Exactly solvable model of surface second-harmonic generation

We develop a model for surface second-harmonic generation (SHG) consisting of a semi-infinite system made up of a continuous distribution of harmonic polarizable entities, each of which responds nonlinearly to the gradient of the field. The near discontinuity of some field components at the surface yields a finite surface susceptibility tensor characterized by the parameters a({ω}) and b({ω}), as well as a bulk nonlinear response charcterized by d({ω}). We obtain analytical expressions for a, b, and d in terms of the linear dielectric functions {ε}({ω}) and {ε}(2{ω}). These expressions are exact within our model, but can be employed to obtain approximate SHG spectra for arbitrary systems. {} 1996 The American Physical Society.