Optical resonances of cylinder and sphere clusters in the quasistatic limit

The solutions of the electrostatic potential problem for clusters consisting of three dielectric cylinders, or a pair of dielectric spheres, with zero applied field are studied. For metallic systems, such optical resonant behaviour is due to plasmon resonances which depend on the size and shape of the components. For dielectric systems, the resonant solutions always involve a negative dielectric constant of the inclusions in a matrix of positive dielectric constant. Here, we show the characteristics of these resonant solutions for the static case, but the theory of such phenomena can be used to clarify the transition from dynamics to statics in the longwave limit.