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 W/
cm2) is determined by the intensity-dependent level width (
6f 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 W/
cm2) are determined by both the intensity-dependent widths and shifts a
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.
A perturbation theory of the ionization of atoms by simultaneous absorption of several photons, each of whose energy is less than the ionization potential, is developed from the evolution-operator formalism. A precise computation is made for the hydrogen atom, giving transition rates as a function of photon energy for two- through twelve-photon photoionization. The eighth-order ionization rate (in cgs units) at the 1.78-eV ruby-laser line is found to be \ensuremath{\sim}${10}^{\ensuremath{-}244}$\ifmmode\times\else\texttimes\fi{}
(photonflux)8 and should be observable using available techniques. Good agreement is obtained with Zernik's exact calculation of the two-photon ionization rate of metastable
2S hydrogen. Approximate calculations are made for the rare gases. Assuming "typical" experimental conditions of a gas density of \ensuremath{\sim}
1020 atoms ${\mathrm{cm}}^{\ensuremath{-}3}$ and a ruby laser focused into a volume of \ensuremath{\sim}${10}^{\ensuremath{-}8}$
cm3, we find that the flux required to liberate one electron during a 10-nsec pulse is \ensuremath{\sim}
1029 ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Xe, Kr, and Ar and \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}
1030 photons ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne and He. These gases ionize with the simultaneous absorption of 7, 8, 9, 13, and 14 photons, respectively. The predicted rate for Xe is found to be in excellent agreement with the recent direct measurements of Voronov and Delone. We conclude that multiphoton ionization provides the initial electrons required for the optical breakdown of gases, though it does not account for the over-all growth of the discharge except possibly at very low pressures. Impurity atoms (particularly heavy rare gases) may be the source of "initiating" electrons in Ne and He.
Non-resonant k-photon ionisation cross sections may be calculated by kth order perturbative treatment. This method is generally considered to be good when the detuning from the closest resonance is much larger than the expected shift and width of this resonance. The aim of this paper is to discuss the validity of this criterion for several realistic cases. By diagonalising an effective Hamiltonian built on a few quasi-resonant states, we have calculated multiphoton ionisation cross sections for ground state caesium by linearly polarised light in frequency ranges containing the tuning range of the ruby laser, the Nd glass laser and its first harmonic. The study is carried out up to an intensity of 10 11 W cm -2 .
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.
We report resonant multiphoton ionization in neon. The study of the interaction volume shows that the size of the focused region depends on the laser power, order of interaction, and energy of photon. Thus we have chosen a resonant approach. The results show a discrepancy of 6 cm−1 between the experimental multiphoton resonance and the theoretically predicted one. We explain this discrepancy by the perturbative effect of the intense electromagnetic field of the laser on the resonant atomic level 11p [3/2]1,2 of neon.
This paper studies the resonant multiphoton ionization (RMPI) phenomenon, in the case of caesium atoms interacting with the intense field of a neodymium-Glass laser. In the first part, we present a recent theory of RMPI, in a simplified form in order to obtain the main informations on the physics of RMPI. Then we present two experiments of RMPI : four-photon ionization of the caesium atom in its ground state, with a three-photon resonance on the 6F level and three-photon ionization of the caesium atom is its 62P3/2 state with a two-photon resonance on the 12F level. In the first experiment, the internal structure of the resonant transition is resolved, enabling us to point out and analyse the important effect of pulse shapes and focusing conditions on our experimental results, which are discussed in detail. We also give some new interpretations of results published previously [1]. In the second experiment, we measure the 12F fine structure — which is found to be (0.016 ± 0.008) cm-1 — and show that we have reached the limits imposed by the Doppler effect. These experimental results are in good agreement with the theoretical predictions suggesting that the physical picture given of RMPI by recent works on this subject is satisfactory.