High-harmonic Generation In Solids Research Articles

The influence of resonant light pulses on high harmonic generation in solids

Abstract We have theoretically studied the high harmonic generation (HHG) in solids driven simultaneously by a mid-infrared (MIR) laser and a high-order harmonic pulse with energy around the band gap between the valence band and conduction band. By adding this resonant harmonic light pulse with the relative intensity ratio of 4\%, the high-order harmonic emission from the crystal is enhanced by 1-2 orders of magnitude. The yield of HHG in solid increases monotonically with the relative strength of the resonant harmonic pulses. In addition, we also found that HHG dynamics from the $k$ channel around the boundary of the Brillouin zone can be selectively enhanced by adjusting the frequency of the resonant high-order harmonic pulse. The resonance-enhanced HHG and $k$ channel selection effect in solids is also investigated by using the three-band semi-conductor Bloch equation for HHG in ZnO. We also find that the harmonic in the plateau region driven by adding a resonant light field to the strong MIR driving field has less red-shifted compared with the case driven by the MIR driving field alone.

High-harmonic generation by a bright squeezed vacuum

AbstractHigh-harmonic generation has been driving the development of attosecond science and sources. More recently, high-harmonic generation in solids has been adopted by other communities as a method to study material properties. However, so far high-harmonic generation has only been driven by classical light, despite theoretical proposals to do so with quantum states of light. Here we observe non-perturbative high-harmonic generation in solids driven by a macroscopic quantum state of light, a bright squeezed vacuum, which we generate in a single spatiotemporal mode. The process driven by a bright squeezed vacuum is considerably more efficient in the generation of high harmonics than classical light of the same mean intensity. Due to its broad photon-number distribution, covering states from 0 to 2 × 1013 photons per pulse, and strong subcycle electric field fluctuations, a bright squeezed vacuum gives access to free carrier dynamics within a much broader range of peak intensities than accessible with classical light.

Enhancing the efficiency of high-order harmonics with two-color non-collinear wave mixing in silica

The emission of high-order harmonics from solids under intense laser-pulse irradiation is revolutionizing our understanding of strong-field solid-light interactions, while simultaneously opening avenues towards novel, all-solid, coherent, short-wavelength table-top sources with tailored emission profiles and nanoscale light-field control. To date, broadband spectra in solids have been generated well into the extreme-ultraviolet (XUV), but the comparatively low conversion efficiency in the XUV range achieved under optimal conditions still lags behind gas-based high-harmonic generation (HHG) sources. Here, we demonstrate that two-color high-order harmonic wave mixing in a fused silica solid is more efficient than solid HHG driven by a single color. This finding has significant implications for compact XUV sources where gas-based HHG is not feasible, as solid XUV wave mixing surpasses solid-HHG in performance. Moreover, our results enable utilizing solid high-order harmonic wave mixing as a probe of structure or material dynamics of the generating solid, which will enable reducing measurement times compared to the less efficient regular solid HHG. The emission intensity scaling that follows perturbative optical wave mixing, combined with the angular separation of the emitted frequencies, makes our approach a decisive step for all-solid coherent XUV sources and for studying light-engineered materials.

Bloch-Wave Phase Matching of High Harmonic Generation in Solids.

There has been a longstanding doubt that the conversion efficiency of high harmonics in solids is much lower than expected at such a high level of electron density. To address this issue, we revisit the dynamical process of high harmonic generation (HHG) in solids in terms of wavelet interference. We find that the constructive interference among the wavelets has intrinsic consistency with the phase matching of coupled waves in nonlinear optics, which we call Bloch-wave phase matching. Our analysis indicates that most of the wavelets are out of phase and coherently canceled out during the solid HHG process, leading to only a small fraction of excited electrons effectively contributing to HHG. Consequently, the conversion from the excited electron to HHG is fairly low. Moreover, a Bloch-wave phase-matching scheme is proposed and a nearly 3 orders of magnitude enhancement of solid HHG can be achieved by engineering the crystal structures. Our Letter addresses a longstanding doubt and provides a novel idea and theoretical guidance for realizing efficient all-solid-state tabletop ultraviolet light sources.

Enhanced high harmonic efficiency through phonon-assisted photodoping effect

High-harmonic generation (HHG) has emerged as a central technique in attosecond science and strong-field physics, providing a tool for investigating ultrafast dynamics. However, the microscopic mechanism of HHG in solids is still under debate, and it is unclear how it is modified in the ubiquitous presence of phonons. Here we theoretically investigate the role of collectively coherent vibrations in HHG in a wide range of solids (e.g., hBN, graphite, 2H-MoS2, and diamond). We predict that phonon-assisted high harmonic yields can be significantly enhanced, compared to the phonon-free case – up to a factor of ~20 for a transverse optical phonon in bulk hBN. We also show that the emitted harmonics strongly depend on the character of the pumped vibrational modes. Through state-of-the-art ab initio calculations, we elucidate the physical origin of the HHG yield enhancement – phonon-assisted photoinduced carrier doping, which plays a paramount role in both intraband and interband electron dynamics. Our research illuminates a clear pathway toward comprehending phonon-mediated nonlinear optical processes within materials, offering a powerful tool to deliberately engineer and govern solid-state high harmonics.

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.