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.

中文翻译：

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各向异性介电薄膜的静电响应

我们研究了线性均匀和各向异性 (LHA) 介电膜对任意外部静电势的静电响应（即忽略了由于电磁波传播而产生的延迟效应），该静电势可能由位于其内部或外部的电荷产生。开发了一种形式来计算薄膜中感应的极化电荷。在我们的推导中，利用了一个想法，即可以将物理边界视为极化快速变化的区域，而不是简单的几何分离。有了这个，在解决相关的静电问题时不需要边界条件。我们的方法清楚地表明响应由两种贡献组成，一种来自表面的存在，而另一种甚至存在于无限介质中。该方法不仅可以应用于静电，还可以应用于许多问题，具有很大的教学价值。根据结果​​，我们讨论了在 LHA 介电膜（如几层六方氮化硼）影响下的石墨烯等离子体波。发现这些波的色散受与薄膜厚度相当的波长处的各向异性的强烈影响。