APPLICATION OF SPECTRAL METHODS OF BOUNDARY INTEGRAL EQUATIONS FOR MODELING OF NANOOPTICAL DEVICES

Abstract

Efficiency of modeling of optical nanostructures depends not only on the accuracy of the description of the new physical processes which appear in the new configurations of resonantly scattering and resonantly absorbing structures, but also on the selection of appropriate algorithms for solving the corresponding mathematical problem and numerical parameters of modeling depending on parameters of elements. This is why solving complicated problems of modeling complex resonantly scattering and resonantly absorbing electrodynamic nanostructures involves deep learning of all groups of new unknown effects. In this work a semi-analytical algorithm is developed based on parametrized by conformal mapping techniques spectral method of boundary integral equations with analytical regularization based on singularity subtraction enhanced by Fast Fourier transform, that contrary to the classical schemes, which are based on finite difference and finite element methods, allows to take into account the complex-valued functional dependence of dielectric permittivity of plasmonic materials on the wavelength (even when its value is tabulated) and to solve the problems with static and dynamic singularities in integral equations. Due to sensibility of plasmon resonances to changes in external medium such nanostructures are used in modern medicine, pharmacy and also as chemical and biological sensors. In this work main efforts are directed on generation of algorithm for investigation of dielectric nanostructures with static singularities.