%0 Journal Article %T Diffractive Interface Theory: Nonlocal polarizability approach to the optics of metasurfaces %A Christopher M. Roberts %A Sandeep Inampudi %A Viktor A. Podolskiy %J Physics %D 2014 %I arXiv %X We present a formalism for understanding the elecromagnetism of metasurfaces, optically thin composite films with engineered diffraction. The technique, diffractive interface theory (DIT), takes explicit advantage of the small optical thickness of a metasurface, eliminating the need for solving for light propagation inside the film and providing a direct link between the spatial profile of a metasurface and its diffractive properties. Predictions of DIT are compared with full-wave numerical solutions of Maxwell's equations, demonstrating DIT's validity and computational advantages for optically thin structures. Applications of the DIT range from understanding of fundamentals of light-matter interaction in metasurfaces to efficient analysis of generalized refraction to metasurface optimization. %U http://arxiv.org/abs/1408.3155v1