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

Physical Review A

Third-harmonic generation and resonant multiphoton ionization: Mean-field model and quasistatic approximation

Michel Poirier

Published Mar 1, 1988• 2 citations
Publisher

Abstract

Harmonic-generation processes at high laser intensity are strongly affected by resonant multiphoton ionization. In this paper coexistence of these phenomena at low pressure and high intensity is taken into account with use of a mean-field theory. New consequences of this model are derived, especially for resonances strongly damped by ionization. Available experimental data on mercury agree qualitatively with this model. A second approach, called the quasistatic approximation, is used to get analytical solutions for mean-field equations, in good agreement with numerical results. Furthermore, possible applications of the quasistatic approximation to the study of harmonic generation at both high pressure and high laser intensity are mentioned.

DOI
10.1103/physreva.37.1620

Related papers

Competition between resonant multiphoton ionization and third-harmonic generation: A mean-field model

Michel Poirier

In connection with a recent experiment of vacuum-ultraviolet generation in multiphoton resonant ionization of xenon at increasing pressure, a model is elaborated to account for the simultaneous effect of a laser excitation tuned near a three-photon resonance and a pressure-induced emission from the resonant state to the ground state. Under certain assumptions usual in various super-radiance treatments, a system of Bloch equations is derived and numerically solved. The dependence of the ionization probability and third-harmonic production versus the interaction time, gas pressure, dynamical detuning, and laser intensity is extensively studied. A transition between a high and low ionization rate is observed when the pressure increases simultaneously with the disappearance of Rabi oscillations and a saturation of third-harmonic generation. An order-of-magnitude calculation reveals that such phenomena are accessible to experiment and a qualitative comparison with the above-mentioned results in xenon is found to be satisfactory.

Physical Review A•Feb 1, 1983•28 citations

Harmonic generation and multiphoton ionization near an autoionizing resonance

G. Alber, P. Zoller

We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses.

Physical Review A•Mar 1, 1983•32 citations

Resonant multiphoton ionisation and third-harmonic generation in mercury vapour

Didier Normand, J. Morellec, Jürgen Reif

The interaction of intense dye laser radiation (up to about 100 GW cm -2 ) with Hg vapour in the pressure region of 10 15 to 10 -1 Torr leads to competition between multiphoton ionisation-dominant at low pressure-and third-harmonic generation ( approximately 1850AA) prevailing at high pressure. In particular, third-harmonic generation enhanced by a four-photon resonance is-to the authors' knowledge-reported for the first time.

Journal of Physics B Atomic and Molecular Physics•Apr 28, 1983•34 citations

Two-Photon Resonant Third Order Harmonic Generation from Atoms and Ions Interacting with Intense Short Laser Pulses

Young Soon Kim, Jung Seock Choi, Baek Il Nam +4 more

We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.

Key engineering materials•Jan 15, 2005•1 citation

Quantum theory of the competition between multiphoton ionization and third-harmonic generation

G. S. Agarwal, Surya P. Tewari

A quantum-mechanical formulation for the generation of third-harmonic radiation in an atomic medium undergoing three-photon resonant multiphoton ionization is given. The generation of the third harmonic is treated as a cooperative emission and its pressure dependence is shown to be in agreement with experiments. The formulation is general enough to include both transient and steady-state phenomena and includes both traveling-wave and standing-wave cases. A comparison of the results of the present theory with those of Jackson and Wynne is given.

Physical Review A•Apr 1, 1984•42 citations

Resonantly Enhanced Multiphoton Ionization and Third-Harmonic Generation in Xenon Gas

John C. Miller, R. N. Compton, M. G. Payne +1 more

Resonantly enhanced multiphoton ionization signals through the $6s[\frac{3}{2}]J=1$ state of Xe rapidly disappear at pressures above 0.30 Torr; concurrently, intense, vacuum-ultra-violet third-harmonic radiation is detected in the forward direction. Laser excitation spectra of the vacuum ultraviolet light exhibit increasing blue shifts and bandwidths with increasing pressure. The observed competition between ionization and third-harmonic generation is discussed in terms of a model involving fast collective emission.

Physical Review Letters•Jul 14, 1980•178 citations
Harmonic-generation processes at high laser intensity are strongly affected by resonant multiphoton ionization. In this paper coexistence of these phenomena at low pressure and high intensity is taken into account with use of a mean-field theory. New consequences of this model are derived, especially for resonances strongly damped by ionization. Available experimental data on mercury agree qualitatively with this model. A second approach, called the quasistatic approximation, is used to get analytical solutions for mean-field equations, in good agreement with numerical results. Furthermore, possible applications of the quasistatic approximation to the study of harmonic generation at both high pressure and high laser intensity are mentioned.
In connection with a recent experiment of vacuum-ultraviolet generation in multiphoton resonant ionization of xenon at increasing pressure, a model is elaborated to account for the simultaneous effect of a laser excitation tuned near a three-photon resonance and a pressure-induced emission from the resonant state to the ground state. Under certain assumptions usual in various super-radiance treatments, a system of Bloch equations is derived and numerically solved. The dependence of the ionization probability and third-harmonic production versus the interaction time, gas pressure, dynamical detuning, and laser intensity is extensively studied. A transition between a high and low ionization rate is observed when the pressure increases simultaneously with the disappearance of Rabi oscillations and a saturation of third-harmonic generation. An order-of-magnitude calculation reveals that such phenomena are accessible to experiment and a qualitative comparison with the above-mentioned results in xenon is found to be satisfactory.
We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses.
We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.
A quantum-mechanical formulation for the generation of third-harmonic radiation in an atomic medium undergoing three-photon resonant multiphoton ionization is given. The generation of the third harmonic is treated as a cooperative emission and its pressure dependence is shown to be in agreement with experiments. The formulation is general enough to include both transient and steady-state phenomena and includes both traveling-wave and standing-wave cases. A comparison of the results of the present theory with those of Jackson and Wynne is given.
Resonantly enhanced multiphoton ionization signals through the 6s[32]J=16s[\frac{3}{2}]J=16s[23​]J=1 state of Xe rapidly disappear at pressures above 0.30 Torr; concurrently, intense, vacuum-ultra-violet third-harmonic radiation is detected in the forward direction. Laser excitation spectra of the vacuum ultraviolet light exhibit increasing blue shifts and bandwidths with increasing pressure. The observed competition between ionization and third-harmonic generation is discussed in terms of a model involving fast collective emission.