Morphology-dependent resonances in a large dielectric sphere: An asymptotic calculation using local coordinates

An asymptotic calculation for the electromagnetic fields at frequencies near low-order high-Q morphology-dependent resonances in a large dielectric sphere is reported. Employing local coordinates in the radial and angular directions, our method takes advantage of the special field distribution within the sphere. Closed-form formulas for the resonance frequencies are derived. Our results turn out to be identical with those obtained in recent independent studies in which these formulas are extracted from Mie's exact solution. Our method is interesting in that it does not require the knowledge of the exact solution to the entire problem and can be extended to fully nonlinear cases.