Decoupling and testing of the generalized Ohm's law

The generalized Ohm's law is an approximation formulated for the description of optical properties of nonhomogeneous thin films beyond the quasistatic approximation, when the inhomogeneity length scale is still much smaller than the wavelength, but is not smaller than the skin depth. Within this approximation, we transform the problem to a form that is similar to a thermoelectric transport problem in a two-dimensional (2D) nonhomogeneous medium. We show that for a general class of nonhomogeneous films with any number of different components, the resulting equations can be decoupled by a universal transformation. This simplifies practical application of the theory by reducing the coupled-field problem in a nonhomogeneous 2D system to two uncoupled conductivitylike problems with the same microgeometry, for which extensive theory already exists. For the purpose of studying the applicability of the generalized Ohm's law, we consider the problem of an electromagnetic plane wave scattered from a film that, although materially homogeneous, has a corrugated surface in the regime where the wavelength is larger than the inhomogeneity length scales. The optical response of such a film is calculated by applying the generalized Ohm's law, and independently by solving the three-dimensional Maxwell's equations, invoking the physical boundary conditions at the surface (Rayleigh method). We compare results of the two approaches for several configurations and materials and thus learn about the range of parameter values for which the generalized Ohm's law can provide a good description of the optical properties of a thin film.