Optical response from a randomly rough surface: Theory and numerical results

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Abstract
A general theory for the calculations of the average electric field and average electric field intensity near a randomly rough surface is given. The average field and field intensity are expressed in terms of averaged one- and two-photon Green's functions which are systematically approximated using the functional method of Baym and Kadanoff. Explicit expressions for the lowest-order contributions to the self-energy and the kernel of the Bethe-Salpeter equation are given. The theory is applied to a semi-infinite metal with a statistical rough surface. For simplicity in our calculations we assume a Gaussian distribution for the surface profiles and a local, space-independent dielectric function for the bounded metal. We find that for typical roughness parameters the averaged local electric field near the surface is quite small but the fluctuations in this field may become very large due to multiple scattering of surface-plasmon polaritons. Numerical results are given for the field intensity near the surface as function of the frequency, polarization, and angle of the incident light and as function of the roughness parameters.