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Le Journal de Physique Colloques

NON-PERTURBATIVE METHODS APPLIED TO MULTIPHOTON IONIZATION

Humberto Siqueira Brandi, L. Davidovich, Nicim Zagury

Published Nov 1, 1982• 3 citations
Publisher

Abstract

We discuss the use of non-perturbative methods in the treatment of atomic ionization. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential, in this manner a criterium concerning the range of application of these non-perturbative scheme is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented.

DOI
10.1051/jphyscol:1982230

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We discuss the use of non-perturbative methods in the treatment of atomic ionization. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential, in this manner a criterium concerning the range of application of these non-perturbative scheme is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented.
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 non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
A nonperturbative treatment of the multiphoton ionization of the hydrogen atom based on the S matrix and devised for nonresonant strong-field situations is analyzed in the weak-field limit. Comparisons are presented with other S matrices as well as other nonperturbative approaches. Our treatment is found to perform generally better than similar S-matrix treatments. The usual perturbative results are recovered provided that the photon wavelengths are sufficiently short and are off resonance with the atomic transitions. Important indications are obtained as to the role of the atomic structure, the relevance of the gauge consistency, and the reliability and improvement of the present nonperturbative treatment. The results represent a significant step toward an assessment of the S-matrix-based treatments of multiphoton ionization.