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Physical Review A

Multiphoton Ionization Induced by Circularly Polarized Radiation

Yves Gontier, M. Trahin

Published Jun 1, 1973• 48 citations
Publisher

Abstract

The ratio ${\ensuremath{\mu}}_{N}$ of the cross section for circularly polarized light to that for linearly polarized is numerically investigated for $N$-photon ionization of atomic hydrogen. For $N<4$, it appears that the gain factor is greater than unity. For $N\ensuremath{\ge}4$, the ratio ${\ensuremath{\mu}}_{N}$ is generally smaller than unity and decreases when the multiphoton order $N$ increases.

DOI
10.1103/physreva.7.2069

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The ratio \ensuremathμN{\ensuremath{\mu}}_{N}\ensuremathμN​ of the cross section for circularly polarized light to that for linearly polarized is numerically investigated for NNN-photon ionization of atomic hydrogen. For N<4N<4N<4, it appears that the gain factor is greater than unity. For N\ensuremath≥4N\ensuremath{\ge}4N\ensuremath≥4, the ratio \ensuremathμN{\ensuremath{\mu}}_{N}\ensuremathμN​ is generally smaller than unity and decreases when the multiphoton order NNN increases.
The infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.
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.