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Journal of Physics B Atomic and Molecular Physics

Dynamics of multiphoton ionisation to multiple continua

Michele Crance, M Aymar

Published Jul 14, 1980• 57 citations
Publisher

Abstract

(n+p)-photon ionisation of atoms is studied when n-photon ionisation is energetically possible. A non-perturbative treatment is described. The corresponding results agree with the predictions of perturbative theory in the weak-field limit. The effect of the light pulse shape is discussed.
DOI
10.1088/0022-3700/13/13/004

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By using a perturbative treatment based on the central field approximation, the authors have calculated multiphoton ionisation probabilities in several cases of experimental interest (two-, three- and four-photon ionisation of the caesium and potassium ground states at the doubled Nd glass laser frequency and one-, two- and three-photon ionisation of some s, p, d and caesium Rydberg states). Some of these probabilities have been calculated beyond the minimum non-vanishing order. They have also performed some calculations for hydrogen. The comparison of their results with previous ones obtained by analytical methods provides a good test of the numerical techniques involved in the calculations.
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In a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.
A model of multiphoton ionisation is presented which can be used when the turn-on of the atom-field interaction is adiabatic or near adiabatic. It is shown that in the adiabatic limit, the probability of the atom not being ionised is given by a single exponential decaying in time. A time-independent perturbation series is developed which can be used to calculate the adiabatic limit ionisation rate to any desired order. A time-dependent perturbation series is used to calculate the ionisation probability in the near-adiabatic limit. Comparison is made between results obtained with this model and those obtained using the more common sudden approximation to the turn-on.
Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.