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Second harmonic generation at crystal surfaces

The authors develop a model for the surface contribution to the second harmonic susceptibility of silver. They use the localized nature of the d bands to account for the interband transitions with screened dipoles immersed in a semi-infinite conduction electron gas. They identify several contributions to the non-linear response, originating from the non-linear dipolar and quadrupolar polarizabilities and from the electronic density inhomogeneities at the crystal surface and they obtain terms that couple the localized and the extended contributions to the response.