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Physical Review Letters

Effect of Intensity on Multiphoton Ionization

Yves Gontier, N. K. Rahman, M. Trahin

Published Mar 31, 1975• 26 citations
Publisher

Abstract

For multiphoton processes, the higher-order terms of the perturbation series are treated by summing the class of irreducible diagrams. This allows the examination of the behavior of the cross section as a function of the incident photon flux at arbitrarily large intensities by means of analytic continuation to the nonperturbative region. The case of four-photon ionization of the ground state of hydrogen is discussed as an example.

DOI
10.1103/physrevlett.34.779

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Journal of Physics B Atomic and Molecular Physics•Apr 21, 1975•2 citations
For multiphoton processes, the higher-order terms of the perturbation series are treated by summing the class of irreducible diagrams. This allows the examination of the behavior of the cross section as a function of the incident photon flux at arbitrarily large intensities by means of analytic continuation to the nonperturbative region. The case of four-photon ionization of the ground state of hydrogen is discussed as an example.
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 summation of all the higher-order contributions to multiphoton absorption in atoms is presented. The nonperturbative expressions for the transition amplitudes are expressed in terms of continued fractions. They account for the whole perturbation originated by the radiation field on the atom but do not exhibit explicit expression for the level shift. In the case of radiation fields of high intensity the only reliable determination of the level shift involves a careful location of the poles of the resolvent operator. The theory has been tested in considering a two-level atom. An extremely rapid convergence of the continued fractions has been observed, and accurate results concerning high-order resonance shifts have been obtained. The expressions for the transition amplitudes being nonperturbative with regard to the field strength, they can be considered as analytic continuations of the perturbation series. This provides a useful approach to the problem of ultraintense fields.
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.
An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.
The cross section for multiphoton ionization of hydrogen is computed using the momentum translation method (MTA) in the cases of linearly and circularly polarized light, alternatively. Extended numerical comparison is made with well-established results obtained from the Nth-order time-dependent perturbation theory in the weak intensity limit. The MTA does not reproduce the values given by perturbation theory and considerable differences are observed. Higher order iterations than the lower one are introduced and an analysis of the leading terms of the development is made: at weak intensities the zeroth-order term that defines the MTA cancels with higher order terms and the final result obtained after making (N-1 iterations is none other than the well-known transition amplitude deduced from standard perturbation theory, defined by the remaining terms of the last iteration after mutual cancellation with lower-order ones. According to the results obtained in this work, it is not possible to affirm that the MTA is adequate to calculate atomic multiphoton ionization cross sections.