Photon-momentum transfer in photoionization: From few photons to many

In most models and theoretical calculations describing multiphoton ionization by infrared light, the dipole approximation is used. This is equivalent to setting the very small photon momentum to zero. Using numerical solutions of the (nondipole) three-dimensional time-dependent Schrödinger equation for one-electron (H-like) systems, we investigate the effect the photon-momentum transfer to the photoelectron in various regimes: from the few (one, two, three, eight) absorbed photons to multiphoton and tunneling regimes. We find that in all regimes the average electron momentum acquired from absorbed photons is a linear function of the average energy of the photoelectron, but the slope is different in the few-photon and multiphoton regimes. In the multiphoton regime, the photon-momentum signature in the photoelectron-momentum distributions (along the photon momentum) depends on the ellipticity of the laser polarization, with linear laser polarization spectra different from circular polarization spectra. For a given laser intensity the average electron-momentum gain from an absorbed photon is over two and a half times smaller for linear polarization than for circular polarization. However, for both polarizations, the average electron-momentum gain is nearly equal to the average electron energy divided by the speed of light.