Laser–matter interaction at solid–gas interface in the A→·p→ gauge: linear, surface and quadratic terms

At gas–solid interface the electron density, the dielectric function and the electric field of the photon vary sharply. Therefore, the usually assumed approximation of the spatially independent field of the photon does not hold anymore. In this paper we approximate the spatial variation of the vector potential A→ perpendicular to the surface from the dielectric function, itself related to the electron density in a jellium model, and the Fresnel relations at abrupt interface. The resulted vector potential A→ is then included in the laser–matter interaction Hamiltonian written in the A→·p→ gauge (notation Ap) with zero scalar potential. For p polarization our detailed theoretical analysis unravel four terms linear in A→: a term perpendicular, two terms parallel and a surface term perpendicular to the surface, all four varying at the interface. There are also two terms quadratic in A→: a term perpendicular and a term parallel to the surface, again all varying at the interface. Using this interaction operator, we calculate all the laser–matter interaction terms for a (0 0 1) metallic surface lightened by a laser of 2 eV. The results for several metals, calculated with an elementary wave function product of a sum of Gaussian functions normal to the surface and plane waves perpendicular to it, show at nondestructive fluences a comparable relative importance for one linear term parallel to the surface and one surface term perpendicular to it but a negligible contribution of the quadratic term.