Manipulating the Quasi-Normal Modes of Radially Symmetric Resonators

Abstract: We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the permittivity of the structure to place a resonance at a particular complex frequency. Next, we employ quasi-normal mode perturbation theory to design radially graded structures with resonances at desired frequencies.