Strong-field tunneling ionization in the relativistic regime

Abstract

We study the photoelectron energy and momentum distributions of strong-field tunneling ionization in the relativistic regime. Using the relativistic strong-field approximation, we have derived the position of the tunnel exit, the initial momentum distributions at the tunnel exit, and the instantaneous ionization rate when the electron tunnels through the Coulomb barrier in the relativistic regime. Since the tunneling electron energy is of the order of 1% of the rest of its mass, those nonadiabatic tunneling coordinates are quite different from the nonrelativistic case. We further incorporate the nonadiabatic relativistic tunneling coordinates into the classical trajectory Monte Carlo model and have calculated photoelectron energy and momentum distributions by accurately considering the field distribution in the focus of relativistic femtosecond laser pulses. We show that the nonadiabatic tunneling effect and the focal field distribution are very crucial to modeling strong-field ionization in the relativistic regime because the quiver radius of electrons can be as large as the beam waist.