Perturbation Theory in the Design of Degenerate Spherical Dielectric Resonators

The design of resonators with degenerate magnetic and electric modes for negative-index metamaterial applications usually requires the ability to perturb one or both types of modes in order to induce alignment of the negative magnetic and electric properties. The incentive behind the resonator designs presented in this paper is to minimize both the losses and the size of the unit cell, particularly in the case of high frequencies such as the infrared or visible. Thus, the designs discussed in this paper are based on degenerate-mode (the fundamental magnetic and electric modes are aligned in frequency) spherical dielectric resonators which rely on only a single-particle resonator and thereby do not require physical or electrical extensions of the unit cell, as might be seen with other negative-index unit cell designs. Cavity-perturbation techniques are used to arrive at the types of inclusions (in terms of material, polarization, and placement) that are necessary to realize a degenerate spherical dielectric resonator, as well as to derive simple formulas which can be used for the design of these types of resonators. Rigorous electromagnetic simulations of the degenerate resonators are also provided for comparison to the theoretical derivations.