Estimation of the influence of finite dielectric substrates on the far-field pattern of an array of metallic scatterers in the infrared

The far-field scattered in the infrared by an arrangement of metallic structures deposited on a dielectric wafer is estimated in this paper. The scattering is modelled by using operators that describe the far field obtained under the regime applicable for the Babinet's principle in its vectorial approach and the Stratton-Chu approximation. The far-field scattered by an arrangement of thin gold layers over a dielectric wafer under infrared illumination is computed. The model assumes a normally incident vectorial Gaussian beam focused over the arrangement plane. An angular spectrum decomposition of the field is done. Then, every plane wave is scattered by the whole structure: arrangement + substrate layer. The reflexions in the substrate layer and the arrangement action have been taken into account in an operator formalism. Numerical results estimating the influence of substrate thickness on the pattern are obtained.