We introduce a numerical recipe for calculating the density of the resonant states of the clusters of dielectric spheres. Using truncated multipole expansions (generalized multisphere Mie solution) we obtain the scattering matrix of the problem. By introducing an infinitesimal absorption in the spheres we express the dwell time of the electromagnetic wave in terms of the elements of the scattering matrix. Using the parameters in recent light localization experiments [Phys. Rev. Lett. 87, 153901 (2001)], we demonstrate that the density of the resonant states, related to the dwell time, shows the formation of the photonic band structure in small clusters of dielectric spheres as the small as five particles. Density of resonant states of a cluster of 32 spheres exhibits a well defined structure similar to the density of electromagnetic states of the infinite photonic crystal. Our results suggest that, due to the formation of small ordered clusters, a significant modification of the density of electromagnetic states can occur in a random collection of monodisperse spheres.
A. Yamilov and H. Cao, "Density of Resonant States and a Manifestation of Photonic Band Structure in Small Clusters of Spherical Particles," Physical Review B (Condensed Matter), vol. 68, no. 8, pp. 851111-851115, American Physical Society (APS), Aug 2003.
The definitive version is available at https://doi.org/10.1103/PhysRevB.68.085111
Keywords and Phrases
Absorption; Crystal Structure; Density; Dielectric Constant; Dispersion; Electric Conductivity; Magnetism; Mathematical Analysis; Particle Size
International Standard Serial Number (ISSN)
Article - Journal
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