Multipolar resonant particle modes as elementary excitations in chain waveguides: Theory, dispersion relations and mathematical modeling

In the framework of linear electrodynamics, the theory of the resonant interaction of multipolar modes in the many body system and associated numerical techniques are proposed in the present paper. The theory rests upon certain integral field equations derived on the basis of the Stratton-Chu integral transforms, the Atkinson-Wilcox and multipole expansions. For the case of spherical geometry of the bodies, the half part of these field equations is reduced to a set of closed form dispersion relations which describe the excitation of nonradiating modes in the particle cluster of arbitrary complexity. For clusters with developed translation symmetry, we propose the method for solving the field equations which is characterized by an effective numerical scaling. For perfectly periodic one dimensional systems (chains), this scaling has a linear character. On the basis of the proposed theory and numerical technique the method of synthesis of chain plasmonic waveguides with low radiation losses is considered. Different checks targeted on the verification of the approaches are fulfilled.