Theory of surface sum frequency generation spectroscopy

We develop simple models for the calculation of optical sum and difference frequency generation spectra at the surface of isotropic centrosymmetric conductors and insulators. One of them consists of a semi-infinite free electron gas with a continuously varying electronic density profile. The other consists of a continuous distribution of polarizable entities that respond nonlinearly to the gradient of the field, We solve the Euler equations for the former ignoring the pressure term. Assuming the response of each polarizable entity to be described by that of a harmonic oscillator, we solve the second model incorporating multipolar contributions to the macroscopic surface and bulk polarization. For both models we obtain analytical expressions that produce the nonlinear bulk and surface susceptibilities in terms of the bulk dielectric response of the system. We found an electric-field-induced second-order magnetic moment whose contribution to the susceptibilities is as large as that of the electric dipolar and quadrupolar moment. This contribution is absent in the particular case of second harmonic generation and has not been discussed previously in the literature. By choosing the appropriate dielectric functions we obtain the approximate nonlinear response and frequency conversion efficiency for different systems. [S0163-1829(98)02803-3].