We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
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.