse DFG front-end.

High-repetition-rate, high-power, few-cycle mid-infrared lasers with carrier-envelope phase (CEP) stabilization are ideal driving sources for studying strong-field nonlinear processes, such as strong-field driven electron emission, solid-state high-harmonic generation, and nonlinear microscopy. Here, we report on a 1-MHz, 1-μJ, femtosecond, 2.1-µm optical parametric amplifier (OPA), pumped by a Yb-doped fiber chirped-pulse amplifier (CPA) and seeded by a chirped-pulse difference-frequency generation (DFG) front-end providing positively chirped 2.1-μm signal pulses. The home-built multi-stage 1030-nm Yb-doped fiber CPA pump laser generates >55-μJ near-transform-limited (245-fs) pulses at 1 MHz repetition rate using a novel 4-pass all-fiber stretcher/front-end for careful dispersion/spectral management. The chirped-pulse DFG scheme is achieved by wave-mixing the 1030 nm pump pulse with a dispersive wave at 645-735 nm generated in a photonic crystal fiber, allowing passive CEP stability of the 2.1-µm pulses. The 2.1-μm pulse is amplified to 1 μJ in a two-stage dispersion-managed optical parametric amplifier (OPA) with a pump energy of ~21 μJ resulting in 95-fs pulses with nice beam profile without additional pulse compression. Multi-μJ, sub-30 fs pulses can be obtained at full pump energy and additional dispersion compensation. The fiber-amplifier-based mid-infrared OPA can be directly applied to high-harmonic generation in solids and optical-field-driven nanophotonic devices and is a compact front-end for a future high-power, high-repetition-rate, long wavelengths CEP-stabilized source for gas-phase high-order harmonic generation.