Carrier-Envelope-Phase Dependence of Emission Properties of High-Order Harmonic Generation

The carrler-envelope-phase （CEP） dependence of the emission properties of high-order harmonic generation （HHG） are quantitatively investigated. Calculation shows that a two-cycle laser with CEP of 15° can produce a single energy distribution pulse peaked at 0.94 radian （tad） and spanned 1.29 tad with the cutoff energy 2.9Up ＋ Ip and a bandwidth 0.86Up （where Up is the ponderomotive potential of the laser field and Ip is the atomic ionization potential）. The CEP dependence of the energy and temporal localizations of the single distribution pulse show interesting 180° periodic structures. These characteristics may be useful in optimizing attosecond x-ray sources and measurements.     

Enhancement of Bichromatic High-Order Harmonic Generation by a Strong Laser Field and Its Third Harmonic

We investigate high-order harmonic generation （HHG） in a linearly polarized bichromatic field composed of a fundamental laser field with frequency w and an additional laser field with frequency 3w. The numerical results show that it is possible to enhance the intensity of most high harmonics in orders of magnitude. A most striking feature in the enhancement is that the intensity of several special high harmonics is practically impaired as compared with that in the monochromatic case. The qualitative explanation to the great enhancement is that the additional high-frequency field can provide new transition paths for electrons to reach the continuum. The relative phase between the fundamental field and its third harmonic field also affects the intensity of high-order harmonics near the cutoff efficiently.     

Single X-Ray Attosecond Pulse Generation by Using Combined Pulses Irradiating on a United Two-Atom System

A scheme of a single x-ray attosecond pulse generation from a two-atom system exposed to the combined laser pulses is proposed. Our numerical results show that a single x-ray attosecond pulse rather than a train one can be produced by modulation of ionization. Furthermore, when we change the peak intensity Ih of the high-frequency pulse and keep the intensity of the low-frequency pulse constant, we can find that a range of Ih where the intensity of the attosecond pulse is optimal is available, and a explanation by the stimulated property of the recombination is also presented.     

Generation of a Super Strong Attosecond Pulse from an Atomic Superposition State Irradiated by a Shape-Optimized Short Pulse

Using a linearly polarized, phase-stabilized 3-fs driving pulse of 800 nm central wavelength shape-optimized on its＇ascending edge by its an amplitude-reduced pulse irradiating on a superposition state of the helium atom, we demonstrate theoretically the generation of a super strong isolated 176-attosecond pulse in the spectral region of 93-124 eV. The unusually high intensity of this attosecond pulse is marked by the Rabi-like oscillations emerging in the time-dependent populations of the ground state and the continuum during the occurrence of the electron recombination, which is for the first time observed in this work.     

A Theoretical Strategy to Generate an Isolated 80-Attosecond Pulse

Using a linearly polarized, phase-stabilized 2.66-femtosecond driving pulse of 400 nm central wavelength orthogonally combined with another linearly polarized long pulse of 800 nm central wavelength irradiating jointly on the helium atom, we demonstrate theoretically the generation of a clean isolated 80-attosecond pulse in the spectral region of 93-155 electron volts in a two-dimensional model.     

Strengthened Hyper-Raman Lines with the Coherent Superposition State

High-order harmonic generations from a one-dimensional Coulomb potential atom are calculated with the initial state prepared as a coherent superposition between its ground and first excited states. When the energy difference of the two states is small, we can choose proper laser pulse such that the first excited state can be excited only to other bound states instead of being ionized. We show that only the hyper-Raman lines are observable instead of the harmonics. The energy difference of the ground and the first excited state can be deduced from the highest peak of the hyper-Raman lines. We further show that the similar results can be obtained by using a combination of two laser pulses with different frequencies interacting with the atom initially at the ground state.     

Ultrahigh Harmonic Generation from an Atom with Superposition of Ground State and Highly Excited States

We investigate the high-order harmonic generation from an atom prepared in a superposition of ground state and highly excited state. When the atom is irradiated by an ultrashort pulse, the cutoff position of the plateau in the harmonic spectrum is largely extended compared with the case that the atom is initially in the ground state. The physics of the extension of the high-order harmonic plateau can be interpreted by the spatial structure of the atomic initial wave packet. We can optimize the generation of high-order harmonics by substituting the excited state for a particular coherent superposition of some highly excited states to form a spatially localized excited wave packet.     

Kilohertz extreme-ultraviolet light source based on femtosecond high-order harmonic generation from noble gases

A compact, versatile table-top kilohertz source of coherent extreme-ultraviolet (XUV) radiation in the wavelength region 18–100 nm, based on high-order harmonic generation from noble gases induced by a 40-femtosecond Ti:sapphire laser system, is presented. The XUV beamline delivers at its output 10⁸ photons/s at a wavelength of 23 nm. The monochromatized XUV radiation is directly focused onto a 10^-2-mm² spot by a toroidal grating, allowing one to reach intensities higher than 10⁶ W/cm². Optimization results are presented for a new XUV-generating geometry, utilizing a ‘semi-infinite’ quasi-static gas cell and strong focusing. In those conditions, we observe an anomalous inversion between the cutoffs of argon and krypton, with the krypton spectrum extending to much higher orders than expected in an adiabatic limit. Received: 9 July 2001 / Revised version: 1 August 2001 / Published online: 7 November 2001     

High-Order Above-Threshold Ionization of H2+ in Intense Laser Field

The nonperturbative quantum electrodynamies method proposed by Fu et al. [Phys. Rev. A 75 （2007） 063419] is employed to study the high-order above-threshold ionization （ATI） of a diatomic molecule. Based on this frequency-domain theory, the high-order ATI process can be regarded as ATI followed by laser-assisted collision, where the total transition amplitude is the coherent summation of the contributions from each ATI channel. The angular-resolved ATI spectrum, which agrees with the results by Becket et al. based on the time-domain method, is obtained by this frequency domain theory. Furthermore, it is demonstrated that the interference characteristics representing the molecular structure in the ATI spectrum originates from the recollision of the electron with two-centre ion in each ATI channel.     

Harmonic Enhancement Mechanism of a Superposition State Atom Irradiated by Short Pulses

We investigate the high-order harmonic generation （HHG） of a model atom whose initial state is prepared in a superposition of its ground state and an excited state irradiated by different duration laser pulses. Compared to the HHG generated from an atom whose initial state is in its ground state, its conversion efficiency obtains some enhancement. The enhancement originates from the higher ionization rate （rather than the ionization yield） of the atom with superposition initial state.     

Tracking individual electron trajectories in a high harmonic spectrum

The harmonic spectrum generated by a few-cycle laser pulse propagating through a gas jet is calculated. Two complementary atomic response models are used, one based on the time-dependent Schrödinger equation and the other on quantum orbits in which only a single pair of electron trajectories are taken into account. The role played by individual electron trajectories in determining particular features of the spectrum are considered and phase-matching maps are used to help understand their structure. A method based on this connection is proposed for diagnosing the carrier-envelope phase and the pulse duration of the incident laser field.     

Approach to extreme ultraviolet supercontinuum in a two-color laser field

In recent years, it has been shown that an intense few-cycle driving pulse combined with a weak control pulse could efficiently extend the harmonic spectrum in the generation of high-order harmonics (HHG). In this paper, we adjust the intensities of the driving and control pulse to generate broader extreme ultraviolet (XUV) supercontinuum. We find that in some special situation when the intensity of the control pulse equals to that of the driving pulse, a clean supercontinuum as long as 80 eV can be realized and a 53-as pulse can be straightforwardly obtained.     

Measurement of Carrier-Envelope Phase and Field Strength of a Few-Cycle Pulse by Non-sequential Double Ionization

We propose a method to measure the carrier-envelop phase （CEP） and the intensity of a few-cycle pulse by controlling the non-sequentiai double ionization （NSDI） process. By using an additional static electric field, we can change the momentum distribution of the double-charged ions parallel to the laser polarization from an asymmetrical double-hump structure to a nearly symmetrical one. It is found that the ratio between the strength of the static electric field and that of the laser field is sensitive to the CEP but robust against the intensity fluctuation. Therefore we can determine the OEP of a few-cycle pulse precisely by measuring the static electric field. Fhrthermore, if the CEP of the few-cycle pulse is fixed at a certain value, we can also calibrate the intensity of the laser pulse by the static electric field.     

Coloured Conical Emission in BBO Crystal Pumped by Second Harmonic Femtosecond Pulses

Coloured conical emission （CCE） is investigated experimentally in a β-barium borate crystal excited by intense second harmonic femtosecond pulses. Contrary sequences of green and red conical emission with variable diameters are observed at different incidence angles, which is consistent with the calculation results based on the phase matching condition. As its broad range spectrum, CCE offers an alternative means to produce an ultrafast broadband light source. It is found that the spectrum of green CE shifts toward longer wavelengths as the length of BBO crystal increased.     

Optimized Second Harmonic Generation of Femtosecond Pulse by Phase-Blanking Effect in Aperiodically Optical Superlattice

In order to minimize the effect of the unconsidered frequency components on the generated compression pulse, the phasing-blanking effect is taken into account of designing the one~dimensionai aperiodic domain reversal structure. Hierarchic genetic algorithm for the design of a domain reversal grating to modulate the spectrum and phase of the generated SH pulse simultaneously are presented. Our simulation shows that the quality of an output pulse is fairly improved.     

Harmonic generation in an ionized gas medium with a 100-femtosecond, high repetition rate laser source at intermediate intensities

 We report the realization of a vacuum-ultraviolet radiation source based on high-order harmonic generation in noble-gas samples, operating at high repetition rate. In particular, we observed up to the 13th harmonic (λ=61 nm) of the fundamental frequency of a short pulse, high repetition rate titanium–sapphire laser after its interaction with a Xe gas jet. The effects of the propagation of the fundamental and harmonic beams through an ionized medium are studied by analysing the spectral profile of the 9th and 7th harmonics. Finally, we report a study of the dependence of the harmonic conversion efficiency on relative position of the focus and the gas target. Received: 29 March 1996/Revised version: 25 July 1996     

Generalized Pseudospectral Method for Solving the Time-Dependent Schrödinger Equation Involving the Coulomb Potential

We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrödinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.     

Extreme Ultraviolet Pulse Shaping with Aligned Molecules

We theoretically propose a simple scheme to shape the extreme ultraviolet pulse on the attosecond timescale with the aligned molecule. This may offer a new way to manipulate and control photon emission on the attosecond timescale.     

Effects of laser pulsewidth on higher-order harmonic generation in the barrier-suppression-ionization intensity regime

We studied the highest harmonic photon energies of high-order harmonic generation (HHG) for He, Ne, Ar, Kr, Xe, and N₂. This research employed 65-fs and 150-fs Ti:sapphire laser pulses, of which the peak intensities in a vacuum are higher than the barrier-suppression-ionization (BSI) intensities. We fitted two analytical formulae to the experimental results of HHG. One formula, which was obtained by fitting an analytical formula to the results by a quantum mechanical simulation of HHG, expresses the highest interaction intensity by a function of the BSI intensity and the Keldysh γ-parameter. The other formula is derived by introducing the saturation intensity of HHG, which was proposed by Chang et al. [Phys. Rev. Lett. 79, 2967 (1997)]. We discuss the highest interaction intensity for the condition when the peak laser intensities are higher than the BSI intensities. Received: 19 March 1999 / Revised version: 13 August 1999 / Published online: 27 October 1999     

Three-Photon Resonant Nondegenerate Six-Wave Mixing in a Dressed Atomic System

We report a three-photon resonant nondegenerate six-wave mixing （NSWM） in a dressed cascade five-level system. It has advantages that phase match condition is not stringent and NSWM signal is enhanced tremendously due to the multiple resonance with the atomic transition frequencies. In the presence of a strong coupling field, the threephoton resonant NSWM spectrum exhibits＂ Autler-Townes splitting. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.