Multiphoton ionization rate with a non-Lorentzian-band-shape laser

A time-independent single-rate theory for multiphoton ionization processes is developed to cover cases with a partially coherent (finite-bandwidth) driving laser. We use the Ornstein-Uhlenbeck fluctuating-phase model to describe the driving field, which has therefore a non-Lorentzian spectrum, and the effective two-level model to represent the atomic system. We present analytic and numerical methods that permit discussion of the effects of non-Lorentzian band-shape laser light, and we give analytically the bandwidth dependence of the rate in the wings of the ionization curve. Our model contains a simple scaling relationship that permits the rate for $N$-photon-resonant ($N+1\mathrm{}$)-photon ionization to be obtained directly from the one-photon-resonant two-photon ionization rate. We treat explicitly the cases $N=1\mathrm{}$ and $N=2\mathrm{}$.