Dependence Of High-order Harmonic Generation Research Articles

Orientation Dependence of High-Order Harmonic Generation from HeH2+ in a Corotating Two-Color Circularly Polarized Laser Field

By numerically solving the time-dependent Schrödinger equation, we study high-order harmonic generation from the asymmetric diatomic molecule HeH2+ in a corotating two-color circularly polarized laser field. Our results reveal a strong correlation between the molecule orientation and the harmonic yield. The harmonics in the plateau region can achieve an intensity modulation of one to two orders of magnitude with the change in the orientation angle. Through the time-dependent evolution of ionized electron wave packets combined with the analysis of the transition dipole moment between the continuum and bound states, the modulation of the harmonic strength may be attributed to the difference in the recollision angle of ionized electron wave packets relative to the molecules. In addition, the harmonic ellipticity is also affected by the molecular orientation. Notably, we found that the harmonic with greater ellipticity and higher intensity can be obtained with an orientation angle of 147°. These findings open up new avenues for achieving enhanced efficiency, the near-circular polarization of harmonics, and precise control over harmonic polarization states.

Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime

Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime

Intensity dependence of high-order harmonic generation in ZnO

Intensity dependence of high-order harmonic generation in ZnO

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.

Ellipticity dependence of high-order harmonic generation in disordered semiconductors

We analyze the ellipticity dependence of high order harmonic generation (HHG) in disordered semiconductors. We show that a disordered crystal can radiated HHG spectra containing only odd harmonics of the laser frequency for all values of the ellipticity of the laser. Furthermore, we show that the HHG yield of our disordered models decreases monotonically with increasing laser ellipticity as observed in recent experiments. I particular, our numerical calculations, based on a coarse grained model, reproduce many of the qualitative features of the experimental HHG spectra of ZnO and GaAs.

Orientation and ellipticity dependence of high-order harmonic generation in nanowires

It has been predicted that high-order harmonic generation (HHG) in nanowires has the potential to scale up photon energy and harmonic yield. However, studies on HHG in nanowires are still theoretical and no relevant experimental results have been reported as yet. Our experimental observation of the high-order harmonic in cadmium sulfide nanowires (CdS NWs) excited by a mid-infrared laser is, to our knowledge, the first of such study, and it verifies some of the theoretical results. Our experimental results show that the observed harmonics are strongest when a pump laser is parallel to the nanowires. Therefore, the theoretical prediction that harmonics are strongest under the nanowires parallel to the laser field is confirmed experimentally, and this can be used to determine the orientation of the nanowire. In addition, harmonics are sensitive to the variation of pump light ellipticities. This orientation dependence opens new opportunities to access the ultrafast and strong-field physics of nanowires.

Semiclassical analysis of ellipticity dependence of harmonic yield in graphene

We theoretically investigate the ellipticity dependence of high-order harmonic generation in graphene driven by the midinfrared laser field. The ellipticity dependence of the harmonic yield in the experiment [N. Yoshikawa, T. Tamaya, and K. Tanaka, Science 356, 736 (2017)] is reproduced perfectly by solving the semiconductor Bloch equations in the Houston basis under the tight-binding approximation. Based on the semiclassical recollision model, it is found that the recollision distance of the electron-hole pair excited from the zone $0.5{\ensuremath{\omega}}_{0}\ensuremath{\leqslant}\mathrm{\ensuremath{\Delta}}E\ensuremath{\leqslant}2.5{\ensuremath{\omega}}_{0}$ instead of the Dirac points can reach a minimum value at finite ellipticity, which enhances the harmonic yield. In addition, the ellipticity dependence of harmonics can be controlled by varying the chemical potential of graphene. When the chemical potential is decreased to $\ensuremath{-}1.52\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, the ellipticity dependence of harmonics can transit into the normal behavior. This work uncovers the microscopic mechanism of the ellipticity dependence of the harmonics in graphene and constructs a clear physical picture to understand the unique ellipticity-dependent behaviors in graphene.

Orientation dependence of high-order harmonic generation in graphene

We investigate the orientation dependence of high-order harmonic generation (HHG) in graphene by solving the semiconductor Bloch equations. The tight-binding approximation including up to the third-nearest-neighbor atoms is used to model the graphene. Our simulations show that the orientation dependence of HHG shows different patterns for different harmonics. With increasing the laser intensity, these patterns become similar except for a double-peak structure shown in lower-order harmonics. The double-peak structure appears at high laser intensity due to the contribution of the harmonic perpendicular to the laser polarization direction. The harmonic yield is decomposed as the contributions of the nearest-neighbor interaction, the second-nearest-neighbor interaction, and the third-nearest-neighbor interaction. Our results show that the harmonic yields are mainly contributed by the nearest-neighbor interaction, but the third-nearest-neighbor interaction also plays an important role and modifies the orientation dependence.

Comparison study on atomic and molecular ellipticity dependence of high-order harmonic generation

We systematically investigate ellipticity dependence of high-order harmonic generation of Ar and ${\mathrm{N}}_{2}$ in intense elliptically polarized laser fields. The experimental normalized ratios of low-order harmonic intensity to high-order harmonic intensity increase with ellipticity for both Ar and ${\mathrm{N}}_{2}$, and quantitatively depend on targets and trajectory paths. The experimental results are well reproduced by a nonadiabatic semiclassical simulation and explained by trajectory-based analysis. In addition, the influence of nuclear distance on the ratios is theoretically investigated. Our work reveals that the difference between atoms and molecules can be attributed to the influence of different ionic potentials, which depends on the molecular structure (internuclear distance) and alignment, on the evolution of the photoelectron.

Orientation dependence of high-order harmonic generation in nanowire

We investigate the orientation dependence of high-order harmonic generation (HHG) in nanowires by solving the time-dependent Schr\odinger equation. It is found that the harmonic spectrum exhibits a two-plateau structure and the two plateaus have different orientation dependences. The harmonic yield of the first plateau reaches a maximum when the laser field is parallel to the nanowire and gets a strong suppression when the laser field is perpendicular to the nanowire. The harmonic yield of the second plateau increases first and reduces eventually with the change of the nanowire orientation. These phenomena can be explained by the time-dependent population imaging and the analysis of the transition probability between different energy bands. Our analysis shows a strong band-sensitive orientation dependence in low-dimensional material.

Carrier-envelope phase-dependent molecular high-order harmonic generation from H2+ in a multi-cycle regime.

Carrier-envelope phase (CEP) dependence of high-order harmonic generation (HHG) from H2+ in a multi-cycle laser pulse is investigated by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). It is found that high harmonics in the plateau exhibit counterintuitive frequency modulation (FM) as the CEP of the multi-cycle laser varies. Based on the classical electron trajectories and time-frequency analysis, this multi-cycle CEP-dependent FM is demonstrated to result from the interference of half-cycle HHG radiations, which is modulated by laser-driven nuclear motion. The mechanism of the CEP-dependent FM is further confirmed by simulations based on a simple algorithm in the time domain, which satisfactorily reproduces the TDSE results. The CEP-dependent FM encodes rich information on the correlated electron and nuclear dynamics, which paves the way for probing nuclear motion with attosecond resolution.

Driving-laser ellipticity dependence of high-order harmonic generation in graphene

High-order harmonic generation in graphene driven by the elliptically polarized midinfrared driving pulse is theoretically investigated by solving the two-band semiconductor Bloch equation in the Houston basis under the tight-binding approximation. It is found that the maximal harmonic yield occurs at a specific driver ellipticity whose value is determined by relaxation processes, so that the proper choice of the dephasing time is key to quantitatively reproducing the recent experiment. We show that the ellipticity dependence mainly originates from the interband harmonic emission, and exhibits an almost stable behavior against the crystal orientation. Furthermore, we also demonstrate that both the large magnitude and the circular vortex structure of the transition dipole near the graphene Dirac point are responsible for forming the unique characteristics. These results demonstrate that high-harmonic generation by the elliptically polarized driving field carries significant information on the dephasing time and the electronic structure signature in the graphene.

Cluster size dependence of high-order harmonic generation

We investigate high-order harmonic generation (HHG) from noble gas clusters in a supersonic gas jet. To identify the contribution of harmonic generation from clusters versus that from gas monomers, we measure the high-order harmonic output over a broad range of the total atomic number density in the jet (from 3×1016 to 3 × 1018 ) at two different reservoir temperatures (303 and 363 K). For the first time in the evaluation of the harmonic yield in such measurements, the variation of the liquid mass fraction, g, versus pressure and temperature is taken into consideration, which we determine, reliably and consistently, to be below 20% within our range of experimental parameters. By comparing the measured harmonic yield from a thin jet with the calculated corresponding yield from monomers alone, we find an increased emission of the harmonics when the average cluster size is less than 3000. Using g, under the assumption that the emission from monomers and clusters add up coherently, we calculate the ratio of the average single-atom response of an atom within a cluster to that of a monomer and find an enhancement of around 100 for very small average cluster size (∼200). We do not find any dependence of the cut-off frequency on the composition of the cluster jet. This implies that HHG in clusters is based on electrons that return to their parent ions and not to neighboring ions in the cluster. To fully employ the enhanced average single-atom response found for small average cluster sizes (∼200), the nozzle producing the cluster jet must provide a large liquid mass fraction at these small cluster sizes for increasing the harmonic yield. Moreover, cluster jets may allow for quasi-phase matching, as the higher mass of clusters allows for a higher density contrast in spatially structuring the nonlinear medium.

Influence of laser contrast on high-order harmonic generation from solid-density plasma surfaces

The influence of laser temporal contrast on high-order harmonic generation from intense laser interactions with solid-density plasma surfaces is experimentally studied. A switchable plasma mirror system is set up to improve the contrast by two orders of magnitude at 10 ps prior to the main peak. By using the plasma mirror and tuning the prepulse, the dependence of high-order harmonic generation on laser contrast is investigated. Harmonics up to the 21st order via the mechanism of coherent wake emission are observed only when the targets are irradiated by high contrast laser pulses by applying the plasma mirror.

High-order harmonic generation of O2 molecules with different nuclear axis orientations

High-order harmonic generation (HHG) is one of the hottest topics in strong field atomic and molecular physics. In this paper, frequency domain theory which is based on formal scattering theory is extended to study the HHG of O2 molecules under a linearly polarized single mode laser field. The dependence of HHG on the angle 0 between the laser polarization direction and nuclear axis is investigated. In our calculation, we only consider the contribution of highest occupied molecular orbital (HOMO) and use the single electron approximation. The HOMO is obtained from quantum chemical software Molpro. The intensity of the laser is 5.181014 W/cm2 and the wavelength is 800 nm. On the one hand, in the case that the nuclear axis lies in the plane perpendicular to the laser propagation direction, we find that the yields of all order harmonics increase with 0 increasing until the yields reach the maximum values when 0 is equal to about 45. Then the yields decrease with 0 increasing and have the minimum values when 0 is equal to about 90. The analysis shows that the yield of HHG is dominated by the density of electrons in HOMO along the laser polarizing direction in momentum space. On the other hand, in the case that the nuclear axis lies in the plane parallel to laser propagation direction, the dependence of HHG on 0 is the same as that when the nuclear axis is in the plane perpendicular to laser propagation direction. The reasons for the same results for the two cases lie in the following fact. The HOMO of O2 molecule has g symmetry which is not rotationally symmetric around nuclear axis. So HHG yield relies on the g extension orientation. Since the g extension orientation cannot be fixed, the HHG of O2 should be averaged over the contributions to HHG at all possible g extension orientations. This average is equivalent to that the electron density is rotationally symmetric around the nuclear axis and hence leads to the fact that the HHG yield of O2 depends on 0 rather than the plane that the nuclear axis lies in.

Extension of high-order harmonic cutoff frequency by synthesizing the waveform of a laser field via the optimization of classical electron trajectory in the laser field

We theoretically investigate high-order harmonic generation by employing strong-field approximation (SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields. The dependence is investigated via detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity—position plane. The classical trajectory consists of three sections (Acceleration Away, Deceleration Away, and Acceleration Back), and their relationship with the electron recollision energy is investigated. The analysis of classical trajectories indicates that, besides the final (Acceleration Back) section, the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to Ip + 20.26Up is presented with a theoretically synthesized waveform of the laser field.

Carrier envelope phase retrieval of a multi-cycle pulse by heterodyne mixing of a pulse containing a few cycles

We present a theoretical routine for carrier envelope phase (CEP) retrieval of a multi-cycle femtosecond pulse by heterodyne mixing with a CEP-known few-cycle pulse using the time-dependent wavepacket quantum dynamics method. Our study is based on the CEP measuring technique and the dependence of high-order harmonic generation (HHG) spectra on CEP. After heterodyne mixing, half-cycle cutoffs (HCOs) in HHG spectra become distinct when the CEPs of multi-cycle and few-cycle pulses are well matched. The well-matched CEP of the heterodyne mixing field has a significant effect on the HHG spectra. Moreover, both quantum analysis and classical calculations are performed to demonstrate our theoretical results. The extension of CEP measurement from few-cycle pulses to multi-cycle pulses strengthens the controllability of laser parameters for femtosecond pulses.

Vibrational-state and isotope dependence of high-order harmonic generation in water molecules

We report calculations on high-order harmonic generation in water molecules. Spectra are determined for various initial vibrational states of ${\mathrm{H}}_{2}\mathrm{O}$ and its isotope ${\mathrm{D}}_{2}\mathrm{O}$. It is demonstrated that the ratio of the spectra for ${\mathrm{D}}_{2}\mathrm{O}$ and ${\mathrm{H}}_{2}\mathrm{O}$ is close to unity when the initial state is the vibronic ground state, indicating that nuclear dynamics is of minor importance. For vibrationally excited initial states, the high-harmonic intensities show a clear dependence on both the initial-state quantum number and the isotopic species.

Wavelength scaling of elliptical-polarization dependence of high-order harmonic generation

We report on an experimental study on the wavelength-scaling law of elliptical-polarization dependence of high-order harmonic generation. In the elliptical-polarization dependence measurements, we keep an identical peak intensity for pump pulses with carrier wavelength ranging from 800 nm to the mid-IR region, and the harmonic emission near the cutoff region is selected for comparison. We find that the experimental measured wavelength scaling of elliptical-polarization dependence could be well fitted with a function (epsilon(1/2) proportional to lambda(-1)) predicted by semiclassical model.

Role of ionization in orientation dependence of molecular high-order harmonic generation

We investigate the orientation dependence of high-order harmonic generation (HHG) from O(2) and CO(2) molecules using the strong-field approximation (SFA). Our simulations reveal the important modulation of the ionization to the HHG orientation dependence, especially at larger orientation angles. By virtue of a simplified model arising from the SFA, we show that this modulation can be read from the harmonic order where the HHG spectra at different orientation angles intersect. These results give suggestions on probing the molecular structure and dynamics using HHG.