Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method

Tong, Xiao-Min; Chu, Shih‐I

doi:10.1016/s0301-0104(97)00063-3

Cited by 416 publications

(264 citation statements)

References 29 publications

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“…These results are corroborated with the ab initio solution of the TDSE in the SAE approximation [2,24,25]. The existence of the shifted ATI peaks with different values of the ponderomotive energy appears also in the TDSE calculations (Fig.…”

Section: The Pe Spectra For a Continuous Envelopesupporting

confidence: 77%

Nonconstant ponderomotive energy in above-threshold ionization by intense short laser pulses

et al. 2016

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We analyze the contribution of the quiver kinetic energy acquired by an electron in an oscillating electric field to the energy balance in atomic ionization processes by a short laser pulse. Due to the time dependence of this additional kinetic energy, a temporal average is assumed to maintain a stationary energy conservation rule. This rule is used to predict the position of the peaks observed in the photo electron spectra (PE). For a flat top pulse envelope, the mean value of the quiver energy over the whole pulse leads to the concept of ponderomotive energy Up. However for a short pulse with a fast changing field intensity a stationarity approximation could not be precise.We check these concepts by studying first the photoelectron (PE) spectrum within the Semiclassical Model (SCM) for a multiple steps pulses. The SCM offers the possibility to establish a connection between emission times and the PE spectrum in the energy domain. We show that PE substructures stem from ionization at different times mapping the pulse envelope. We also present the analysis of the PE spectrum for a realistic sine-squared envelope within the Coulomb-Volkov and ab initio calculations solving the time-dependent Schrödinger equation. We found that the electron emission amplitudes produced at different times interfere with each other and produce a new additional pattern, that overlap the above-threshold ionization (ATI) peaks.

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Section: The Pe Spectra For a Continuous Envelopesupporting

confidence: 77%

Nonconstant ponderomotive energy in above-threshold ionization by intense short laser pulses

et al. 2016

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“…(2.14) can be solved by expanding the Ψ( r, t) in terms of eigenfunctions, R nl Y lm (r), of the laser-free Hamiltonian, within the box of r ∈ [0, r max ], 15) where radial functions R nl (r) are expanded in a discrete variable representation (DVR) basis set [83] associated with Legendre polynomials, while c nl are calculated using the splitoperator method [84].…”

Section: Semiclassical Theorymentioning

confidence: 99%

“…[202,203]. using the split-operator method [84,150]. After the pump laser is turned off, the rotational wave packet will continue to propagate in the free space,…”

Section: Theory Of Alignment For Linear Moleculesmentioning

confidence: 99%

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

Jin

2013

Springer Theses

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In this thesis, we establish the theoretical tools to investigate high-order harmonic generation (HHG) by intense infrared lasers in a gaseous medium. The macroscopic propagation of both the fundamental and the harmonic fields is taken into account by solving Maxwell's wave equations, while the single-atom (or single-molecule) response is obtained by quantitative rescattering theory. The initial spatial mode of the fundamental laser is assumed either a Gaussian or a truncated Bessel beam. On the examples of Ar, N 2 and CO 2 , we demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continuous harmonic spectrum of Xe due to the reshaping of the fundamental laser field can be used to produce an isolated attosecond pulse by spectral and spatial filtering in the far field. For on-going application of using HHG to ionize aligned molecules, we present the photoelectron angular distribution from aligned N 2 and CO 2 in the laboratory frame, which can be compared directly with future experiments. demonstrate that the available experimental HHG spectra with isotropic and aligned target media can be accurately reproduced theoretically even though the HHG spectra are sensitive to the experimental conditions. We show that the macroscopic HHG can be expressed as a product of a macroscopic wave packet and a photorecombination cross section, where the former depends on laser and experimental conditions while the latter is the property of the target only. The factorization makes it possible to retrieve the single-atom or single-molecule structure information from experimental HHG spectra. As for the multiple molecular orbital contribution in HHG, it causes the disappearance of the minimum in the HHG spectrum of aligned N 2 with the increase of laser intensity, and the position of minimum in HHG spectrum of aligned CO 2 depending on many factors is also attributed to it, which could explain why the minima observed in different laboratories may differ. For an important application of HHG as ultrashort light source, we show that measured continu...

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“…Here we briefly present the method developed by Kulander et al for an atom initially in an s state. There are also other methods, such as the pseudo-spectral method (Tong & Chu, 1997) and those using the velocity gauge (Muller, 1999;Bauer & Koval, 2006). Since we assume linear polarization in the z direction, the angular momentum selection rule tells us that the magnetic angular momentum remains m = 0.…”

Section: Direct Simulation Of the Time-dependent Schrödinger Equationmentioning

confidence: 99%

“…〉 , which in turn we calculate, employing the Ehrenfest theorem, through the relation (Tong & Chu, 1997), where the second term can be dropped as it does not contribute to the HHG spectrum. V(r) is the bare Coulomb potential for a hydrogenic atom.…”

Section: Direct Simulation Of the Time-dependent Schrödinger Equationmentioning

confidence: 99%

High Harmonic Generation

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Field Guide to Nonlinear Optics

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Theoretical study of multiple high-order harmonic generation by intense ultrashort pulsed laser fields: A new generalized pseudospectral time-dependent method

Cited by 416 publications

References 29 publications

Nonconstant ponderomotive energy in above-threshold ionization by intense short laser pulses

Nonconstant ponderomotive energy in above-threshold ionization by intense short laser pulses

Theory of Nonlinear Propagation of High Harmonics Generated in a Gaseous Medium

High Harmonic Generation

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