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Electrostatic responses of anisotropic dielectric films

We study the electrostatic responses (i.e. retardation effects due to the propagation of electromagnetic waves are ignored) of a linear homogeneous and anisotropic (LHA) dielectric film to an arbitrary external electrostatic potential, which may be generated by charges located either inside or outside it. A formalism is developed to calculate the polarization charges induced in the film. In our derivation, the idea is exploited that a physical boundary can be looked upon as a region of rapid variation in polarization rather than a simple geometric separation. With this no boundary conditions are needed in solving the relevant electrostatics problem. Our approach makes it clear that the responses consist of two contributions, one arising from the very presence of surfaces while the other existing even in an infinite medium. The approach can be applied not just to electrostatic but also many problems and is of great pedagogical value. In light of the results, we discuss graphene plasma waves under the influence of a LHA dielectric film such as a few-layer hexagonal boron nitride. It is found that the dispersion of these waves is strongly affected by the anisotropy at wavelengths comparable to the film thickness.