Three wave mixing via electronic states at the surface of the noble metals

Abstract

Presented here is a study of the nonlinear optical response of the surfaces of the noble metals. Second harmonic generation is forbidden, in the dipole approximation, in centrosymmetric materials. Nonetheless, using pulsed lasers, it is readily observed in reflection. The signal originates in a narrow layer at the surface where the center of inversion is removed by the termination of the lattice. The goal is to go beyond the jellium model, and incorporate into the formulation of the response the nature of the electronic states at the surface, including both surface modified bulk states and intrinsic surface states. The foundation of the approach is the description of the three wave mixing phenomenon as a superposition of three step processes in which each step consists of an electronic transition between states of the system accompanied by the annihilation or creation of a photon. The symmetries of the wavefunctions determine how the strength of a particular mechanism depends on the polarization of the photons, and the energies of the states determine the frequency dependence. The formulation is applied to the problem of second harmonic generation in reflection from Cu(110). Using the published results of bandstructure calculations, and photoemission and inverse photoemission experiments, important three step processes involving surface-modified bulk states and intrinsic surface states are identified, and the polarization properties of the input and output photons are ascertained for certain important processes. A frequency dependence for a model of the surface band structure near the Y point of the surface Brillouin zone is calculated, showing in particular that the contribution from the states at Y should be resonantly enhanced for the case of second harmonic generation using a Nd:YAG laser. An experiment of this type was conducted in ultrahigh vacuum, designed to test polarization properties. These, together with experiments on sensitivity to O\sb2 adsorption, support the conjecture that surface-modified band states and intrinsic surface states play an essential role in the nonlinear optical response