Nonlocal semiquantum theory of optical second-harmonic generation in free-electron-like metals

Abstract

A nonlocal theory of parametric second-harmonic generation from centrosymmetric free-electron-like metals is established. On the basis of a semiquantum infinite-barrier model with specular-conduction electron surface scattering, the structure of the driven nonlinear, nonlocal current density is analyzed. A physically appealing integral representation of the general solution to the nonlinear integrodifferential equation for the field, in which the dispersion relations for transverse and longitudinal electromagnetic bulk waves enter in a natural way, is obtained. Polarization-selection rules that are valid in the regime of nonlocal optics are determined. Polarization-dependent nonlinear, nonlocal reflection coefficients are given. The mode structure of the nonlinear field in the metal is analyzed by contour integration. Coherently coupled irrotational and solenoidal free and forced exponentially damped inhomogeneous plane waves are identified. Through a multipole expansion of the nonlinear current density, contact with previous hydrodynamic models based on the magnetic-dipole plus electric-quadropole approximation is made.