Strong-field ionization of atoms beyond the dipole approximation

Abstract

Strong-field ionization of atoms by an elliptically polarized laser field is discussed beyond the dipole approximation. We develop a theory based on the strong-field approximation which includes nondipole effects by expanding vector potential up to the first order in $1/c$. Both direct and rescattered electrons are investigated. The differential ionization rate is calculated numerically or using the saddle-point method. We find that nondipole effects are mostly pronounced in the regions near and beyond the cutoff. The existence of additional regions in the photoelectron momentum plane where nondipole effects are significant is explained using the saddle-point method and the interference of partial contributions of particular saddle-point solutions to the differential ionization rate, which is modified when nondipole effects are taken into consideration. These regions are well defined for a linearly polarized field as well as for an elliptically polarized field with ellipticity lower than 0.4. For the rescattered electrons we find saddle-point solutions which contribute significantly to the differential ionization rate. These solutions are classified in a similar way as in the framework of the dipole approximation. The agreement of the results obtained by numerical integration and the results obtained using the saddle-point method is excellent.