ISOTROPIC AND ANISOTROPIC BULK CONTRIBUTIONS TO 2ND-HARMONIC GENERATION FROM SIMPLE METALS

Quantum-mechanical calculations are carried out for the non-linear current in the bulk of simple metals. The energy bands and matrix elements for optical transitions are calculated using a two-band model which is known to give accurate results for the description of the linear dielectric response of these systems. The frequency dependence of the isotropic and anisotropic components of the non-linear polarizability tensor shows characteristic resonances due to various interband transitions in the optical region. In the adiabatic limit, excellent agreement is obtained with results derived within the Boltzmann equation approach. The emitted harmonic radiation is calculated to illustrate the influence of the non-linear volume current on the variation of the intensity with polar and azimuthal angles of incidence. Using recent experimental data for optical second-harmonic generation from Al(111) and the calculated bulk polarizability, predictions are made concerning the magnitude and relative phase of the surface anisotropy.