Optimization of High-Order Harmonic by Genetic Algorithm for the Chirp and Phase of Few-Cycle Pulses

The brightness of a particular harmonic order is optimized for the chirp and initial phase of the laser pulse by genetic algorithm. The influences of the chirp and initial phase of the excitation pulse on the harmonic spectra are discussed in terms of the semi-classical model including the propagation effects. The results indicate that the harmonic intensity and cutoff have strong dependence on the chirp of the laser pulse, but slightly on its initial phase. The high-order harmonics can be enhanced by the optimal laser pulse and its cutoff can be tuned by optimization of the chirp and initial phase of the laser pulse.     

Plasma effect on the phase matching of high harmonic generation

By optimizing the phase matching condition of high harmonic generation(HHG) from a supersonic neon gas jet,the enhanced HHG in the region of 60-70 eV has been selected.Three-dimensional numerical calculation shows that plasma plays a significant role in the phase matching process of HHG in a supersonic gas jet with short medium length.Due to plasma formation,the harmonic emission decays as the laser intensity reaches over 3.5 × 10 14 W/cm 2.The plasma induces the broadening and blue shift of the HHG spectra,which provides a method for fine-tuning the harmonic wavelength.     

Theoretical investigation on generating terahertz radiation from gas plasma induced by three-color ultrashort lasers

Generation of intense broadband terahertz(THz) waves from gas plasma induced by tri-color ultrashort(fundamental(ω), second harmonic(2ω), and third harmonic(3ω)) laser pulses is theoretically investigated. Simulation results show that the 3ω laser pulse can greatly enhance or suppress the generation of THz wave at different values of relative phase(θ 3) between the 3ω and ω fields. Moreover, the polarities of the generated THz waves can be controlled by changing θ 3,with the relative phase θ 2(between the 2ω and ω fields) fixed to be a certain value. All of our results show that θ 3 plays a key role in the generation process, which promises to control the intensity as well as the polarity of gas plasma-induced THz radiation.     

Frequency dependence of quantum path interference in non-collinear high-order harmonic generation

High-order harmonic generation(HHG) driven by two non-collinear beams including a fundamental and its weak second harmonic is numerically studied. The interference of harmonics from adjacent electron quantum paths is found to be dependent on the relative delay of the driving pulse, and the dependences are different for different harmonic orders.This frequency dependence of the interference is attributed to the spatial frequency chirp in the HHG beam resulting from the harmonic dipole phase, which in turn provides a potential way to gain an insight into the generation of high-order harmonics. As an example, the intensity dependent dipole phase coefficient α is retrieved from the interference fringe.     

Generation of high-order harmonic continuum with two-hump-structure infrared laser pulse

We experimentally investigate the high-order harmonic generation in argon gas cell driven by a multi-cycle broadband infrared laser pulse from a tunable optical-parametric-amplifier （OPA） source. The generation of high-order harmonic continuum with the cut-off photon energy up to 110 eV is observed by tuning the chirp of the 800-nm laser pulse which pumps OPA source. The generation of harmonic continuum is understood in terms of the two-hump structure of the OPA output spectrum and the optimal relative phase of the two humps. The demonstrated scheme is of importance for the generation of extreme ultraviolet （XUV） continuum at higher photon energy region.     

Optimization of Single or Range of Harmonics by Using Two Gas Jets

The interference of high-order harmonics generated by two successive gas jets within a single laser pulse is discussed by a modeling with the inclusion of macroscopic propagation of the fundamental and harmonic fields in an ionizing medium. Based on the interference, we show that one can extract the laser Rayleigh range from the interference of harmonics and the accuracy of retrieve is independent of carrier-envelope phase while dependent on the pulse duration. Moreover~ we demonstrate that it is possible to optimize the single or range of harmonics with a high ratio relative to the adjacent orders by changing the separation of two gas jets, which is unavailable by using a single gas jet and linear polarized laser pulse.     

Fifth—Order Harmonic Generation using a Coherent Controlled Two—Pulsed Optical Field

We have experimentally studied the characteristics of fifth-order harmonic radiation produced by two coherent femtosecond laser pulses with a changeable relative phase.The intensities of harmonic generation are found to increase with the coherent degree.In one optical Period,the temporal variation of harmonics exhibits an asymmetric characteristic,which is interpreted in terms of ionization theory and the deformation of the wave packets of fundamental field contribution to harmonic generation.     

Experimental study of conversion from atomic high—order harmonics to x—ray emissions

There are two physical phenomena in a strong laser intensity. One is the high-order harmonic emission; the other is x-ray emission from optical-field ionized plasmas. The experiment of conversion from high-order harmonics to x-ray emissions was given with a 105fs Ti:sapphire laser by adjusting laser intensities. The ingredient in plasma was investigated by the numerical simulations.Our experimental results suggested that the free electrons have detrimental effects on harmonic generation but are favourable for x-ray emission from optical-field ionized plasmas. If we want to obtain more intense harmonic signals as a coherent light source in the soft x-ray region, we must avoid the production of free electrons in plasmas. At the same time, if we want to observe x-rays for the development of high-repetition-rate table-top soft x-ray lasers, we should strip all atoms in the plasmas to a necessary ionized stage by the optical-field-ionization in the field of a high-intensity laser pulse.     

Phase Control of Few-Cycle Coherent Terahertz Radiation Pulses

We report a method to control the carrier-envelope phase shift in nearly single-cycle coherent terahertz (THz) radiation pulses, in which we used Kerr effect and two-photon absorption in the generated crystals due to the pump beam peak intensity. Dependence of relative carrier-envelope phase shift of THz pulses on the pump beam intensity in the ZnTe crystal was measured experimentally. Under our experimental condition, we measured that maximum relative phase shift is 0.29 radians.     

Phase Relation of Harmonics in Nonlinear Focused Ultrasound

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimentally.The nonlinear Westervelt equation is solved to model nonlinear focused sound held by using the finite difference time domain method.Experimental waveforms are measured by a robust needle hydrophone.Then the relative phase quantity is introduced and obtained by using the zero-phase filter.The results show that the nth harmonic relative phase quantity is approximately(n—1)π/3 at geometric center and increases along the axial direction.Moreover,the relative phase quantity decreases with the increase of source amplitude.This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.     

The focus steering for high intensity focused ultrasound phased array based on real-time phase shift calculation

When time reversal technique is used in phased array high intensity focused ultrasound system to obtain self-adaptive focusing,it is needed to calculate the initial phases of the elements.Because of the frequency oscillation when the phase lock loop is initiated,different results are got in different segments using conventional methods.A method of calculating the phase difference was presented,that can display the changes of phase difference in real-time, and the steady phase differences can be regarded as the initial phases of the elements.The experimental results show that using the phase difference obtained by this method can get a better distribution of sound field in a certain spatial region.     

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.     

Symmetries and variational calculation of discrete Hamiltonian systems

We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.     

Sideband manipulation of population inversion in a three-level Λ atomic system

Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to π, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion ρ00 〉 ρ11 also becomes wider evidently.     

Coherent phase control in electron argon scattering in a bichromatic laser field

This paper theoretically investigates the coherent phase control in electron--argon scattering assisted by a bichromatic laser field. The laser field is composed of a fundamental component and its second harmonic. The incoming and out going states of electron are described by the Volkov wave functions, and the electron--target interaction is treated as a screening potential. Numerical results for differential cross section of multiphoton processes vs the phase difference between the two components of laser field are discussed for several scattering angles and impact energies.     

Rotating soliton clusters in nonlocal nonlinear media

From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π     

High-Order Harmonic Generation by Two Non-Collinear Femtosecond Laser Pulses in CO

We have experimentally studied the high order harmonic generation (HHG) in CO molecules by two femtosecond laser pulses using a pump-probe technique. The delay time between two pulses is longer than the pulse duration, and the pump intensity is about 6.2 x 10^14 W/cm^2. It is found that the HHG signal is independent of the time delay in the picosecond region, but it is dependent on the distance between the centres of focuses of the two beams. The phase modulation induced by the pump pulse is regarded to be responsible for this.     

Frequency doubling of phase-modulated femtosecond laser pulses in periodically poled and chirped nonlinear crystals

The second harmonic generation (SHG) at a wavelength of 0.8 μm by 50-and 10-fs pulses with and without phase modulation (PM) was systematically studied in LiNbO₃ crystals with regular domain structure and linearly varied domain thickness. The main results were obtained by numerical method, taking into account the difference between group velocities of interacting pulses and the group-velocity dispersion. In the approximation of the given field of the fundamental radiation, an analytical expression was derived for the spectral density of the second harmonic in the periodically poled nonlinear crystal (PPNC) under nonstationary excitation conditions. It was numerically found that the conversion efficiency of about 90% can be achieved by doubling the frequency of 50-fs laser pulses without PM in the LiNbO₃ PPNC. The maximum conversion efficiency for the SHG by PM pulses is achieved at a certain optimum chirp step in the crystal domain length, which depends on both the value and sign of frequency modulation.     

Carrier Envelope Phase Controlled High-Order Harmonic Generation in Ultrashort Laser Pulse

We investigate the carrier envelope phase （CEP） effects on high-order harmonic generation （HHG） in ultrashort pulses with the pulse duration 2.5 fs when the laser intensity is high enough so that the initial state is ionized effectively during the laser pulse but remains about 20% population at the end of the laser pulse. We find that the ionization process of the initial state is very sensitive to the CEP during the laser pulse. The ionization process of the initial state determines the continuum state population and hence influences dramatically the weights of the classical trajectories that contribute to HHG. In such a case we can not predict the cutoff and the structure of the harmonic spectrum only by the number and the kinetic energy of the classical trajectories. The harmonic spectrum exhibits abundant characters for different CEP cases. As a result, we can control the cutoff frequency and the plateau structure of the harmonic spectrum with CEP by controlling the time behaviour of the ionization of the initial state.