Laser fields at flat interfaces: I. Vector potential

Abstract

A model calculating the laser fields at a flat structureless surface taking into account the surface photoelectric effect is presented. The photon is p or transverse magnetic linearly polarized, continuous and its wave length is long, i.e. λ vac ≥ 12.4 nm. The sharp rise of the electron density at the interface generates an atomic scale spatial dependence of the laser field. In real space and in the temporal gauge, the vector potential A of the laser is obtained as a solution of the classical Ampere-Maxwell and the material equations. The susceptibility is a product of the electron density of the material system with the surface and of the bulk tensor and non-local isotropic (TNLI) polarizability. The electron density is obtained quantum mechanically by solving the Schrodinger equation. The bulk TNLI polarizability including dispersion is calculated from a Drude-Lindhard-Kliewer model. In one dimension perpendicular to the surface the components \hbox{$\mathcal{A}_x(z,\omega)$} 𝒜 x (z,ω) and \hbox{$\mathcal{A}_z(z,\omega)$}𝒜 z (z,ω) of the vector potential are solutions of the Ampere-Maxwell system of two coupled integro-differential equations. The model, called vector potential from the electron density-coupled integro-differential equations (VPED-CIDE), is used here to obtain the electron escape probability from the power density absorption, the reflectance, the electron density induced by the laser and Feibelman’s parameters d ∥ and d ⊥. Some preliminary results on aluminium surfaces are given here and in a companion paper the photoelectron spectra are calculated with results in agreement with the experiment.