Edge modes of two dimensional bounded photonic crystal structures composed of small plasmonic particles and their interaction with inner structure's waves

Specific optical eigenmodes are considered of finite clusters of metallic nanoparticles with plasmonic resonance as well as an excitation transfer along linear chain of particles between clusters. Simple analytic and physically transparent results are presented for the problem solution of collective modes exciting inside two dimensional circular clusters and the problem excitation transfer along one dimensional linear array of coupled small plasmonic spherical particles. The results are obtained with the aid of equations’ system for self-consistent currents excited inside particles by incident electromagnetic wave field. For circular cluster of particles the coupling matrix between their currents becomes under definite conditions of such favorite properties that enables one immediately to write out the Bloch–like eigenmodes with corresponding eigenfrequencies and their half widths. What is more we get also a simple analytic expressions for coupling factor between inner part of a square structure arranged in a circular shape and its bound part. Considering linear array of particles we use a closest neighbor interaction approach which makes the linear array like the electric filter. In this approximation an analytic expression are obtained for extinction rate of exciting currents’ transfer depending on array particles number and for resonance filtering frequencies.