Coupled Dielectric Nanoparticles Manipulating Metamaterials Optical Characteristics

In this paper, we investigate the concept and theory of all-dielectric metapatterned structures that manipulate electric and magnetic optical characteristics. A 3-D array of dielectric particles is designed, where the spheres operate in their magnetic modes and their couplings offer electric modes. An analytical solution for the problem of plane wave scattering by 3-D array of dielectric nanospheres is presented. FW multipole expansion method is applied to express the optical fields in terms of the electric and magnetic dipole modes and the higher order moments. By enforcing the boundary conditions at the surface of each sphere, with the use of the translational addition theorem for vector spherical wave functions, required equations to determine the scattering coefficients are obtained. Novel materials features in optics are demonstrated. Electric and magnetic scattering coefficient resonances around the same frequency band are obtained. It is highlighted how a metapatterned structure constructed from dielectric nanosphere unit cells can provide electric and magnetic modes resulting in backward wave phenomenon. A comprehensive circuit model based on the RLC (resistor, inductor, and capacitor) realization is presented to successfully analyze the scattering performance of a dielectric nanosphere. To better understand the physics of an array of spheres, circuit models for the interactions, and couplings between spheres are also accomplished. The engineered dispersion diagram for a 3-D array of identical highly coupled nanospheres is scrutinized, verifying that the high couplings between spheres can offer the backward wave characteristics.