Effective order of non-linearity in resonant multiphoton ionisation

The effective order of non-linearity in multiphoton ionisation is defined by k=( delta lg N)/( delta lg I) where N is the number of ions created by the electromagnetic field with intensity I. Strong variations of k are observed in the vicinity of a resonance. Using a simple model for resonant multiphoton ionisation the author derives an expression for k. He takes into account the spatial distribution when excitation is produced by a Gaussian beam. Both long- and short-pulse excitation are investigated. Theoretical results are applied to the interpretation of four-photon ionisation of Cs I near the 6f resonance. The theoretical results are in good agreement with the experimental data on the effective order of non-linearity.