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Physical Review A

Calculations of high-order harmonic-generation processes in xenon at 1064 nm

Anne L’Huillier, Ph. Balcou, Sébastien M. Candel, Kenneth J. Schäfer, K. C. Kulander

Published Sep 1, 1992• 264 citations
Publisher

Abstract

We perform detailed calculations of harmonic conversion in a 15-Torr jet of xenon into which a 1064-nm-wavelength 36-ps-pulse-width laser has been tightly focused, so that the peak intensity ranges from 5\ifmmode\times\else\texttimes\fi{}${10}^{12}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{13}$ W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. The single-atom emission rates are obtained by integrating the time-dependent Schr\"odinger equation. We employ an improved atomic model which includes excitation and ionization through states with both low-lying ionic cores. The propagation equations are solved using a general and efficient finite-difference technique. Excellent agreement with experimental data is obtained. We consider the effect of the defocusing of the pump beam by the free electrons in the saturation regime, and find it to be small for the conditions studied here. The spatial, temporal, and spectral profiles of the harmonic emission are presented. Significant blueshifts of the harmonics' spectral line shapes are observed in the saturation regime. Finally, using model polarizations, we discuss how the harmonic fields build up in the nonlinear medium, through a series of interferences. It allows us to understand why efficient phase matching can be achieved in a strong-field regime for the laser-atom interaction.

DOI
10.1103/physreva.46.2778

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We perform detailed calculations of harmonic conversion in a 15-Torr jet of xenon into which a 1064-nm-wavelength 36-ps-pulse-width laser has been tightly focused, so that the peak intensity ranges from 5\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012 to 5\ifmmode\times\else\texttimes\fi{}1013{10}^{13}1013 W cm\ensuremath−2{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}cm\ensuremath−2. The single-atom emission rates are obtained by integrating the time-dependent Schr"odinger equation. We employ an improved atomic model which includes excitation and ionization through states with both low-lying ionic cores. The propagation equations are solved using a general and efficient finite-difference technique. Excellent agreement with experimental data is obtained. We consider the effect of the defocusing of the pump beam by the free electrons in the saturation regime, and find it to be small for the conditions studied here. The spatial, temporal, and spectral profiles of the harmonic emission are presented. Significant blueshifts of the harmonics' spectral line shapes are observed in the saturation regime. Finally, using model polarizations, we discuss how the harmonic fields build up in the nonlinear medium, through a series of interferences. It allows us to understand why efficient phase matching can be achieved in a strong-field regime for the laser-atom interaction.
We present ab initio calculations using the RRR-matrix with time dependence (RMT) method for high-order harmonic generation (HHG) in argon in a short, intense pulse regime. The calculations employ a 666-cycle sin⁡2\sin^2sin2 pulse at 850850850 nm with peak intensity 2.3×10142.3\times 10^{14}2.3×1014 W/cm2^22 and, for comparison with the experiment by Guo et al. [J. Phys. B: At. Mol. Opt. Phys. 51, 034006 (2018)], a Gaussian pulse with the same frequency and peak intensity. Both pulse shapes yield the expected harmonic structure in the region above the ionization threshold (approximately 15.8215.8215.82 eV in LSLSLS-coupling). The spectra exhibit strong carrier-envelope-phase (CEP) sensitivity. The energy region leading up to the ionization threshold contains spectral features arising from residual coherent dipole oscillations (free-induction decay) that strongly depend on spectral windowing and the post-pulse propagation time. We show that the HHG spectrum, particularly below the ionization threshold, is a defined quantity that depends on analysis choices rather than being a uniquely determined observable. Comparison between theoretical predictions and experimental observations in this energy regime, therefore, requires explicit specification of these parameters.
The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schr\"odinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26--45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments.
Excitation of xenon near the two-photon resonance between the ground state and the 6p(1/2,0) state produces forward conical emission at a wavelength close to the 828-nm 6p(1/2,0)—6s(3/ 2,1) excited-state transition. We describe experimental features of this process as excited by 600-ps pulses of 250-nm radiation from a frequency-doubled dye laser with intensity up to 1.3 × 108 W/ cm2 in xenon at pressures of 1-20 Torr. The conical emission occurs most prominently when the driving field is a few gigahertz above the frequency at which spontaneous emission from the excited 6p state peaks. The cone angle increases with xenon pressure in the 1-10-Torr range. The dependence appears consistent with the predictions based on noncollinearly phase-matched four-wave mixing. In this interpretation, the fourth wave would be near resonance with the 146.9-nm first resonance transition of xenon and detuned to the low-frequency side. The conical emission co-exists (and may compete with) an axial stimulated process which may be either two-photon driven amplified spontaneous emission or stimulated hyper-Raman scattering. The different tuning characteristics for the two processes make the extent of their competition unclear.
We extend our recently developed semiclassical strong-field Herman-Kluk propagator (SFHK) method to calculate high-order harmonic generation (HHG) for atoms in intense lasers. We show that our method, based on a combination of the Herman-Kluk propagator and the strong-field approximation, can provide highly accurate results for both HHG yield and phase, nearly identical to those from the exact numerical solutions of the time-dependent Schrödinger equation. We provide detailed analyses of our method and its applications to the HHG process, particularly the recombination time. The main computational task in this method is to solve the classical Newton equations for the active electron in the combined atomic potential and laser-electron interaction. The motion of the centers of the electron wave packets, modeled by coherent states, is governed by independent classical trajectories so that the computation can therefore be parallelized very efficiently.
Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-\AA{} radiation by a five-photon mixing process in Li+{\mathrm{Li}}^{+}Li+ is considered.