Spectral boundary integral equation method for the characterization of novel photonic nanomaterials

Abstract

The Spectral Boundary Integral Equation method for the numerical modeling of superlenses formed by metamaterial is proposed. The corresponding transmission problem is formulated using a classical approach based on layer-potential technique. The obtained system of integral equations is solved by using the Galerkin's method with approximations based on spectral harmonics on the unit circle. A singularity subtraction technique is applied to avoid numerical instabilities caused by the integral equation singularities. The novel idea is the global parameterization of the non-smooth boundaries of the rods in terms of Fourier series by using a conformal mapping technique. The numerical instabilities that may be caused by the geometrical singularities of the rods are eliminated. The developed simulation tool based on this method provides solutions with high accuracy and reduced complexity. These features permit to investigate the dependence of the lens characteristics on the shape and orientation of its structural details, and their material properties.