An expression for the N-photon ionisation probability for a many-level atom is obtained as a function of the laser pulse duration, t. It is shown that the leading term in the power series expansion is of order t 2N-1 . The relevance of these calculations to some recent experiments by Lompre et al. (1976, 1977) is discussed.
An expression is derived for the amount of two-photon ionisation produced by sub-nanosecond laser pulses under resonance conditions. On this time scale damping effects can be neglected and the ionisation probability becomes proportional to the cube of the pulse duration. A similar prediction for resonance multiphoton processes of higher order leads to a qualitative agreement with recent experimental observations. Finally, it is demonstrated that the same result can be obtained from a simple analysis of a two-step model.
The authors treat a model for photoionisation in which the atom has many bound atomic levels and the laser may be either monochromatic or possess a finite bandwidth. The treatment is restricted to the case where the laser is not sufficiently intense to cause Stark splitting of the atomic energy levels. They obtain an expression for the two-photon ionisation probability as a function of time which covers both resonant and non-resonant excitation. They identify several time regimes where the probability takes on a particularly simple form. In particular they discuss the short time behaviour and the conditions under which a time-independent transition rate exists. Numerical plots of the ionisation probability against laser frequency for a wide range of pulse durations are given for the two-level model.
A theory of two-photon ionisation of atomic systems is developed incorporating into the treatment details of the laser spectrum. A general expression for the time-integrated two-photon ionisation probability is obtained together with general expressions for the induced shifts and widths of the atomic levels. These expressions are valid near resonance, when in the ordinary perturbation treatment the energy denominators vanish. The general expressions are then evaluated for the special case of a Lorentzian laser spectrum, when simple analytic results are obtained. The treatment is not confined to the two-level atom or the rotating-wave approximation.
The near-threshold behaviour of four-photon ionisation is studied in an energy region where the third laser photon crosses the Rydberg threshold. Particular emphasis is given to the role played by the Stark shift (raising of the ionisation potential) in a Gaussian laser pulse. As a function of the laser frequency the ionisation probability shows (i) a region where individual Rydberg resonances are well resolved, followed by (ii) a smoothly decreasing ionisation probability in the bound-state region, and (iii) an almost energy-independent above-threshold ionisation signal.