Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

High-Order Harmonic Generation in the Ionization Process

Jing Chen, Chen Shi–gang, Liu Jie

Published Oct 1, 2000• 1 citation
Publisher

Abstract

Based on the nonperturbative quantum electrodynamics scattering theory for multiphoton ionization developed recently, high-order harmonic generated in the ionization process is discussed. The influence of the Coulomb potential is treated as a perturbation in the expansion of the transition matrix. It is deduced that the harmonic photons are emitted in the resonant process during ionization and the width of the harmonic peaks is just the ionization rate of the atom.

DOI
10.1088/0256-307x/17/10/008

Related papers

Theory of resonant multiphoton processes

C. S. Chang

The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order ${10}^{8}$ W/${\mathrm{cm}}^{2}$) is determined by the intensity-dependent level width ($6f$ configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order ${10}^{12}$ W/${\mathrm{cm}}^{2}$) are determined by both the intensity-dependent widths and shifts a$\stackrel{\mathrm{`}}{\mathrm{s}}$ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.

Physical Review A•May 1, 1974•14 citations

Nonperturbative theory of harmonic generation in helium under a high-intensity laser field: The role of intermediate resonance and of the ion

Huale Xu, Xian Tang, P. Lambropoulos

The time-dependent Schr\"odinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.

Physical Review A•Sep 1, 1992•68 citations

Quantum-optical analysis of high-order harmonic generation

Javier Rivera Deán

High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.

•Sep 9, 2019•1 citation

Theory of the effect of third-harmonic generation on three-photon resonantly enhanced multiphoton ionization in focused beams

M. G. Payne, W. R. Garrett

Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for $n$-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.

Physical Review A•Dec 1, 1983•72 citations

Quantum Electrodynamic Perspective on Multiphoton Ionization

Jing Chen, X. T. He, Jie Liu

A fully quantum nonperturbative method is developed to describe multiphoton ionization in intense fields. It is shown that, treating the radiation field with quantum electrodynamic(QED) theory enables us to obtain the above-threshold ionization energy distribution spectrum in analytical form firstly. Moreover, in addition to the well-known semiclassical theory, the framework presented here, derived from a QED perspective, provides a new picture of the multiphoton ionization.

Chinese Physics Letters•Dec 1, 1999•2 citations

NONLINEAR EFFECTS IN ELECTRON AND PHOTON EMISSION FROM ATOMS IN INTENSE LASER FIELDS

Kenneth J. Schäfer, Jeffrey L. Krause, K. C. Kulander

Atoms subject to intense laser fields are capable of absorbing many more photons than the minimum number needed to ionize. This leads to two striking nonlinear phenomena, above-threshold ionization, and high-order harmonic generation. We have used time-dependent methods to calculate both these processes nonperturbatively for realistic, three-dimensional atoms. This allows us to clarify the relationships between photon and electron emission rates in the strong field regime.

Journal of Nonlinear Optical Physics & Materials•Apr 1, 1992•12 citations
Based on the nonperturbative quantum electrodynamics scattering theory for multiphoton ionization developed recently, high-order harmonic generated in the ionization process is discussed. The influence of the Coulomb potential is treated as a perturbation in the expansion of the transition matrix. It is deduced that the harmonic photons are emitted in the resonant process during ionization and the width of the harmonic peaks is just the ionization rate of the atom.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
The time-dependent Schr\"odinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.
High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.