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Journal of Physics B Atomic and Molecular Physics

Model study of above threshold multiphoton ionisation in strong fields

M Edwards, Laura L. Pan, L Armstrong

Published May 28, 1985• 45 citations
Publisher

Abstract

In a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.

DOI
10.1088/0022-3700/18/10/011

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In a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.
We present an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.
The photoionization of atoms in a strong electromagnetic field leads to the effect of "above-threshold" ionization, displaying a number of peaks in the energy spectrum of the photoelectrons. In the case of a one-electron model atom in a circularly polarized field, we derive expressions that describe the position as well as the intensity of those peaks as a function of the field parameters by means of a nonperturbative method. It is immediately clear from our formulas that the lowest-energy peaks in general disappear with increasing field intensity, for Coulomb-like as well as shortrange potentials. For a zero-range potential, a numerical evaluation is easily performed, leading to results that are in every respect qualitatively similar to the experimental results obtained thus far on these kinds of processes.
Two-laser multiphoton ionisation under the autoionising-like resonance condition is studied theoretically within an extended atomic model dictated by the experiment of Feldmann et al (1986). Ordinary coupling between a selected pair of bound states via the continuum only is supplemented in the author's model by Raman-type coupling involving the atomic spectrum below the ionisation threshold. In the case considered this additional Raman coupling enhances the ionisation rate to a much greater extent than the coupling via the continuum can do. The Raman coupling modifies the autoionising-like shape parameter and is decisive as far as the resonance peak profile is concerned. Exploiting this Raman coupling within the atomic model with four effective bound states, the author gives explanations for all the details of the ionisation spectrum detected by Feldmann et al, i.e. the number of resonance peaks, their strength, fine structure, shape, relative heights and sensitivity to the laser field.
The effective order of non-linearity in multiphoton ionisation is defined by k=( delta lg N)/( delta lg I) where N is the number of ions created by the electromagnetic field with intensity I. Strong variations of k are observed in the vicinity of a resonance. Using a simple model for resonant multiphoton ionisation the author derives an expression for k. He takes into account the spatial distribution when excitation is produced by a Gaussian beam. Both long- and short-pulse excitation are investigated. Theoretical results are applied to the interpretation of four-photon ionisation of Cs I near the 6f resonance. The theoretical results are in good agreement with the experimental data on the effective order of non-linearity.