Energy and angular distribution of relativistic electrons in the tunnelling ionization of atoms by circularly polarized light

Simple analytic expressions are obtained for relativistic electron energies and angular distributions produced in tunnelling ionization of atoms by intense laser radiation. Circularly polarized radiation is considered, using the Landau-Dykhne approach. Major differences have been found as compared with the previously investigated case of linearly polarized laser radiation: a circularly polarized intense held produces mainly relativistic electrons, while a linearly polarized intense held produces mainly non-relativistic electrons. In the limit of a weak field we obtain well known expressions for the non-relativistic energy spectrum and angular distribution of ejected electrons in the tunnelling ionization of atoms. (Limited, of courser to the case where the so-called Keldysh parameter corresponds to the tunnelling regime of ionization.) Simple expressions have been found for: (1) the angle between the direction at which most of the relativistic electrons are ejected and the plane of polarization of the laser radiation; (2) the energy spectrum at this angle; (3) the width of the energy spectrum and the position of its maximum; (4) the angular distribution near this angle and the width of this distribution. Our simple purely analytical results for energy and angular distributions are in agreement with the numerical derivations of Reiss based on the strong held approximation.