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Electrostatics of optical rectification in metallic particles

We present an electrostatic theory of the optical rectification, namely, the static photovoltage or photocurrent generation under a light illumination, in metallic particles. The hydrodynamical model for the charge carriers in the metals is employed. By solving the hydrodynamic equation and Maxwell equation perturbatively, we obtain analytically the second-order susceptibility, from which the optical rectification is explained. Electrostatic potential problems involved in the optical rectification under the local response approximation are formulated in arbitrary geometries, and then are solved for simple geometries of metallic planar interfaces, slabs, cylinders, and spheres. The photovoltage and photocurrent spectra, their incident-angle dependence, and the electrostatic potential distribution for a incident plane-wave light are demonstrated and discussed in a context of plasmonic resonances.