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.

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.

Wavelike dynamics for high harmonic generation in solids

Wavelike dynamics for high harmonic generation in solids

High-Order Harmonic Generation in Solids: The Role of Intraband Transitions in Extreme Nonlinear Optics.

High-order harmonic generation (HHG) in gases is frequently used nowadays to produce attosecond pulses and coherent radiation in the visible-to-soft X-ray spectral range. HHG in solids is a natural extension of the idea of HHG in gases, and its first observation about ten years ago opened the door to investigations on attosecond electron dynamics in solids and the development of solid-state attosecond light sources. The common process in both types of HHG is nonlinear photocarrier generation, and thus, transitions between different bands (interband transitions) are always important for HHG. As well, in the case of solids, the transitions within a band (intraband transitions) also need to be considered, because efficient carrier acceleration is possible due to them. This Perspective focuses on experimental findings that show how intraband transitions can be controlled because such an understanding will be essential in the development of unique optoelectronics that can operate at petahertz frequencies.

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.

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.

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.

Control of high-order harmonic generation in solids by orthogonally polarized laser fields

We theoretically investigate the high-order harmonic generation (HHG) from ZnO crystals driven by orthogonally polarized two-color (OTC) laser fields. By solving the semiconductor Bloch equation (SBE) in two dimensions, it is found that the HHG yields show a high sensitivity to the relative phase between the two fields. By changing the laser intensity, the yields of HHG show two maxima in the high-order region. To reveal the physical origin of these phenomena, we analyze the behavior of the electron-hole pair in the real and reciprocal spaces by the recollision model, respectively. It could qualitatively interpret the results by SBE simulations. Our analysis demonstrates that the OTC laser fields could control the electron-hole dynamics and HHG processes efficiently.

Numerical Study on Surface Roughness Measurement Based on Nonlinear Ultrasonics in Through-Transmission and Pulse-Echo Modes.

Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures.

Two-color-driven enhanced high-order harmonic generation in solids

We theoretically investigate the emission of high-harmonic (HH) radiation in model crystals by bichromatic few-cycle driving pulses that are composed as the phase-coherent superposition of a mid-infrared fundamental pulse and its second harmonic. Adjusting the model-crystal parameters to reproduce the lowest band gap of MgO, we examine the extent to which distinct domains of the HH spectrum can be controlled and enhanced by tuning the temporal profile of the bichromatic driving laser electric field. We change the driving-pulse shape by varying its fundamental-versus-second-harmonic pulse amplitude ratio and delay, while keeping the energy of the driving laser pulse fixed. For suitable amplitude ratios and delays, we find an up to fivefold enhancement of the spectral HH yield and significant shifts of the HH cutoff frequency.

High harmonic generation in AlN due to out-of-surface electron orbitals

High harmonic generation in solids is commonly considered as a bulk process. However, there is a controversy whether the experimentally observed effects can in their entirety be described by a pure bulk model. Our results based on beam propagation and spectral characteristics provide a clear signature of the importance of surface effects on the origin of the harmonic generation in solids. Computations performed with a time-dependent density-functional approach corroborate the experimental measurements.

Intense-laser-driven electron dynamics and high-order harmonic generation in solids including topological effects

A theory for laser-driven electron dynamics and high-harmonic generation in bulk solids with two lattice sites per unit cell of arbitrary dimension is formulated. In tight-binding approximation, such solids can be described by $2\times 2$ Bloch-Hamiltonians. Our theory is able to fully capture topological effects in high-harmonic generation by such systems because no simplifications beyond tight-binding, dipole approximation, and negligible depletion of the valence band are made. An explicit, analytical expression for the electron velocity is given. Exemplarily, the theory is applied to the Su-Schrieffer-Heeger chain and the Haldane model in strong laser fields.

Control of the high-order harmonic generation by sculpting waveforms with chirp in solids

Novel method for controlling the high-order harmonic generation in solids with few cycle nonlinear chirped driver laser pulses is proposed. High-order-harmonic generation (HHG) is simulated by solving the one-dimensional (1D) time-dependent Schrödinger equation. The quantum path of HHG is complex in solid system, multichannel contribution in the plateau region is identified and manipulated in this paper. Our results show that negative chirp can broaden the second plateau of HHG when the time point of the chirped central frequency remains unchanged. The physical mechanism is discussed by the time-frequency, quasi-classical analysis and population in each energy band.

Role of virtual band population for high harmonic generation in solids

We study the sub-band-gap high harmonic generation (HHG) in a methylammonium lead trichloride single crystal. Anisotropy in the crystal orientation dependence of the high harmonic yield is observed, and the yield varies substantially with the electric field strength of the midinfrared laser pulse used for excitation. Our real-time ab initio simulations reproduce the experimental results well and also show that the HHG is independent of the interband decoherence time. Based on a microscopic analysis of the intraband current, we reveal that the orientation dependence of the HHG in this perovskite semiconductor is governed by the virtual band population, rather than the anharmonicity of the electronic band structure.

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.

Probing structural chirality of crystals using high-order harmonic generation in solids

Structural chirality plays an important role in solid state physics and leads to a variety of novel physics. The feasibility of probing structural chirality of crystals using high harmonic generation in solids is explored in this work. Through first-principles calculations based on the time-dependent density functional theory framework, we demonstrate that evident circular dichroism (CD) effects can be induced in the high harmonic spectra from a chiral crystal -- bulk tellurium. The CD signal reverses for crystals with opposite structural chirality. Besides, the high harmonic spectroscopy also provides an all-optical method for probing lattice symmetry properties and determining orientation of the tellurium crystal.

Structure gauges and laser gauges for the semiconductor Bloch equations in high-order harmonic generation in solids

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges, and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: an 1D model of ZnO and the 2D monolayer hexagonal boron nitride (h-BN). The omittance of Berry connections or TDPs in the SBEs for h-BN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process, and are applicable to all strong-field matter simulations with SBEs.