Random-phase-approximation study of the response function describing optical second-harmonic generation from a metal selvedge

Optical second-harmonic generation in centrosymmetric metals stems from the breaking of inversion symmetry in the selvedge and from nonlocal effects. In the present work a random-phase-approximation description of the nonlocal nonlinear conductivity tensor of an inhomogeneous jellium is given. Main emphasis is devoted to a study of the electric dipole response from the selvedge, and to the magnetic dipole and electric quadrupole responses from the profile region and the bulk. A detailed analysis of the tensor symmetry schemes associated with the p{·}A and A{·}A interactions is presented. Dipole and quadrupole transitions are identified, and the role of direct and indirect quantum processes is discussed. On the basis of the so-called infinite-barrier model, a few numerical results are given.