Shadowing effect in a subwavelength-sized 2D circular chain of a few spherical plasmonic particles and the transverse polarization of an incident field

The shadowing effect is featured in ensembles of two small spherical plasmonic particles and three particles arranged at the vertices of a triangle on the basis of the equation system for self-consistent currents excited inside dielectric and conducting particles by an incident electromagnetic wave field. The system for self-consistent currents is a solution of the collective modes excitation problem inside a 2D circular chain composed of small spherical plasmonic particles with an electric dipole coupling. The modes are classified depending on current distribution among different particles. For a circular chain of particles the coupling matrix between their currents becomes the Toeplitz matrix with a stochastic property under transverse polarization perpendicular to the circular plane. These peculiarities of the coupling matrix enable one to derive directly the Bloch-like fundamental (stochastic) and overtone eigenmodes with corresponding eigenvalues excited inside the chain. The shadowing effect manifests itself as an equality of the extinction cross-sections both in a bisphere and in three spheres arranged triangularly as is it were an individual plasmonic particle at the frequency of the stochastic mode of the two and three particles systems, respectively.