Energy Conservation and the Manley-Rowe Relations in Surface Nonlinear-Optical Spectroscopy

We consider the energy conservation problem for nonlinear-optical three-wave mixing processes at the surface and in the bulk of semi-infinite centrosymmetric lossless media. Because of the intrinsic nonlocality of these processes, the corresponding Manley-Rowe relations differ from those of noncentrosymmetric media. The ensuing restrictions link the surface and bulk nonlinear susceptibility components and may be used to test theories of nonlinear response. Our analysis permits a clear separation of the intrinsic surface contribution that contains the information about the surface structure.