Optical modes in linear arrays of dielectric spherical particles: a numerical investigation
Abstract
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 numerical methods to calculate eigenoptical modes for various arrays of particles. These numerical methods involve the use of the multisphere scattering formalism as the entries in N×N matrices where N represents the number of particles in the chain. Eigenmodes of these matrices correspond to the eigenoptical modes of interest. We identified the eigenmodes with the highest quality factor by the application of a modified version of the NewtonRaphson algorithm. We found that convergence is strong using this algorithm for linear chains of up to several hundreds of particles. By comparing the dipolar approach with the more complex approach which utilizes a combination of both dipolar and quadrupolar approaches, we demonstrated that the dipolar approach has an accuracy of approximately 99%. We found that the quality factor Q of the mode increases with the cubed value of the number of particles in chain in agreement with the previously developed theory, the effects of disordering of particle sizes and interparticle distances will be discussed.
 Publication:

Laser Resonators and Beam Control IX
 Pub Date:
 February 2007
 DOI:
 10.1117/12.714584
 arXiv:
 arXiv:physics/0701069
 Bibcode:
 2007SPIE.6452E..12B
 Keywords:

 Physics  Optics;
 Physics  Computational Physics
 EPrint:
 Submitted to Proceedings of SPIE