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Spectral super-resolution in metamaterial composites

Last modified: 2012-01-03

#### Abstract

We investigate the optical properties of periodic composites containing inclusions having a frequency dependent negative electrical permittivity, with a very small imaginary part,in a normal material matrix. We consider the case where these inclusions have sharp corners, and following Hetherington and Thorpe, use analytic results to argue that it is then possible to deduce the shape of the corner (its included angle) by measurements of the absorptance of such composites when the scale size of the inclusions and period cell is much finer than the wavelength. These analytic arguments are supported by highly accurate numerical results for the effective permittivity function of such composites as a function of the permittivity ratio of inclusions to matrix. The results show that this function has a continuous spectral component with limits independent of the area fraction of inclusions, and with the same limits for both square and staggered square arrays. In other words, the composite absorbs significant energy over a range of frequencies with limits controlled by the corner angle. In this range energy flows towards each corner where it ends up being absorbed in an infinitesimal neighborhood of the corner. For staggered arrays where the squares are almost touching, the absorption spectrum is an extremely sensitive probe of the inclusion separation distance and acts like a Vernier scale

#### Keywords

metamaterials; quasistatics; superresolution