Laser waveform control of extreme ultraviolet high harmonics from solids

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.

Analysis on the minimum structure of harmonic spectra from MgO crystals

Recent theoretical and experimental findings have demonstrated the minimum characteristic in the harmonic spectrum of bulk MgO crystals subjected to intense laser pulses. However, the dominant mechanism behind this minimum structure is still under debate. This study simulates the harmonic spectrum from a MgO crystal in a linearly polarized laser pulse by solving multi-band semiconductor Bloch equations. The results show that the minimum feature at 20 eV in the MgO harmonic spectra from 1700 and 800 nm laser pulses is due to band dispersion and interference between interband harmonics. Notably, the disappearance of the minimum structure at 14 eV in the harmonic spectrum from the 800 nm laser is attributed to the intensity suppression of higher energy harmonics, caused by decreased electron population at the boundary of the first Brillouin zone in the multi-band case. These findings offer insights into the spectral structure of solid-state harmonics, contributing to the all-optical reconstruction of the crystal band based on its harmonic spectrum.

High-Harmonic Generation Spectroscopy of Gas-Phase Bromoform

High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.

Observation of interband Berry phase in laser-driven crystals

Ever since its discovery1, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena2. However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

Effect of stacking configuration on high harmonic generation from bilayer hexagonal boron nitride

High harmonic generation from bilayer h-BN materials with different stacking configurations is theoretically investigated by solving the extended multiband semiconductor Bloch equations in strong laser fields. We find that the harmonic intensity of AA'-stacking bilayer h-BN is one order of magnitude higher than that of AA-stacking bilayer h-BN in high energy region. The theoretical analysis shows that with broken mirror symmetry in AA'-stacking, electrons have much more opportunities to transit between each layer. The enhancement in harmonic efficiency originates from additional transition channels of the carriers. Moreover, the harmonic emission can be dynamically manipulated by controlling the carrier envelope phase of the driving laser and the enhanced harmonics can be utilized to achieve single intense attosecond pulse.

Interferometric carrier-envelope phase stabilization for ultrashort pulses in the mid-infrared

We demonstrate an active carrier-envelope phase (CEP) stabilization scheme for optical waveforms generated by difference-frequency mixing of two spectrally detuned and phase-correlated pulses. By performing ellipsometry with spectrally overlapping parts of two co-propagating near-infrared generation pulse trains, we stabilize their relative timing to 18 as. Consequently, we can lock the CEP of the generated mid-infrared (MIR) pulses with a remaining phase jitter below 30 mrad. To validate this technique, we employ these MIR pulses for high-harmonic generation in a bulk semiconductor. Our compact, low-cost, and inherently drift-free concept could bring long-term CEP stability to the broad class of passively phase-locked OPA and OPCPA systems operating in a wide range of spectral windows, pulse energies, and repetition rates.

Review on the Reconstruction of Transition Dipole Moments by Solid Harmonic Spectrum

In the process of intense laser–matter interactions, the transition dipole moment is a basic physical quantity at the core, which is directly related to the internal structure of the solid and dominates the optical properties of the solid in the intense laser field. Therefore, the reconstruction of the transition dipole moment between solid energy bands is extremely important for clarifying the ultrafast dynamics of carriers in the strong and ultrashort laser pulse. In this review, we introduce recent works of reconstructing transition dipole moment in a solid, and the advantages and drawbacks of different works are discussed.

Proposal for High-Energy Cutoff Extension of Optical Harmonics of Solid Materials Using the Example of a One-Dimensional ZnO Crystal

We propose a novel approach based on the subcycle injection of carriers to extend the high-energy cutoff in solid-state high harmonics. The mechanism is first examined by employing the standard single-cell semiconductor Bloch equation (SC SBE) method for one-dimensional (1D) Mathieu potential model for ZnO subjected to the intense linearly polarized midinfrared laser field and extreme-ultraviolet pulse. Then, we use coupled solution of Maxwell propagation equation and SC SBE to propagate the fundamental laser field through the sample, and find that the high-harmonics pulse train from the entrance section of the sample can inject carriers to the conduction bands with attosecond timing, subsequently leading to a dramatic extension of high-energy cutoff in harmonics from the backside. We predict that for a peak intensity at 2×10^{11}  W/cm^{2}, as a result of the self-seeding, the high-energy cutoff shifts from 20th (7.75 eV) order to around 50th (19.38 eV) order harmonics.

Probing phonon dynamics with multidimensional high harmonic carrier-envelope-phase spectroscopy

We explore pump-probe high harmonic generation (HHG) from monolayer hexagonal-boron-nitride, where a terahertz pump excites coherent optical phonons that are subsequently probed by an intense infrared pulse that drives HHG. We find, through state-of-the-art ab initio calculations, that the structure of the emission spectrum is attenuated by the presence of coherent phonons and no longer comprises discrete harmonic orders, but rather a continuous emission in the plateau region. The HHG yield strongly oscillates as a function of the pump-probe delay, corresponding to ultrafast changes in the lattice such as specific bond compression or stretching dynamics. We further show that in the regime where the excited phonon period and the pulse duration are of the same order of magnitude, the HHG process becomes sensitive to the carrier-envelope phase (CEP) of the driving field, even though the pulse duration is so long that no such sensitivity is observed in the absence of coherent phonons. The degree of CEP sensitivity versus pump-probe delay is shown to be a highly selective measure for instantaneous structural changes in the lattice, providing an approach for ultrafast multidimensional HHG spectroscopy. Remarkably, the obtained temporal resolution for phonon dynamics is ∼1 femtosecond, which is much shorter than the probe pulse duration because of the inherent subcycle contrast mechanism. Our work paves the way toward routes of probing phonons and ultrafast material structural changes with subcycle temporal resolution and provides a mechanism for controlling the HHG spectrum.

High-order harmonic generation from the interference of intra-cycle trajectories in the k-space

Considering the crystal momenta of the entire k-space, we demonstrate that constructive intra-cycle interference of electrons enhances the high-order harmonic generation (HHG) of a GaN crystal from dominant interband Bloch oscillations. This results in a higher plateau of the HHG spectrum at a driven yield strength below the Bloch field strength. This phenomenon is confirmed in both the two-band and three-band models. Using two-color laser fields, the constructive or destructive interference of interband Bloch oscillations can be tuned. Our findings reveal the essential impact of intra-cycle interference in the full k-space on the HHG in solids.

All-optical reconstruction of three-band transition dipole moments by the crystal harmonic spectrum from a two-color laser pulse

When a bulk solid is irradiated by an intense laser pulse, transition dipole moments (TDMs) between different energy bands have an important influence on the ultra-fast dynamic process. In this paper, we propose a new all-optical method to reconstruct the k-dependent TDMs between multi-bands using a crystal high-order harmonic generation (HHG). Taking advantage of an obvious separation of bandgaps between three energy bands of an MgO crystal along the <001 > direction, a continuous harmonic spectrum with two plateaus can be generated by a two-color laser pulse. Furthermore, the first harmonic platform is mainly dominated by the polarization between the first conduction band and the valence band, and the second one is largely attributed to the interband HHG from the second conduction band and the valence band. Therefore, the harmonic spectrum from a single quantum trajectory can be adopted to map TDMs between the first, second conduction bands, and the valence one. Our work is of great significance for understanding the instantaneous properties of solid materials in the strong laser field, and will strongly promote the development of the HHG detection technology.

Controlling of the harmonic generation induced by the Berry curvature

High-order harmonic generation in solid state has attracted a lot of attentions. The Berry curvature (BC), a geometrical property of the Bloch energy band, plays an important role for the harmonic generation in crystal. As we all know, the influence of BC on the harmonic emission has been investigated before and BC is simplified as a 1D structure. However, many other materials including MoS₂ are 2D materials. In this work, we extend the investigation for BC to 2D structure and get a generalized equation, which not only gives a new method to control the harmonic emission with BC, but also gives a deeper understanding for the influence of the BC. We show the ability to control the harmonic emission related to the BC using the orthogonal two-color (OTC) laser field. By tuning the delay of OTC laser field, one can steer the trajectory of electrons and modulate the emission of harmonics. This study can provide us a deeper insight into the role of the BC which is difficult to be measured experimentally.

High-harmonic generation in metallic titanium nitride

High-harmonic generation is a cornerstone of nonlinear optics. It has been demonstrated in dielectrics, semiconductors, semi-metals, plasmas, and gases, but, until now, not in metals. Here we report high harmonics of 800-nm-wavelength light irradiating metallic titanium nitride film. Titanium nitride is a refractory metal known for its high melting temperature and large laser damage threshold. We show that it can withstand few-cycle light pulses with peak intensities as high as 13 TW/cm², enabling high-harmonics generation up to photon energies of 11 eV. We measure the emitted vacuum ultraviolet radiation as a function of the crystal orientation with respect to the laser polarization and show that it is consistent with the anisotropic conduction band structure of titanium nitride. The generation of high harmonics from metals opens a link between solid and plasma harmonics. In addition, titanium nitride is a promising material for refractory plasmonic devices and could enable compact vacuum ultraviolet frequency combs.

Transverse phase matching of high-order harmonic generation in single-layer graphene

The efficiency of high-harmonic generation (HHG) from a macroscopic sample is strongly linked to the proper phase matching of the contributions from the microscopic emitters. We develop a combined micro+macroscopic theoretical model that allows us to distinguish the relevance of high-order harmonic phase matching in single-layer graphene. For a Gaussian driving beam, our simulations show that the relevant HHG emission is spatially constrained to a phase-matched ring around the beam axis. This remarkable finding is a direct consequence of the non-perturbative behavior of HHG in graphene-whose harmonic efficiency scaling is similar to that already observed in gases- and bridges the gap between the microscopic and macroscopic HHG in single-layer graphene.

Control of High-Harmonic Generation by Tuning the Electronic Structure and Carrier Injection

High-harmonic generation (HHG), which is the generation of light with multiple optical harmonics, is an unconventional nonlinear optical phenomenon beyond the perturbation regime. HHG, which was initially observed in gaseous media, has recently been demonstrated in solid-state materials. Determining how to control such extreme nonlinear optical phenomena is a challenging subject. Here, we demonstrate the control of HHG through tuning the electronic structure and carrier injection using single-walled carbon nanotubes (SWCNTs). We reveal systematic changes in the high-harmonic spectra of SWCNTs with a series of electronic structures ranging from a metal structure to a semiconductor structure. We demonstrate enhancement or reduction of harmonic generation by more than 1 order of magnitude by tuning the electron and hole injection into the semiconductor SWCNTs through electrolyte gating. These results open a path toward the control of HHG in the context of field-effect transistor devices.

Characterizing the carrier-envelope phase stability of mid-infrared laser pulses by high harmonic generation in solids

We present a novel approach for measuring the carrier-envelope phase (CEP) stability of a laser source by employing the process of high harmonic generation (HHG) in solids. HHG in solids driven by few-cycle pulses is very sensitive to the waveform of the driving pulse, therefore enabling to track the shot-to-shot CEP fluctuations of a laser source. This strategy is particularly practical for pulses at long central wavelength up to the mid-infrared spectral range where usual techniques used in the visible or near-infrared regions are challenging to transpose. We experimentally demonstrate this novel tool by measuring the CEP fluctuations of a mid-infrared laser source centered at 9.5~μm.

Determination of Electron Band Structure using Temporal Interferometry

We propose an all-optical method to directly reconstruct the band structure of semiconductors. Our scheme is based on the temporal Young's interferometer realized by high harmonic generation with a few-cycle laser pulse. As a time-energy domain interferometer, temporal interference encodes the band structure into the fringe in the energy domain. The relation between the band structure and the emitted harmonic frequencies is established. This enables us to retrieve the band structure from the spectrum of high harmonic generation with a single-shot measurement. Our scheme paves the way to study matters under ambient conditions and to track the ultrafast modification of band structures.

Observation of Rapid Adiabatic Passage in Optical Four-Wave Mixing

We observe clear evidence of adiabatic passage between photon populations via a four-wave mixing process, implemented through a dispersion sweep arranged by a core diameter taper of an optical fiber. Photonic rapid adiabatic passage through the cubic electric susceptibility thus opens precise control of frequency translation between broadband light fields to all common optical media. Areas of potential impact include optical fiber and on-chip waveguide platforms for quantum information, ultrafast spectroscopy and metrology, and extreme light-matter interaction science.

High-field mid-infrared pulses derived from frequency domain optical parametric amplification

We present a novel, to the best of our knowledge, approach for scaling the peak power of mid-infrared laser pulses with few-cycle duration and carrier-to-envelope phase stabilization. Using frequency domain optical parametric amplification (FOPA), selective amplification is performed on two spectral slices of broadband pulses centered at 1.8 µm wavelength. In addition to amplification, the Fourier plane is used for specific pulse shaping to control both the relative polarization and the phase/delay between the two spectral slices of the input pulses. At the output of the FOPA, intrapulse difference frequency generation provides carrier-envelope phase stabilized two-cycle pulses centered at 9.5 µm wavelength with 25.5 µJ pulse energy. The control of the carrier-envelope phase is demonstrated through the dependence of high-harmonic generation in solids. This architecture is perfectly adapted to be scaled in the future to high average and high peak powers using picosecond ytterbium laser technologies.

Carrier-envelope-phase measurement of few-cycle mid-infrared laser pulses using high harmonic generation in ZnO

High-harmonic generation (HHG) in crystals offers a simple, affordable and easily accessible route to carrier-envelope phase (CEP) measurements, which scales favorably towards longer wavelengths. We present measurements of HHG in ZnO using few-cycle pulses at 3.1µm. Thanks to the broad bandwidth of the driving laser pulses, spectral overlap between adjacent harmonic orders is achieved. The resulting spectral interference pattern provides access to the relative harmonic phase, and hence, the CEP.

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.

All-optical reconstruction of k-dependent transition dipole moment by solid harmonic spectra from ultrashort laser pulses

Band structure and transition dipole moment play important roles in high-order harmonic generation from solid materials. In this work we provide a new all-optical technique to reconstruct the momentum-dependent transition dipole moment using the harmonic spectrum from MgO crystal driven by an ultrashort mid-infrared laser pulse. Under the influence of the ultrashort laser pulse, the emitted photon energy and the crystal momentum form a one-to-one match, in the same way between the intensity of the harmonic above the minimum bandgap and the square of the amplitude of the transition dipole moment, resulting in a realization of directly probing the transition dipole moment. Our all-optical method paves a way to image the two-dimensional transition dipole moment of crystals with the inversion symmetry.

High-harmonic generation in solids driven by counter-propagating pulses

We used two 800 nm laser pulses propagating in the opposite directions, to drive the emission of high-order vacuum ultra-violet harmonics off of the surface of an MgO (100) single crystal. We demonstrated the advantages that our approach provides compared to a single beam geometry, in both forward and backward emission.

Near-octave intense mid-infrared by adiabatic down-conversion in hollow anti-resonant fiber

We show that adiabatic down-conversion can be made the dominant four-wave mixing process in an anti-resonant hollow-core fiber for nearly a full octave of mid-infrared bandwidth with energy exceeding 10 μJ, allowing the generation of energetic and shapeable two-cycle pulses. A numerical study of a tapered fiber with an applied gas pressure gradient predicts the efficient conversion of a 770-860 nm near-infrared frequency band to 3-5 μm, while a linear transfer function allows pre-conversion pulse shaping and simple dispersion management. Our proposed system may prove to be useful in diverse research topics employing nonlinear spectroscopy or strong light-matter interactions.

Attosecond temporal confinement of interband excitation by intraband motion

High order harmonic generation (HHG) in semiconductors opens a new frontier in strong field physics and attosecond science. However, the underlying physical mechanisms are not yet fully understood and lively debated. Here, we identify and discuss carrier-wave population transfer as a novel and important dynamical effect. We find that the interband excitation occurs in an extremely short time window due to the intraband motion. Our analysis based on this finding allows for a physically intuitive interpretation of the anomalous carrier-envelope phase dependence observed in HHG from MgO and to understand the dominant role of the interband polarization as reported in a series of recent semiconductor HHG experiments. Motivated by the discovered coupling mechanism, we demonstrate that the interband excitation can be controlled by an appropriately tailored two-color field. An ultrabroad supercontinuum spectrum covering the entire plateau region can be generated which directly creates an isolated-attosecond pulse even without phase compensation. Our results provide remarkable insight into the basic physics governing the sub-cycle electron motion with significant implications for the generation of isolated-attosecond light pulses in semiconductor materials.

Crystal orientation-dependent polarization state of high-order harmonics

We analyze the crystal orientation-dependent polarization state of extreme ultraviolet high-order harmonics from bulk magnesium oxide crystals subjected to intense linearly polarized laser fields. We find that only along high-symmetry directions do high-order harmonics follow the polarization direction of the laser field. In general, there are strong deviations that depend on harmonic order, strength of the laser field, and crystal orientation. We use a real-space electron trajectory picture to understand the origin of polarization deviations. These results have implications in all-optical probing of electronic band structure in momentum space and valence charge distributions in real space, and in producing attosecond pulses with time-dependent polarization in compact setups.

Generation of sub-two-cycle CEP-stable optical pulses at 3.5 μm by multiple-plate pulse compression for high-harmonic generation in crystals

Multiple-plate pulse compression of femtosecond mid-infrared pulses is demonstrated using YAG and Si windows. With this robust compression scheme, we produce sub-two-cycle, CEP-stable optical pulses and observe CEP-dependent high harmonic generation in crystals.

Spatiotemporal filtering of high harmonics in solids

We study the macroscopic spatial and temporal properties of harmonic radiation generated by a model solid in the interaction with an intense, focused laser beam. We show that different temporal contributions to the harmonic yield can be separated in the spatial domain because they lead to radiation with different divergences, similar to what is observed in gas-phase harmonic generation. We show that applying a spatial filter in the far field results in a temporal separation of the two contributions upon refocusing, which yields spatially collimated harmonics, a spectrum with well-resolved peaks, and a subcycle time profile of the harmonic radiation with only one burst per half-cycle.

Non-perturbative generation of DUV/VUV harmonics from crystal surfaces at 108 MHz repetition rate

We demonstrate non-perturbative 3rd (267 nm) and 5th (160 nm) harmonic generation in solids from a Ti:sapphire frequency comb (800 nm) at 108 MHz repetition rate. The experiments show that non-perturbative low harmonics are dominantly generated on the surface and on the interface between solids, and that they are not produced by bulk processes from the near-surface layer of the material. Measurements reveal that due to the lack of phase matching, the generated harmonics in bulk are suppressed by orders of magnitude compared to the signal generated on the surface. Our results pave the way for the development of all-solid-state high repetition rate harmonic sources for vacuum ultraviolet spectroscopy and high precision frequency comb metrology.

Role of the Transition Dipole Amplitude and Phase on the Generation of Odd and Even High-Order Harmonics in Crystals

Since the first observation of odd and even high-order harmonics generated from ZnO crystals in 2011, the dependence of the harmonic yields on the orientation of the laser polarization with respect to the crystal axis has never been properly interpreted. This failure has been traced to the lack of a correct account of the phase of the transition dipole moment between the valence band and the conduction band. Using a simple one-dimensional two-band model, here we demonstrate that the observed odd harmonics is directly related to the orientation dependence of the magnitude of the transition dipole, while even harmonics is directly related to the phase of the transition dipole. Our result points out the essential role of the complex transition dipole moment in understanding harmonic generation from solids that has long been overlooked so far.

High-harmonic generation in solids driven by subcycle midinfrared pulses from two-color filamentation

Carrier-envelope-phase (CEP) controlled subcycle midinfrared pulses generated through two-color filamentation have been applied for high-harmonic (HH) generation in a crystalline silicon (Si) membrane. The HH spectrum reaches the ultraviolet region (<300  nm), beyond the direct band gap of Si. The shape of the HH spectrum strongly depends on the CEP. The complex CEP dependence can be explained with the interference between different orders of the harmonics. The complete waveform characterization of the subcycle driver pulse using frequency-resolved optical gating capable of CEP determination plays a crucial role for investigation of the subcycle dynamics.

High-harmonic generation in amorphous solids

High-harmonic generation in isolated atoms and molecules has been widely utilized in extreme ultraviolet photonics and attosecond pulse metrology. Recently, high-harmonic generation has been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruct electronic band structures, as well as compact extreme ultraviolet light sources. So far these studies are confined to crystalline solids; therefore, decoupling the respective roles of long-range periodicity and high density has been challenging. Here we report the observation of high-harmonic generation from amorphous fused silica. We decouple the role of long-range periodicity by comparing harmonics generated from fused silica and crystalline quartz, which contain the same atomic constituents but differ in long-range periodicity. Our results advance current understanding of the strong-field processes leading to high-harmonic generation in solids with implications for the development of robust and compact extreme ultraviolet light sources.

Although higher harmonic generation from solids has become of interest in many fields, its observation is typically limited to crystalline solids. Here, the authors demonstrate that higher harmonics can be generated from amorphous solids.

Generation of octave-spanning mid-infrared pulses from cascaded second-order nonlinear processes in a single crystal

We report on experimental generation of a 6.8 μJ laser pulse spanning from 1.8 to 4.2 μm from cascaded second-order nonlinear processes in a 0.4-mm BiB₃O₆ (BIBO) crystal. The nonlinear processes are initiated by intra-pulse difference frequency generation (DFG) using spectrally broadened Ti:Sapphire spectrum, followed by optical parametric amplification (OPA) of the DFG pulse. The highest energy, 12.6 μJ, is achieved in a 0.8-mm BIBO crystal with a spectrum spanning from 1.8 to 3.5 μm. Such cascaded nonlinear processes are enabled by the broadband pump and the coincident phase matching angle of DFG and OPA. The spectrum is initiated from the DFG process and is thus expected to have passive stable carrier-envelope phase, which can be used to seed either a chirped pulse amplifier (CPA) or an optical parametric chirped pulse amplifier (OPCPA) for achieving high-energy few-cycle mid-infrared pulses. Such cascaded second-order nonlinear processes can be found in many other crystals such as KTA, which can extend wavelengths further into mid-infrared. We achieved a 0.8 μJ laser pulse spanning from 2.2 to 5.0 μm in KTA.

Enhancement of the second plateau in solid high-order harmonic spectra by the two-color fields

We theoretically investigate high-order harmonic generation (HHG) from solids in two-color fields. It is found that under the premise of maintaining the same amplitude, the intensity of the second plateau can be enhanced by two to three orders in a proper two-color field compared with the result in the monochromatic field with the same frequency as the driving pulse of the two-color field. This can be attributed to the fact that most excited electrons can be driven to the top of the first conduction band due to the larger vector potential of the two-color fields, which leads to the higher electron population of upper conduction bands. Moreover, we also find that isolated attosecond pulses can be generated from solids by choosing a proper two-color field that allows the electrons to reach the top of the first conduction band only once. This work provides a promising method for extending the range of solid HHG spectra in experiments.