We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schr...We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schrodinger equation(TDSE)and performing a time-frequency analysis,we investigate the influence of individual excited states on the harmonic spectrum.Our results reveal that the 2s excited state primarily contributes to the enhancement of high-energy harmonic yields by facilitating long electron trajectories,while the 2p excited state predominantly suppresses harmonic yields in the lower-energy region(20th-50th orders)by altering the contributions of electron trajectories.Our results highlight the critical role of the excited states in the HHG process,even at longer laser wavelengths.展开更多
We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating ...We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating the methane molecule with an elliptically polarized laser pulse polarized in the x–y plane, we observed significant even-order harmonic emission in the z-direction. By analyzing the electron dynamics in the electric field and the multi-orbital effects of the molecule, we revealed that electron recombination near specific atoms in methane is the primary source of highorder harmonic generation in the z-direction. Furthermore, we identified the dominant molecular orbitals responsible for the enhancement of harmonics in this direction and demonstrated the critical role played by multi-orbital effects in this process.展开更多
Multi-electron and multi-orbital effects play a crucial role in the interaction of strong laser fields with complex molecules.Here,multi-electron effects encompass not only electron-electron Coulomb interactions and e...Multi-electron and multi-orbital effects play a crucial role in the interaction of strong laser fields with complex molecules.Here,multi-electron effects encompass not only electron-electron Coulomb interactions and exchangecorrelation effects but also the interference between the dynamics of different electron wave packets.展开更多
The spatial distribution in high-order harmonic generation（HHG） is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HH...The spatial distribution in high-order harmonic generation（HHG） is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HHG demonstrates that the harmonic spectra are sensitive to the carrier envelope phase and the duration of the laser pulse. The HHG can be restrained by a pulse with the duration of 5 fs in the region from the 90 th to 320th order. This characteristic is illustrated by the probability density of electron wave packet distribution. The electron is mainly located near the nucleus along the positive-x direction from 3.0 o.c. to 3.2 o.c., which is an important time to generate the HHG in the plateau area. We also demonstrate the time-frequency distribution in the region of the positive-and negative-x direction to explain the physical mechanism.展开更多
The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equatio...The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equation（TDSE）. The spatial distribution of the HHG spectra shows that there is little contribution in HHG around the geometric center of two nuclei（z = 1.17 a.u.） and the equilibrium internuclear position of the H nucleus（z = 3.11 a.u.）. We demonstrate the carrier envelope phase（CEP） effect on the spatial distribution of HHG in a few-cycle laser pulse. The HHG process is investigated by the time evolution of the electronic density distribution. The time–frequency analysis of HHG from two nuclei in HeH^（2＋） is presented to further explain the underlying physical mechanism.展开更多
The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree we...The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schro¨dinger equation(TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.展开更多
Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, ...Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.展开更多
The generation of high-order harmonics and the attosecond pulse of the N2 molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spec...The generation of high-order harmonics and the attosecond pulse of the N2 molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.展开更多
The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of ...The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.展开更多
We theoretically study the high-order harmonic generation （HHG） in a two-color laser field using the Bohmian mechanics. Our results show that, for tile case of a weak second-color laser field, the simulation of the ...We theoretically study the high-order harmonic generation （HHG） in a two-color laser field using the Bohmian mechanics. Our results show that, for tile case of a weak second-color laser field, the simulation of the HHG with only one central Bohmian trajectory is in a good agreement with the ab initio time-dependent Schrodinger equation （TDSE） results. In contrast, with the increase of the amplitude of the second-color laser field, the HHG spectra from the single central Bohmian trajectory deviate from the TDSE results more and more significantly. By analyzing the Bohmian trajectories, we find that the significant deviation is due to the fact that the central Bohmian trajectory leaves the core quickly in the two-color laser field with the breaking of inversion symmetry. Interestingly, we find that another Bohmian trajectory with different initial position, which keeps oscillating around the core, could qualitatively well reproduce the TDSE results. Furthermore, we study the HHG spectrum in a two-color laser field with inversion symmetry and find that the HHG spectrum in TDSE can be still well simulated with the central Bohmian trajectory. These results indicate that, similar to the case of one color laser field, the HHG spectra in a two-color laser field can be also reproduced with a single Bohmian trajectory, although the initial position of the trajectory is dependent on the symmetry of the laser field. Our work thus demonstrates that Bohmian trajectory theory can be used as a promising tool in investigating the HHG process in a two-color laser field.展开更多
We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field. We also investigate the em...We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field. We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation. We calculate the ionization rate using the Ammoso Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays. We find that the width of the harmonic plateau can be extended when the control electric field is added, and a supercontinuum from 198 to 435 eV is generated, from which an isolated 61-as pulse can be directly obtained.展开更多
We demonstrate theoretically that the high-order harmonic of an atom can be generated by a circularly polarized laser pulse.The harmonic spectrum shows a clear cutoff with an energy Ip ＋ 2Up.In particular,the high-or...We demonstrate theoretically that the high-order harmonic of an atom can be generated by a circularly polarized laser pulse.The harmonic spectrum shows a clear cutoff with an energy Ip ＋ 2Up.In particular,the high-order harmonic generation comes from the multiple recombination of the ionized electron with non-zero initial velocity.These results are verified by the classical model theory and the time-frequency analysis of a harmonic spectrum.展开更多
With the development of laser technologies,multi-color light-field synthesis with complete amplitude and phase control would make it possible to generate arbitrary optical waveforms.A practical optimization algorithm ...With the development of laser technologies,multi-color light-field synthesis with complete amplitude and phase control would make it possible to generate arbitrary optical waveforms.A practical optimization algorithm is needed to generate such a waveform in order to control strong-field processes.We review some recent theoretical works of the optimization of amplitudes and phases of multi-color lasers to modify the single-atom high-order harmonic generation based on genetic algorithm.By choosing different fitness criteria,we demonstrate that：（i） harmonic yields can be enhanced by 10 to 100 times,（ii） harmonic cutoff energy can be substantially extended,（iii） specific harmonic orders can be selectively enhanced,and（iv） single attosecond pulses can be efficiently generated.The possibility of optimizing macroscopic conditions for the improved phase matching and low divergence of high harmonics is also discussed.The waveform control and optimization are expected to be new drivers for the next wave of breakthrough in the strong-field physics in the coming years.展开更多
We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger ...We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.展开更多
The extreme ultraviolet(XUV)light beam carrying orbital angular momentum(OAM)can be produced via high-order harmonic generation(HHG)due to the interaction of an intense vortex infrared laser and a gas medium.Here we s...The extreme ultraviolet(XUV)light beam carrying orbital angular momentum(OAM)can be produced via high-order harmonic generation(HHG)due to the interaction of an intense vortex infrared laser and a gas medium.Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node(from 0 to 2)in the driving laser consisting of two mixed Laguerre-Gaussian(LG)beams.We find that due to the change in spatial profile of HHG,the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node.We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes.Through the map of coherence length and the evolution of harmonic field in the medium,we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node.We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.展开更多
We investigate the plasmonic-field-enhanced high-order harmonic generation（HHG） of H atom driven by few-cycle laser pulses, by solving the time-dependent Schr？dinger equation（TDSE）. Compared with the homogeneous ...We investigate the plasmonic-field-enhanced high-order harmonic generation（HHG） of H atom driven by few-cycle laser pulses, by solving the time-dependent Schr？dinger equation（TDSE）. Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase（CEP） of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.展开更多
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 expe...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.展开更多
Subcycle spectral structures and dynamics of high-order harmonic generation(HHG)processes of atoms and molecules driven by intense laser fields on the attosecond time scale have been originally studied theoretically a...Subcycle spectral structures and dynamics of high-order harmonic generation(HHG)processes of atoms and molecules driven by intense laser fields on the attosecond time scale have been originally studied theoretically and ex-perimentally.However,the time scale of HHG dynamics in crystals is in the order of sub-femtosecond,and the carrier dynamics of HHG in crystals driven by subcycle laser pulses are largely unexplored.Here we perform a theoretical study of subcycle structures,spectra,and dynamics of HHG of crystals in mid-infrared laser fields subject to excitation by a subcycle laser pulse with a time delay.The HHG spectra as a function of time delay between two laser fields are cal-culated by using a single-band model for the intra-band carrier dynamics in crystal momentum space and by solving the time-dependent Schr?dinger equation in velocity gauge for the treatment of multi-band crystal systems.The results exhibit a complex time-delay-dependent oscillatory pattern,and the enhancement and suppression of the HHG related to subcycle pulse are observed at the given time delay in either single-band or multi-band crystal systems.To understand oscillation structures with respect to the dependence for the subcycle laser fields,the time-frequency characteristics of the HHG as well as the probability density distribution of the radiation are analyzed in detail.展开更多
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 cry...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.展开更多
High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduce...High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.展开更多
基金supported by the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi。
文摘We present a comprehensive study on the role of various excited states in high-order harmonic generation of hydrogen atoms driven by a long-wavelength(1500 nm)laser field.By numerically solving the time-dependent Schrodinger equation(TDSE)and performing a time-frequency analysis,we investigate the influence of individual excited states on the harmonic spectrum.Our results reveal that the 2s excited state primarily contributes to the enhancement of high-energy harmonic yields by facilitating long electron trajectories,while the 2p excited state predominantly suppresses harmonic yields in the lower-energy region(20th-50th orders)by altering the contributions of electron trajectories.Our results highlight the critical role of the excited states in the HHG process,even at longer laser wavelengths.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12204214)the National Key Research and Development Program of China (Grant No. 2022YFE0134200)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. GK202207012), QCYRCXM-2022-241the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011117)。
文摘We performed real-time and real-space numerical simulations of high-order harmonic generation in the threedimensional structured molecule methane(CH_(4)) using time-dependent density functional theory. By irradiating the methane molecule with an elliptically polarized laser pulse polarized in the x–y plane, we observed significant even-order harmonic emission in the z-direction. By analyzing the electron dynamics in the electric field and the multi-orbital effects of the molecule, we revealed that electron recombination near specific atoms in methane is the primary source of highorder harmonic generation in the z-direction. Furthermore, we identified the dominant molecular orbitals responsible for the enhancement of harmonics in this direction and demonstrated the critical role played by multi-orbital effects in this process.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFE0134200)the National Natural Science Foundation of China(Grant No.12204214)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.GK202207012)QCYRCXM-2022-241。
文摘Multi-electron and multi-orbital effects play a crucial role in the interaction of strong laser fields with complex molecules.Here,multi-electron effects encompass not only electron-electron Coulomb interactions and exchangecorrelation effects but also the interference between the dynamics of different electron wave packets.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11504221,61575077,11404204,and 11447208)the Natural Science Foundation for Young Scientists of Shanxi Province,China(Grant No.2015021023)Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province,China
文摘The spatial distribution in high-order harmonic generation（HHG） is theoretically investigated by using a few-cycle laser pulse from a two-dimensional model of a hydrogen molecular ion. The spatial distribution in HHG demonstrates that the harmonic spectra are sensitive to the carrier envelope phase and the duration of the laser pulse. The HHG can be restrained by a pulse with the duration of 5 fs in the region from the 90 th to 320th order. This characteristic is illustrated by the probability density of electron wave packet distribution. The electron is mainly located near the nucleus along the positive-x direction from 3.0 o.c. to 3.2 o.c., which is an important time to generate the HHG in the plateau area. We also demonstrate the time-frequency distribution in the region of the positive-and negative-x direction to explain the physical mechanism.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11271158,11574117,and 61575077)
文摘The spatial distribution in high-order harmonic generation（HHG） from the asymmetric diatomic molecule He H^（2＋） is investigated by numerically solving the non-Born–Oppenheimer time-dependent Schr？dinger equation（TDSE）. The spatial distribution of the HHG spectra shows that there is little contribution in HHG around the geometric center of two nuclei（z = 1.17 a.u.） and the equilibrium internuclear position of the H nucleus（z = 3.11 a.u.）. We demonstrate the carrier envelope phase（CEP） effect on the spatial distribution of HHG in a few-cycle laser pulse. The HHG process is investigated by the time evolution of the electronic density distribution. The time–frequency analysis of HHG from two nuclei in HeH^（2＋） is presented to further explain the underlying physical mechanism.
基金Project supported by the NSAF,China(Grant No.U1730449)the National Natural Science Foundation of China(Grant Nos.11904341,11774322,91850201,and 11874066)
文摘The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schro¨dinger equation(TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse.
基金supported by the National Natural Science Foundation of China (Grant Nos.10774153 and 61078080)the National Basic Research Program of China (Grant Nos.2010CB923203 and 2011CB808103)
文摘Using a nonperturbative quantum electrodynamics theory of high-order harmonic generation （HHG）, a scaling law of HHG is established. The scaling law states that when the atomic binding energy Eb, the wavelength ）, and the intensity I of the laser field change simultaneously to kEb, λ/k, and k3I, respectively. The characteristics of the HHG spectrum remain unchanged, while the harmonic yield is enhanced k3 times. That HHG obeys the same scaling law with above-threshold ionization is a solid proof of the fact that the two physical processes have similar physical mechanisms. The variation of integrated harmonic yields is also discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.61575077,11271158,and 11574117)
文摘The generation of high-order harmonics and the attosecond pulse of the N2 molecule in two-color circularly polarized laser fields are investigated by the strong-field Lewenstein model. We show that the plateau of spectra is dramatically extended and a continuous harmonic spectrum with the bandwidth of 113 eV is obtained. When a static field is added to the x direction, the quantum path control is realized and a supercontinuum spectrum can be obtained, which is beneficial to obtain a shorter attosecond pulse. The underlying physical mechanism is well explained by the time-frequency analysis and the semi-classical three-step model with a finite initial transverse velocity. By superposing several orders of harmonics in the combination of two-color circularly polarized laser fields and a static field, an isolated attosecond pulse with a duration of 30 as can be generated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11271158,61575077,and 11574117)
文摘The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11334009,11474321,and 11527807)
文摘We theoretically study the high-order harmonic generation （HHG） in a two-color laser field using the Bohmian mechanics. Our results show that, for tile case of a weak second-color laser field, the simulation of the HHG with only one central Bohmian trajectory is in a good agreement with the ab initio time-dependent Schrodinger equation （TDSE） results. In contrast, with the increase of the amplitude of the second-color laser field, the HHG spectra from the single central Bohmian trajectory deviate from the TDSE results more and more significantly. By analyzing the Bohmian trajectories, we find that the significant deviation is due to the fact that the central Bohmian trajectory leaves the core quickly in the two-color laser field with the breaking of inversion symmetry. Interestingly, we find that another Bohmian trajectory with different initial position, which keeps oscillating around the core, could qualitatively well reproduce the TDSE results. Furthermore, we study the HHG spectrum in a two-color laser field with inversion symmetry and find that the HHG spectrum in TDSE can be still well simulated with the central Bohmian trajectory. These results indicate that, similar to the case of one color laser field, the HHG spectra in a two-color laser field can be also reproduced with a single Bohmian trajectory, although the initial position of the trajectory is dependent on the symmetry of the laser field. Our work thus demonstrates that Bohmian trajectory theory can be used as a promising tool in investigating the HHG process in a two-color laser field.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11075069, 91026021, and 11075068)the Fundamental Research Funds for the Central Universities, China (Grant No. lzujbky-2010-k08)the Scholarship Award for Excellent Doctoral Student granted by the Ministry of Education,China
文摘We theoretically investigate the electron dynamics of the high-order harmonics generation process by combining a near-infrared 800 nm driving pulse with a mid-infrared 2000 nm control field. We also investigate the emission time of harmonics using time-frequency analysis to illustrate the physical mechanisms of high-order harmonic generation. We calculate the ionization rate using the Ammoso Delone-Krainov model and interpret the variations in harmonic intensity for different control field strengths and delays. We find that the width of the harmonic plateau can be extended when the control electric field is added, and a supercontinuum from 198 to 435 eV is generated, from which an isolated 61-as pulse can be directly obtained.
基金Project supported by the National Basic Research Program of China (Grant No. 2013CB922200)the National Natural Science Foundation of China (GrantNos. 11274141 and 11034003)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6110578)
文摘We demonstrate theoretically that the high-order harmonic of an atom can be generated by a circularly polarized laser pulse.The harmonic spectrum shows a clear cutoff with an energy Ip ＋ 2Up.In particular,the high-order harmonic generation comes from the multiple recombination of the ionized electron with non-zero initial velocity.These results are verified by the classical model theory and the time-frequency analysis of a harmonic spectrum.
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Grant No.30916011207)Chemical Sciences,Geosciences and Biosciences Division,Office of Basic Energy Sciences,Office of Science,U.S.Department of Energy(Grant No.DE-FG02-86ER13491)Air Force Office of Scientific Research,USA(Grant No.FA9550-14-1-0255)
文摘With the development of laser technologies,multi-color light-field synthesis with complete amplitude and phase control would make it possible to generate arbitrary optical waveforms.A practical optimization algorithm is needed to generate such a waveform in order to control strong-field processes.We review some recent theoretical works of the optimization of amplitudes and phases of multi-color lasers to modify the single-atom high-order harmonic generation based on genetic algorithm.By choosing different fitness criteria,we demonstrate that：（i） harmonic yields can be enhanced by 10 to 100 times,（ii） harmonic cutoff energy can be substantially extended,（iii） specific harmonic orders can be selectively enhanced,and（iv） single attosecond pulses can be efficiently generated.The possibility of optimizing macroscopic conditions for the improved phase matching and low divergence of high harmonics is also discussed.The waveform control and optimization are expected to be new drivers for the next wave of breakthrough in the strong-field physics in the coming years.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12274230,91950102,and 11834004)the Funding of Nanjing University of Science and Technology (Grant No.TSXK2022D005)the Postgraduate Research&Practice Innovation Program of Jiangsu Province of China (Grant No.KYCX230443)。
文摘We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12274230,91950102,and 11834004)the Funding of Nanjing University of Science and Technology (Grant No.TSXK2022D005)。
文摘The extreme ultraviolet(XUV)light beam carrying orbital angular momentum(OAM)can be produced via high-order harmonic generation(HHG)due to the interaction of an intense vortex infrared laser and a gas medium.Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node(from 0 to 2)in the driving laser consisting of two mixed Laguerre-Gaussian(LG)beams.We find that due to the change in spatial profile of HHG,the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node.We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes.Through the map of coherence length and the evolution of harmonic field in the medium,we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node.We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11264036,11364038,and 11465016)
文摘We investigate the plasmonic-field-enhanced high-order harmonic generation（HHG） of H atom driven by few-cycle laser pulses, by solving the time-dependent Schr？dinger equation（TDSE）. Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase（CEP） of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91950203,11874374,61690223,and 11774363)the Youth Innovation Promotion Association of the Chinese Academy Sciencesthe Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB16)。
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12074239 and 91850209)the Natural Science Foundation of Guangdong Province,China(Grant Nos.2020A1515010927 and 2020ST084)+3 种基金Department of Education of Guangdong Province,China(Grant Nos.2019KTSCX038 and 2020KCXTD012)Shantou University(Grant No.NTF18030)the Natural Science basic Research Program of Shaanxi Province,China(Grant No.2022JM-015)Scientific Research Foundation of SUST(Grant No.2017BJ-30).
文摘Subcycle spectral structures and dynamics of high-order harmonic generation(HHG)processes of atoms and molecules driven by intense laser fields on the attosecond time scale have been originally studied theoretically and ex-perimentally.However,the time scale of HHG dynamics in crystals is in the order of sub-femtosecond,and the carrier dynamics of HHG in crystals driven by subcycle laser pulses are largely unexplored.Here we perform a theoretical study of subcycle structures,spectra,and dynamics of HHG of crystals in mid-infrared laser fields subject to excitation by a subcycle laser pulse with a time delay.The HHG spectra as a function of time delay between two laser fields are cal-culated by using a single-band model for the intra-band carrier dynamics in crystal momentum space and by solving the time-dependent Schr?dinger equation in velocity gauge for the treatment of multi-band crystal systems.The results exhibit a complex time-delay-dependent oscillatory pattern,and the enhancement and suppression of the HHG related to subcycle pulse are observed at the given time delay in either single-band or multi-band crystal systems.To understand oscillation structures with respect to the dependence for the subcycle laser fields,the time-frequency characteristics of the HHG as well as the probability density distribution of the radiation are analyzed in detail.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11764038, 11864037, 11765018, and 11664035)the Science Foundation of Northwest Normal University, China (Grant No. NWNU-LKQN-17-1).
文摘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.
基金supported by the Natural Science Foundation of Jilin Province (Grant No.20220101010JC)the National Natural Science Foundation of China (Grant No.12074146)。
文摘High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.
