Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method

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Abstract
The resonance locations and quality factors (Q’s) of morphology-dependent resonances in an inhomogeneous sphere with a small refractive-index perturbation are computed by using the T-matrix method for layered axisymmetric objects and a time-independent perturbation method. The resonance locations computed are similar. The changes in the Q computed with the two methods are typically within a factor of 2 or 3 of each other when the change from the unperturbed Q is less than 50%. For the type of perturbation that we consider here, an increase in the refractive index in a nonconcentric spherical region inside the larger sphere, the resonance frequencies always decrease, but the Q’s decrease or increase depending on the unperturbed Q and the location and shape of the perturbation. The change in frequency and the change in Q depend on the overlap of the perturbation with the energy-density distribution of the morphology-dependent resonance. For the same overlap, the change in Q is much larger for higher-Q modes than for lower-Q modes. A refractive index perturbation that causes a relatively small change in Q may cause the resonance frequency of a high-Q MDR to shift by many linewidths.