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

Theory of photoelectron angular distributions in resonant multiphoton ionization

S. N. Dixit, P. Lambropoulos

Published Feb 1, 1983• 121 citations
Publisher

Abstract

In this paper, we present the theory of photoelectron angular distributions in resonant multiphoton ionization that rigorously takes into account the saturation, ac Stark-shift, and the laser-linewidth effects. The influence of these effects on the distribution is incorporated through the coupling equations between the angle-resolved ionization probabilities and the (time-dependent) bound-state density-matrix elements. General expressions for the angular distributions are derived and several properties of these distributions are arrived at from these expressions. Finally, numerical results are presented to illustrate the effects of saturation, of ac Stark shifts, and of the laser line shape.

DOI
10.1103/physreva.27.861

Related papers

Angular Distribution of Photoelectrons in Strongly Driven Multiphoton Transitions

S. N. Dixit, P. Lambropoulos

The behavior of photoelectron angular distributions in a strongly driven resonant multiphoton ionization process is discussed. It is shown that the angular distribution changes drastically with increasing intensity as a result of the ac Stark shifting of the levels. Moreover, under strong saturation conditions the distribution reaches a limiting form significantly different from the form predicted by perturbation theory. The effects of the laser bandwidth on the angular distribution are also discussed briefly.

Physical Review Letters•May 11, 1981•36 citations

Influence of the dynamic Stark effect on photoelectron angular distributions in multiphoton ionization

W. Ohnesorge, F. Diedrich, Gerd Leuchs +2 more

The influence of the dynamic Stark effect on photoelectron angular distributions for two-photon-resonant three-photon ionization of sodium by way of the $4^{2}D$ fine-structure components has been investigated. Owing to the dynamic Stark shift of the atomic transition frequency, the angular distributions expected at low laser intensities were modified as different transitions were intensity tuned into and out of resonance with the laser frequency. The distributions are in good qualitative agreement with theory.

Physical Review A•Mar 1, 1984•23 citations

ac-Stark-shift-induced photoelectron spin polarization in resonant multiphoton ionization

S. N. Dixit

The influence of the ac-Stark shifts on the spin polarization (SP) of the photoelectron in a resonant multiphoton ionization is discussed. It is shown that the Stark shifts of various levels are different and this removes any initial fine-structure degeneracy of the excited states. This increased dynamic separation between the states increases the SP of the ejected photoelectron. Numerical results are presented to illustrate this effect. By expressing the equations of motion in the spin basis set the precise conditions necessary to observe nonzero SP are identified. It is shown on the basis of these conditions that although the removal of the fine-structure degeneracy occurs independent of whether the atom has any spin-orbit coupling, this does not induce any spin polarization if the atom has no spin-orbit coupling.

Physical Review A•Sep 1, 1982•2 citations

Photoelectron angular distributions from multiphoton ionization of cesium atoms

R. N. Compton, John A. D. Stockdale, C. Dewey Cooper +2 more

We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed $7p^{2}P_{\frac{1}{2},\frac{3}{2}}$ and $8p^{2}P_{\frac{1}{2},\frac{3}{2}}$ intermediate states and three-photon ionization via the two-photon-allowed $8d^{2}D_{\frac{5}{2},\frac{3}{2}}$ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the $^{2}P_{\frac{1}{2}}$ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the $^{2}P_{\frac{3}{2}}$ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the $^{2}P_{\frac{3}{2}}$ data.

Physical Review A•Oct 1, 1984•37 citations

Multiphoton ionization of Ba atoms with photoelectron spectroscopy

A. Yu. Elizarov

An experimental and theoretically study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2(omega) -excited intermediate state 6p2 (1So) and the auto- ionized state 6p8s(3P1). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. Employing the density-matrix formalism, expressions have been obtained for angular dependence of the differential ionizations probability. Possible experiments are discussed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 15, 1999•0 citations

Polarization phenomena in multiphoton ionization of atoms

V. L. Jacobs

The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.

Journal of Physics B Atomic and Molecular Physics•Aug 1, 1973•28 citations
In this paper, we present the theory of photoelectron angular distributions in resonant multiphoton ionization that rigorously takes into account the saturation, ac Stark-shift, and the laser-linewidth effects. The influence of these effects on the distribution is incorporated through the coupling equations between the angle-resolved ionization probabilities and the (time-dependent) bound-state density-matrix elements. General expressions for the angular distributions are derived and several properties of these distributions are arrived at from these expressions. Finally, numerical results are presented to illustrate the effects of saturation, of ac Stark shifts, and of the laser line shape.
The behavior of photoelectron angular distributions in a strongly driven resonant multiphoton ionization process is discussed. It is shown that the angular distribution changes drastically with increasing intensity as a result of the ac Stark shifting of the levels. Moreover, under strong saturation conditions the distribution reaches a limiting form significantly different from the form predicted by perturbation theory. The effects of the laser bandwidth on the angular distribution are also discussed briefly.
The influence of the dynamic Stark effect on photoelectron angular distributions for two-photon-resonant three-photon ionization of sodium by way of the 42D4^{2}D42D fine-structure components has been investigated. Owing to the dynamic Stark shift of the atomic transition frequency, the angular distributions expected at low laser intensities were modified as different transitions were intensity tuned into and out of resonance with the laser frequency. The distributions are in good qualitative agreement with theory.
The influence of the ac-Stark shifts on the spin polarization (SP) of the photoelectron in a resonant multiphoton ionization is discussed. It is shown that the Stark shifts of various levels are different and this removes any initial fine-structure degeneracy of the excited states. This increased dynamic separation between the states increases the SP of the ejected photoelectron. Numerical results are presented to illustrate this effect. By expressing the equations of motion in the spin basis set the precise conditions necessary to observe nonzero SP are identified. It is shown on the basis of these conditions that although the removal of the fine-structure degeneracy occurs independent of whether the atom has any spin-orbit coupling, this does not induce any spin polarization if the atom has no spin-orbit coupling.
We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed 7p2P12,327p^{2}P_{\frac{1}{2},\frac{3}{2}}7p2P21​,23​​ and 8p2P12,328p^{2}P_{\frac{1}{2},\frac{3}{2}}8p2P21​,23​​ intermediate states and three-photon ionization via the two-photon-allowed 8d2D52,328d^{2}D_{\frac{5}{2},\frac{3}{2}}8d2D25​,23​​ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the 2P12^{2}P_{\frac{1}{2}}2P21​​ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the 2P32^{2}P_{\frac{3}{2}}2P23​​ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the 2P32^{2}P_{\frac{3}{2}}2P23​​ data.
An experimental and theoretically study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2(omega) -excited intermediate state 6p2 (1So) and the auto- ionized state 6p8s(3P1). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. Employing the density-matrix formalism, expressions have been obtained for angular dependence of the differential ionizations probability. Possible experiments are discussed.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.