Optical Modes in Linear Arrays of Dielectric Spherical Particles: A Numerical Investigation

We have investigated bound modes in finite linear chains of dielectric particles of various lengths, interparticle spacing and particle materials. Through a unique application of the multisphere Mie scattering formalism, we have developed a numerical method to calculate eigen-optical modes for various arrays of particles by reducing the problem to the analysis of a uniform system of linear equations. A modified Newton-Raphson algorithm is applied to find the eigen modes of the task that correspond to the eigen-optical modes of interest. We have analyzed the behavior of the eigen modes having the highest quality factor Q. In particular, we investigated the dependence of Q on the number of particles in the chain. We demonstrated that the dipolar approach has an accuracy of approximately 99% in comparison with the quadrupole approach. The quality factor Q of the mode is found to increase proportionally to the cube of the number of particles in the chain in agreement with previously developed theory. The effects of disordering of particle sizes and inter-particle distances is discussed.