Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters

Dielectric spheres which are much smaller than a wavelength and made of a large permittivity can support magnetic dipole modes of great purity. We investigate the coupling of such magnetic dipoles by studying sub-wavelength dielectric spheres arranged in clusters as pairs, chains, and rings. The coupling among the spheres creates hybridized modes, which may be used to engineer metamaterials with more degrees of freedom than by using single particles. Two methods of analysis are used: an approximate coupled dipole model and an exact transition-matrix approach. An experimental setup employs a focused Gaussian beam excitation. The magnetic coupling presented here is similar to the coupling of plasmonic modes in metal nanoparticles. Therefore, these experimental results are also a verification of several analogous plasmonic systems.