High-harmonic Generation In Solids Research Articles

Wavelike dynamics for high harmonic generation in solids

Wavelike dynamics for high harmonic generation in solids

UV-induced resonant excitations of electrons near the Brillouin zone boundary in solid high harmonic generation

Abstract We propose a novel mechanism to manipulate the electron dynamics at the boundary of the Brillouin zone (BZ) through resonant excitation induced by ultraviolet (UV) laser pulses in solid high harmonic generation (HHG). When adding weak UV pulses to a stronger mid-infrared (MIR) driving field, we show that UV pulses with specific wavelengths generate a resonant excitation zone around the Γ point in k − space, which facilitates the interband transition of electrons in the BZ boundary region. The scheme is not only significant for achieving higher harmonic yield, but also exhibits strong robustness at a relatively low MIR driving intensity due to the inherent manipulation of UV pulses for interband dynamics of BZ boundary electrons. The semiclassical four-step model is adopted to elucidate underlying physics.

Orbital perspective on high-harmonic generation from solids

High-harmonic generation in solids allows probing and controlling electron dynamics in crystals on few femtosecond timescales, paving the way to lightwave electronics. In the spatial domain, recent advances in the real-space interpretation of high-harmonic emission in solids allows imaging the field-free, static, potential of the valence electrons with picometer resolution. The combination of such extreme spatial and temporal resolutions to measure and control strong-field dynamics in solids at the atomic scale is poised to unlock a new frontier of lightwave electronics. Here, we report a strong intensity-dependent anisotropy in the high-harmonic generation from ReS2 that we attribute to angle-dependent interference of currents from the different atoms in the unit cell. Furthermore, we demonstrate how the laser parameters control the relative contribution of these atoms to the high-harmonic emission. Our findings provide an unprecedented atomic perspective on strong-field dynamics in crystals, revealing key factors to consider in the route towards developing efficient harmonic emitters.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses.

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

The defect-state-assisted enhancement of high harmonic generation in bulk ZnO

Optical modulation of high harmonic generation (HHG) at ultrashort timescales is of fundamental interest and central importance for emerging photonic applications. Traditionally, this modulation is realized by injecting incoherent electrons into the conduction band, which can only result in the suppression of HHG intensity. In this work, we have proposed and demonstrated an all-optical route to amplify a specific order of high harmonic generation in (11-20)-cut wurtzite zinc oxide (ZnO) based on the pump-probe configuration. Specifically, intensity enhancement is demonstrated by tuning the wavelength of the generation middle-infrared pulse when the wavelength of HHG matches the energy of a specific defect state. The maximum enhancement factor is observed to be 1.8, while the modulation speed varies with different defect states, which are 0.1 ps for the 5th HHG and 1.5 ps for the 4th HHG. This work might enlighten a new path for ultrafast modulation of HHG in solids for the future development of all-optical devices.

Characterizing Anomalous High-Harmonic Generation in Solids.

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, originating from a Berry-curvature-induced perpendicular anomalous current. The observation of pure anomalous harmonics is, however, often prohibited by contamination from harmonics stemming from interband coherences. Here, we fully characterize the anomalous HHG mechanism, via development of an abinitio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two unique properties of the anomalous harmonic yields: an overall yield increase with laser wavelength; and pronounced minima at certain laser wavelengths and laser intensities around which the spectral phases drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from competing HHG mechanisms, and thus pave the way for the experimental identification and time-domain control of pure anomalous harmonics, as well as reconstruction of Berry curvatures.

High harmonic generation in solids: Real versus virtual transition channels

A closed-form formalism for modeling high harmonic generation (HHG) in solids is derived; its validity is tested for one-dimensional two-band inversion symmetric model solids; excellent agreement with the exact von Neumann equation is found. From the closed-form expressions, a diagnostic method is developed that allows one to separate resonant from nonresonant processes in nonlinear optics. This opens a deeper view into the dominant laser- and material-dependent mechanisms of high harmonic generation in solids. Midinfrared-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, comparison to experiments indicates the potential importance of little-explored processes, such as dephasing of the strong-field dynamics from coupling to the many-body environment of solids.

Dual-Wavelength Spectrum-Shaped Mid-Infrared Pulses and Steering High-Harmonic Generation in Solids

Mid-infrared (MIR) ultra-short pulses with multiple spectral-band coverage and good freedom in spectral and temporal shaping are desired by broad applications such as steering strong-field ionization, investigating bound-electron dynamics, and minimally invasive tissue ablation. However, the existing methods of light transient generation lack freedom in spectral tuning and require sophisticated apparatus for complicated phase and noise control. Here, with both numerical analysis and experimental demonstration, we report the first attempt, to the best our knowledge, at generating MIR pulses with dual-wavelength spectral shaping and exceptional freedom of tunability in both the lasing wavelength and relative spectral amplitudes, based on a relatively simple and compact apparatus compared to traditional pulse synthesizers. The proof-of-concept demonstration in steering the high-harmonic generation in a polycrystalline ZnSe plate is facilitated by dual-wavelength MIR pulses shaped in both spectral and temporal domains, spanning from 5.6 to 11.4 μm, with multi-microjoule pulse energy and hundred- milliwatt average power. Multisets of harmonics corresponding to different fundamental wavelengths are simultaneously generated in the deep ultraviolet region, and both the relative strength of individual harmonics sets and the spectral shapes of harmonics are harnessed with remarkable freedom and flexibility. This work would open new possibilities in exploring femtosecond control of electron dynamics and light–matter interaction in composite molecular systems.

Polarization spectroscopy of high-order harmonic generation in gallium arsenide.

An interesting property of high harmonic generation in solids is its laser polarization dependent nature which in turn provides information about the crystal and band structure of the generation medium. Here we report on the linear polarization dependence of high-order harmonic generation from a gallium arsenide crystal. Interestingly, we observe a significant evolution of the anisotropic response of above bandgap harmonics as a function of the laser intensity. We attribute this change to fundamental microscopic effects of the emission process comprising a competition between intraband and interband dynamics. This intensity dependence of the anisotropic nature of the generation process offers the possibility to drive and control the electron current along preferred directions of the crystal, and could serve as a switching technique in an integrated all-solid-state petahertz optoelectronic device.

Multiband Dynamics of Extended Harmonic Generation in Solids under Ultraviolet Injection

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 second region is emitted through ‘general’ trajectory, where electrons tunneling earlier and recombining earlier contribute significantly. The novel characteristics deepen the understanding of high harmonic generation in solids and may have great significance in attosecond science and reconstruction of band dispersion beyond the band edge.

Inline amplification of mid-infrared intrapulse difference frequency generation.

We demonstrate an ultrafast mid-infrared source architecture that implements both intrapulse difference frequency generation (iDFG) and further optical parametric amplification (OPA), in an all-inline configuration. The source is driven by a nonlinearly compressed high-energy Yb-doped-fiber amplifier delivering 7.4 fs pulses at a central wavelength of 1030 nm, at a repetition rate of 250 kHz. It delivers 1 µJ, 73 fs pulses at a central wavelength of 8 µm, tunable over more than one octave. By enrolling all the pump photons in the iDFG process and recycling the long wavelength pump photons amplified in the iDFG in the subsequent OPA, we obtain an unprecedented overall optical efficiency of 2%. These performances, combining high energy and repetition rate in a very simple all-inline setup, make this technique ideally suited for a growing number of applications, such as high harmonic generation in solids or two-dimensional infrared spectroscopy experiments.

Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids

Since the discovery of high-order harmonic generation (HHG) in solids, much effort has been devoted to understanding its generation mechanism and both interband and intraband transitions are known to be essential. However, intraband transitions are affected by the electronic structure of a solid, and how they contribute to nonlinear carrier generation and HHG remains an open question. Here, we use mid-infrared laser pulses to study HHG in CdSe and CdS quantum dots (QDs), where quantum confinement can be used to control the intraband transitions. We find that both the HHG intensity per excited volume and the generated carrier density increase when the average QD size is increased from about 2 nm to 3 nm. We show that the reduction of the subband gap energy in larger QDs enhances intraband transitions, and this in turn increases the rate of photocarrier injection by coupling with interband transitions, resulting in enhanced HHG.

Parameter sensitivities in tilted-pulse-front based terahertz setups and their implications for high-energy terahertz source design and optimization.

Despite the popularity and ubiquity of the tilted-pulse-front technique for single-cycle terahertz (THz) pulse generation, there is a deficit of experimental studies comprehensively mapping out the dependence of the performance on key setup parameters. The most critical parameters include the pulse-front tilt, the effective length of the pump pulse propagation within the crystal as well as effective length over which the THz beam interacts with the pump before it spatially walks off. Therefore, we investigate the impact of these parameters on the conversion efficiency and the shape of the THz beam via systematically scanning the 5D parameter space spanned by pump fluence, pulse-front-tilt, crystal-position (2D), and the pump size experimentally. We verify predictions so far only made by theory regarding the optimum interaction lengths and map out the impact of cascading on the THz radiation generation process. Furthermore, distortions imposed on the spatial THz beam profile for larger than optimum interaction lengths are observed. Finally, we identify the most sensitive parameters and, based on our findings, propose a robust optimization strategy for tilted-pulse-front THz setups. These findings are relevant for all THz strong-field applications in high demand of robust high-energy table-top single-cycle THz sources such as THz plasmonics, high-harmonic generation in solids as well as novel particle accelerators and beam manipulators.

Visualization of the Preacceleration Process for High-Harmonic Generation in Solids

The high-order harmonic generation (HHG) in ZnO is investigated by numerically solving semiconductor Bloch equations (SBEs), which can be explained well by a four-step model. In this model, preacceleration is the first step, in which the electron is accelerated in the valence band until it reaches the point of the minimum band gap. To prove the existence of the preacceleration process, SBE-based k-resolved harmonic spectra and the transient conduction-band population are presented. The results show that the contribution of crystal-momentum channels away from the minimum band gap via preacceleration is non-negligible. Furthermore, the X-shaped distribution in the k-resolved spectra can be described well by the preacceleration process. Based on the above analysis, we can conclude that the preacceleration process plays an important role in HHG.

Demonstration of nonperturbative and perturbative third-harmonic generation in MgO by altering the electronic structure

The surge of interest in nonperturbative high-harmonic generation in solids has been driven by the appeal of compact solid-state extreme ultraviolet sources and the prospect of untangling the material properties through high-harmonic generation response to strong fields. The traditional assumption is that the brighter, lower-order harmonics are purely perturbative in nature. However, the border between the perturbative and nonperturbative regimes often remains unclear. Here, we show that third-harmonic generation (THG) using 800-nm, 40-fs pulses displays a nonperturbative response in a wide-band-gap insulator MgO. Furthermore, we show that with the introduction of dopants, the nonperturbative THG reverts to the perturbative behavior. We attribute this to the blocking of intraband oscillations and the increased linear absorption pathways introduced by the dopant energy levels.

Optimal generation of delay-controlled few-cycle pulses for high harmonic generation in solids

Delay-controlled two-color, few-cycle pulses are powerful tools for ultrafast nonlinear optics. In this Letter, 35-fs, 800 nm pulses were injected into a noble-gas-filled hollow-core fiber to obtain over-octave spectra (450–1000 nm) and were divided into two parts for dispersion management by a Mach–Zehnder–type interferometer. Two few-cycle pulses with pulse widths of 9.3 and 4.5 fs were generated in the long-wavelength side and the short-wavelength side, respectively. The temporal profiles were measured as the function of the different delay between the two pulses. The shortest 3.6 fs, 0.75 mJ near-single-cycle pulses were synthesized at an optimal delay. The delay-controlled high-harmonic generation in MgO was experimentally demonstrated leading to twofold enhancement of high-order harmonic (HH) yields at 10.3 eV and the extension of HH frequency under time-delay modulation. This method provides an extensive way for manipulating delay-controlled multi-color pulses, which can be used for controlling ionization dynamics in extreme nonlinear optics. We believe that it will be a powerful tool for ultrafast science.

Sub-50 fs pulses at 2050 nm from a picosecond Ho:YLF laser using a two-stage Kagome-fiber-based compressor

The high-energy few-cycle mid-infrared laser pulse beyond 2 μm is of immense importance for attosecond science and strong-field physics. However, the limited gain bandwidth of laser crystals such as Ho:YLF and Ho:YAG allows the generation of picosecond (ps) long pulses and, hence, makes it challenging to generate few-cycle pulse at 2 μm without utilizing an optical parametric chirped-pulse amplifier (OPCPA). Moreover, the exclusive use of the near-infrared wavelength has limited the generation of wavelengths beyond 4 μm (OPCPA). Furthermore, high harmonic generation (HHG) conversion efficiency reduces dramatically when driven by a long-wavelength laser. Novel schemes such as multi-color HHG have been proposed to enhance the harmonic flux. Therefore, it is highly desirable to generate few-cycle to femtosecond pulses from a 2 μm laser for driving these experiments. Here, we utilize two-stage nonlinear spectral broadening and pulse compression based on the Kagome-type hollow-core photonic crystal fiber (HC-PCF) to compress few-ps pulses to sub-50 fs from a Ho:YLF amplifier at 2 μm at 1 kHz repetition rate. We demonstrate both experimentally and numerically the compression of 3.3 ps at 140 μJ pulses to 48 fs at 11 μJ with focal intensity reaching 10 13 W / cm 2 . Thereby, this system can be used for driving HHG in solids at 2 μm. In the first stage, the pulses are spectrally broadened in Kagome fiber and compressed in a silicon-based prism compressor to 285 fs at a pulse energy of 90 μJ. In the second stage, the 285 fs pulse is self-compressed in air-filled HC-PCF. With fine-tuning of the group delay dispersion (GDD) externally in a 3 mm window, a compressed pulse of 48 fs is achieved. This leads to a 70-fold compression of the ps pulses at 2050 nm. We further used the sub-50 fs laser pulses to generate white light by focusing the pulse into a thin medium of YAG.

Introduction to theory of high-harmonic generation in solids: tutorial

High-harmonic generation (HHG) in solids has emerged in recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter and the atomic, molecular, and optics communities. It has exciting prospects for the engineering of new light sources and the probing of ultrafast carrier dynamics in solids, and the theoretical understanding of this process is of fundamental importance. This tutorial provides a hands-on introduction to the theoretical description of the strong-field laser–matter interactions in a condensed-phase system that give rise to HHG. We provide an overview ranging from a detailed description of different approaches to calculating the microscopic dynamics and how these are intricately connected to the description of the crystal structure, through the conceptual understanding of HHG in solids as supported by the semiclassical recollision model. Finally, we offer a brief description of how to calculate the macroscopic response. We also give a general introduction to the Berry phase, and we discuss important subtleties in the modeling of HHG, such as the choice of structure and laser gauges, and the construction of a smooth and periodic structure gauge for both nondegenerate and degenerate bands. The advantages and drawbacks of different structure and laser-gauge choices are discussed, both in terms of their ability to address specific questions and in terms of their numerical feasibility.

Huygens-Fresnel Picture for High Harmonic Generation in Solids.

High harmonic generation (HHG) is usually described by the laser-induced recollision of particlelike electrons, which lies at the heart of attosecond physics and also inspires numerous attosecond spectroscopic methods. Here, we demonstrate that the wavelike behavior of electrons plays an important role in solid HHG. By taking an analogy to the Huygens-Fresnel principle, an electron wave perspective on solid HHG is proposed by using the wavelet stationary-phase method. From this perspective, we have explained the deviation between the cutoff law predicted by the particlelike recollision model and the numerical simulation of semiconductor Bloch equations. Moreover, the emission times of HHG can be well predicted with our method involving the wave property of electrons. However, in contrast, the prediction with the particlelike recollision model shows obvious deviations compared to the semiconductor Bloch equations simulation. The wavelike properties of the electron motion can also be revealed by the HHG in a two-color field.

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.