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Le Journal de Physique Colloques

ATOMS INTERACTING WITH ELECTROMAGNETIC FIELDS, MULTIPHOTON IONIZATION

G. Mainfray

Published Nov 1, 1982• 1 citation
Publisher

Abstract

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.

DOI
10.1051/jphyscol:1982228

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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.
The advent of the laser has brought about a revolution in the kinds of experimental phenomena that can be investigated. In particular, ultra-high power monochromatic, collimated sources have intensities of sufficient magnitude to enable studies to be carried out in the regime where 'non-linear' effects are important, even dominant. Important among these are processes which are characterised by the simultaneous absorption of two or more optical photons. While multiple photon processes are not completely new, those in the optical part of the spectrum, like Raman scattering, have, until the advent of the laser, been thought of as linear in the incident intensity, or, like the two-quantum decay of the metastable 2s states of hydrogen-like atoms and ions, been confined to theory. Of the multiple photon, non-linear optical processes, multiquantum ionization is one of the more fruitful for detailed, quantitative measurements, and for comparison with theory, since (1) one does not require precise coincidence between the laser light and an absorption line (2) the ionizations can be detected unambiguously with 100% efficiency (3) atomic wave functions are simple, and sufficiently accurate to enable one to make reasonable precise calculations.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.
The most important results of study of multiphoton ionization of atoms are reviewed. Discussions are presented of specific features of the process, theoretical methods of description of ionization of atoms in a strong light field, the basic principles of design of experiments in which intense laser radiation is used, results of investigation of direct and resonance processes of multiphoton ionization, and the mutual relation between multiphoton processes (multiphoton excitation and ionization) and various phenomena leading to perturbation of the spectrum of bound states of an electron in an atom under the influence of a strong light field.
We present a detailed analysis of the effects of photon statistics on multiphoton ionization. Through a detailed study of the role of intermediate states, we evaluate the conditions under which the premise of nonresonant processes is valid. The limitations of its validity are manifested in the dependence of the process on the stochastic properties of the radiation and found to be quite sensitive to the intensity. The results are quantified through detailed calculations for coherent, chaotic, and squeezed vacuum radiation. Their significance in the context of recent developments in radiation sources such as the short-wavelength free-electron laser and squeezed vacuum radiation is also discussed.
We present experimental and theoretical data on the electron energy spectra from resonance-enhanced multiphoton ionization of atoms. In experiments performed with 594-nm wavelength, linearly polarized laser pulses of 300-fs and 600-fs durations, it is found that excitation of the intermediate resonances during the rising edge of the laser pulse can dominate the electron spectrum. Good agreement is found between the experimental results and a model based on the Landau-Zener energy level crossing theory. Theoretical results obtained with direct integration of the Schrödinger equation show that intermediate resonances can be excited appreciably off resonance if the coupling between the ground state and the excited state is highly nonlinear. The excitation of the intermediate state is not localized at the intensity which makes it six-photon resonant with the ground state. A multilevel model used to simulate the experimental spectra, based on direct integration of the Schrödinger equation, shows excellent agreement with the data.
We have demonstrated an interference between multiphoton ionization processes that results in a phase-sensitive enhancement or inhibition of the net ionization rate. We focus two laser beams, either of which can induce an atomic transition between the same two states, into a cell containing atomic mercury. One of the fields is at a wavelength of 185 nm and can linearly induce the 6s 1S0 → 6p 1P1 transition in mercury. The other field is at a wavelength precisely three times as long, and it can excite the 6p resonance by a three-photon process. The absorption of two additional visible photons ionizes the mercury. In the presence of both fields, the transition amplitudes interfere, and their relative phases become very important. Their phases can be controlled by controlling the phases of the optical fields inducing the transitions. Coherence between the two fields, vital for the interference, is ensured by generating one field from the other using a nonlinear third-harmonic process. We have also demonstrated the effect of spatial phase variations between the two fields on the local photo-ionization rate.