Generalized Volkov wave functions: Application to laser-assisted scattering.

Abstract

Wave equations---nonrelativistic and relativistic---describing the motion of a charged particle in a multimode laser field are considered and solutions are derived that may serve as asymptotic wave functions in the evaluation of amplitudes for laser-assisted scattering and multiphoton ionization. Unlike the well-known Volkov solutions that can be used only for fields of the plane-wave type, the wave functions obtained here are appropriate for the wider class of fields for which the different modes need not all have the same direction of propagation. This generalization allows in principle for the construction of wave packets, fields that are localized in space as well as time and hence capable of providing a more realistic description. The treatment of the nonrelativistic case is essentially exact, in the sense that errors introduced, of order (v/c${)}^{2}$, are comparable to those inherent in the nonrelativistic approximation. As an illustration, a low-frequency approximation for potential scattering in a multimode field is derived based on the use of the generalized Volkov solutions as asymptotic wave functions. Generalized Volkov solutions of the Klein-Gordon and Dirac equations are derived as well, though here in an approximation requiring a limitation on the strength of the external field.