Effect of Short Wavelength Pumping in High-Order Harmonic Generation by Gallium Ions in Laser Field

We investigated the two-dimensional electron momentum distributions of atomic negative ions in an intense laser field by solving the time-dependent Schr\odinger equation (TDSE) and using the first- and second-order strong-field approximations (SFAs). We showed that photoelectron energy spectra and low-energy photoelectron momentum distributions predicted from SFAs are in reasonable agreement with the solutions from the TDSE. More importantly, we showed that accurate electron-atom elastic scattering cross sections can be retrieved directly from high-energy electron momentum spectra of atomic negative ions in the laser field. This opens up the possibility of measuring electron-atom and electron-molecule scattering cross sections from the photodetachment of atomic and molecular negative ions by intense short lasers, respectively, with temporal resolutions in the order of femtoseconds.

We present a non-perturbative theory of a single atom interaction with the multicolor laser field. The theory is based on the use of exact mathematical solutions of the boundary value problem for "an atom in the external field", as a result the case of arbitrary orientation of atomic angular momentum and electromagnetic wave polarization vector can be described in the consistent mathematical form. We also present the results of numerical simulations on silver and argon atoms interaction with single-and two-color laser fields formed by fundamental frequency and second harmonic of Ti:Sapphire laser. The results of numerical calculations show that the efficiency of high-order harmonic generation (HHG) depends strongly on the laser field parameters (especially on the orientation of polarization vectors and chirp of the two-color laser field components). We have demonstrated the saturation of the cut-off frequency in the laser fields of near-atomic strength and investigated the impact of the field phase in the case of ultrashort laser pulses.

<sec> High-order-harmonic generation (HHG) is a fundamental atomic and molecular process in strong laser fields and plays a crucial role in the development of ultrafast science and technology. The essential features in HHG, such as the above-threshold harmonic plateau and cutoffs, can be well understood by the semiclassical three-step model. The HHG cutoff occurs approximately at the energy <inline-formula><tex-math id="M1">\begin{document}$3.17{U_{\rm p}} + {I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}${I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.png"/></alternatives></inline-formula> is the atomic ionization potential, and <inline-formula><tex-math id="M3">\begin{document}${U_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.png"/></alternatives></inline-formula> is the ponderomotive potential.</sec><sec> In the past, most studies focused on the HHG above the ionization threshold, and the general pattern of the HHG spectrum can be qualitatively explained by means of the strong field approximation (SFA) and the quantum treatment of three-dimensional time-dependent Schr?dinger equation (TDSE). However, the SFA results in inadequate description for the process in the harmonic generation below the ionization threshold since it neglects the Coulomb potential and the detailed electronic structure of atoms. Recently, as a promising method to produce vacuum-ultraviolet frequency comb, the HHG in the near- and below-ionization threshold has been increased considerably. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored.</sec><sec> Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of hydrogen atom by means of the time-dependent generalized pseudospectral method. We study the intensity dependence of the harmonic spectra below the ionization threshold of hydrogen atom in the intense laser field. The high-order harmonic spectra are calculated by the Fourier transform of the atom induced dipole moment in the laser field. The below-threshold harmonic spectra yield is scaled as a function of the laser peak intensity. We find that the spectra yield in below-threshold harmonic generation (BTHG) dependents on the light intensity in the multiphoton ionization regime. And the laser intensity plays an important role in the channel selection process for BTHG. There are mainly two kinds of quantum channels to be responsible for the BTHG. Namely, the generalized short trajectories and the long trajectories, in which the long trajectories are more sensitive to the laser field intensity. Combining with wavelet time-frequency transform, semiclassical trajectories simulation, and quantum channel analysis associated with the laser intensity, the dynamical origin of the BTHG is uncovered.</sec>

We perform a nonperturbative study of the effect of static magnetic fields on the multiple high-order harmonic generation (HHG) processes of atomic H in intense pulsed laser fields. The time-dependent Schrödinger equation in three spatial dimensions can be solved accurately and efficiently by means of the recently developed time-dependent generalized pseudospectral method (Tong X M and Chu S I 1997 Chem. Phys. 217 119). We found that the presence of a static magnetic field perpendicular to the laser field polarization direction can introduce a second HHG plateau, allowing significant extension of the cut-off. The high harmonics in the second plateau reach a maximum enhancement when the cyclotron frequency of the electron is about equal to one half of the laser frequency. Through a detailed time-frequency wavelet analysis of the HHG spectra, we have identified a `synchrotron radiation'-like new mechanism responsible for the production of the second plateau.

We present an ab initio study of the quantum dynamics of high-order harmonic generation (HHG) near the cutoff in intense laser fields. To uncover the subtle dynamical origin of the HHG near the cutoff, we extend the Bohmian mechanics (BM) approach for the treatment of attosecond electronic dynamics of H and Ar atoms in strong laser fields. The time-dependent Schrödinger equation and the self-interaction-free time-dependent density functional theory are numerically solved accurately and efficiently by means of the time-dependent generalized pseudospectral method for nonuniform spatial discretization of the Hamiltonian. We find that the most devoting trajectories calculated by the BM to the plateau harmonics are shorter traveling trajectories, but the contributions of the short trajectories near the cutoff are suppressed in HHG. As a result, the yields of those harmonics in the region near the cutoff are relatively weak. However, for the last few harmonics just above the cutoff, the HHG intensity becomes a little higher. This is because the HHG just above the cutoff arises from those electrons ionized near the peak of the laser pulse, where the ionization rate is the highest. In addition, the longer Bohmian trajectories return to the core with lower energies, these trajectories contribute to the below-threshold harmonics. Our results provide a deeper understanding of the generation of supercontinuum harmonic spectra and attosecond pulses via near cutoff HHG.

We perform a dynamical symmetry analysis (DSA) of the high-order harmonic generation (HHG) spectrum of an atom interacting with a bichromatic laser field. Within the framework of the conventional Hermitian quantum mechanics (QM), the HHG spectrum calculated using a single Floquet state, or any finite number of Floquet states, is invariant under the inversion of the relative phase of the two-frequency components, $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\phi}$. The asymmetry with respect to the phase inversion seen in the simulated HHG spectra is obtained in the conventional QM only when the Floquet spectrum is continuous and ionization is taken into consideration. However, when the Hamiltonian is complex scaled the description is different. Even a single eigenstate of the complex scaled Floquet operator is enough to describe the breaking of the $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\phi}$ symmetry in the HHG spectra. We find that there is a direct correlation between the strength of the asymmetry with respect to the relative phase inversion and the magnitude of the ionization rate. For illustration purposes, the DSA is accompanied by the results obtained for a one-dimensional effective single-electron model Hamiltonian mimicking xenon atom interacting with strong laser field.

We find that, for the first time in the investigation of high-order harmonic generation in two color laser fields that atomic energy level structure will greatly affect high order harmonic generation. For a certain atomic level structure, a specially chosen high frequency and relatively low intensity laser field can greatly enhance the efficiency of high order harmonic generation.

High-order harmonic generation (HHG), the highly nonlinear nonperturbative response of atoms and/or molecules to ultrafast intense laser pulses of femtosecond (\(1\text { fs}=10^{-15}\) s) duration, can be modeled as a recollision process after tunneling ionization of an electron in linear polarization. In general, recollision is suppressed at high intensities with monochromatic circularly polarized pulses. Combinations of bicircular pulses with frequencies \(\omega _1/\omega _2=n_1/n_2\) where \(n_1\) and \(n_2\) are integers, induce recollisions and HHG, seen in a rotating frame Hamiltonian. Molecules are preferred systems for circularly polarized HHG due to lower rotational symmetry as compared to infinite symmetry in atoms where emission selection rules dominate. We simulated HHG spectra from numerical solutions of time-dependent Schrodinger equations for linear and cyclic one and two electron molecular models by intense circularly polarized pulses with both co-rotating and counter-rotating components. Simulations show that the bicircular HHG spectrum is universal, with a cut-off at \(N_m=(I_p+3.17U_p)/\hbar \omega \), where \(I_p\) is the molecular ionization potential and the ponderomotive energy \(U_p=e^2E^2/4m_e\omega ^2\) for maximum electric field amplitude E. The rotating frame Hamiltonian model predicts the recollision (ponderomotive) frequency \(\omega =(\omega _1+\omega _2)/2\). The simulated HHG spectra confirm the recollision model in a rotating frame at frequency \(\bar{\omega }=(\omega _2-\omega _1)/2\). The results show that the circularly polarized HHG with definite helicity occurs efficiently when the total electric field E(t) rotational symmetry \(C_n\) of bicircular pulses is the same as the symmetry of the molecule. A mismatch of symmetry produces a random HHG spectrum, thus confirming the role of field-molecular symmetry in molecular HHG with circularly polarized pulses.

年 第 47 卷 第 3 期 目前影响高次谐波广泛应用的一个主要瓶颈 是它的光通量很低, 对于常用的 Ti:sapphire 激光 (800 nm) 而言谐波的转换效率通常小于 10 -5 [25][26][27] .若使用波长更长的红外激光可以有效提高光子的最 大能量 -截止位置, 但是转换效率急剧下降 (单原 子 ∼ λ -5 ).从实际应用的角度来看, 高次谐波的产生 需要解决以下几个问题 [28] : 提高转换效率、扩展截 止位置、选择性增强和抑制某阶或某一范围的谐波 (见图 1).实验中观察到的高次谐波通常都是在稠密的气 体中产生, 它不仅与单个原子在激光场中的响应 (诱 导偶极矩) 有关 [29]

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~1013-1014 W/cm2) is focused into a dense (~1017 particles/cm3) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.

High-order harmonic generation (HHG) of bulk crystals in strong laser field is typically investigated with semiconductor Bloch equations (SBEs). However, in the length gauge, it suffers from the divergence for the crystals with a zero band gap, such as graphene, using both Bloch- and Houston-states expansion methods. Here, we present a method of solving the SBEs based on time-dependent Bloch basis, which is equivalent to semiconductor Bloch equations in the velocity gauge. Using this method, we investigate the HHG of a single-layer graphene. It is found that our results for population are in good agreement with the other results. For a initial condition py = 0, we find the electrons just move in single valence band or conduction band, which are in accord with classical results. Our simulations on the HHG dependence of polarization of driving laser pulse confirm that 5th, 7th, and 9th harmonic yields increase to the maximal value when laser ellipticity ε ≈ 0.3. What is more, similar to the case of atoms in the laser field, the total strength of 3rd harmonic decrease monotonically with the increase of ε. In addition, we simulate the dependence of HHG on crystallographic orientation with respect to the polarization direction of linear mid-infrared laser pulse, and the results reveal that for higher harmonics, their radiation along with the change of rotation angle θ reflects exactly the sixfold symmetry of graphene. Our method can be further used to investigate the behaviors of other materials having Dirac points (i.e., surface states of topological insulators) in the strong laser fields.

We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency $\ensuremath{\omega}$. In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schr\odinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually $\ensuremath{\omega}$ and $2\ensuremath{\omega}$), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having $p$ ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity $\ensuremath{-}1$. For lower energies the harmonics having helicity $+1$ prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).

High-order harmonics generated by a linearly polarized laser field are also linearly polarized. Having in mind that for various application, such as the exploration of magnetic materials, chiral molecules etc., we need circularly polarized high harmonics which serve as coherent soft x-rays, we explore high-order harmonic generation by the so-called bicircular laser field. This field consists of two coplanar counter-rotating circularly polarized fields of different frequencies equal to integer multiples of a fundamental frequency ω. High harmonics generated by such field are circularly polarized with helicity alternating between +1 and −1. Combining a group of such harmonics, instead of obtaining a circularly polarized attosecond pulse train, one obtains a pulse with unusual polarization properties. But, if the harmonics of particular helicity are stronger, i.e., if we have helicity asymmetry in a high-harmonic energy interval, then it is possible to generate an elliptical or even circular pulse train. We theoretically investigated a wide range of bicircular field-component intensities (I1 and I2) and found regions where both the harmonic intensity is high and the helicity asymmetry is large. Particular attention is devoted to the ω−2ω and ω−3ω bicircular fields and atoms having the s and p ground states. In our calculations we use strong-field approximation and quantum-orbit theory. We show that, even in the extreme case of I2 = 8I1, for an ω−3ω bicircular field, high-order harmonic generation is more efficient than in the I2 = I1 case. The obtained results are explained analyzing the relevant electron trajectories and velocities, which follow from the quantum-orbit theory. For the atoms having p ground state the helicity asymmetry parameter is large for a wide range of high-harmonic photon energies, while for the atoms having s ground state the helicity asymmetry parameter can be large only for low harmonics. We confirm this by averaging the obtained results over the intensity distribution in the laser focus.

We present a theoretical investigation of the multiphoton resonance dynamics driven by intense frequency-comb and cavity-mode fields inside a femtosecond enhancement cavity (fsEC). The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and laser fields. The quasienergy structure driven by the frequency-comb laser field is modified by coupling the cavity-mode field and the multiphoton resonance processes between modified quasienergy states, resulting in the generation of even-order harmonics. The high-order harmonic generation (HHG) from a two-level system driven by the laser fields can be coherently controlled by tuning the laser parameters. In particular, the tuning intensity of the cavity-mode field allows one to coherently control the HHG power spectra without changing the absolute positions of comb frequencies.

High-order harmonic generation (HHG) by hydrogenlike atoms or ions in the field of counterpropagating laser beams of standing-wave configuration, with linear polarizations and relativistic intensities, is studied. The relativistic quantum theory of HHG in such field configurations (homogeneous), at which the impeding factor of relativistic magnetic drift of superstrong laser fields can be eliminated, is presented.