K. M. Pang

Morphology-dependent resonances in dielectric spheres with many tiny inclusions

The morphology-dependent resonances (MDRs) in a dielectric sphere that contains many tiny inclusions are studied by use of a recently developed degenerate perturbation method. Degenerate MDRs in the sphere split into multiplets because of the loss of spherical symmetry and manifest themselves as broadened spectral lines in the scattering cross section. Furthermore, the distribution of MDRs in a multiplet is found to obey Wigners semicircular theorem.

Iterative perturbation scheme for morphology-dependent resonances in dielectric spheres

The properties of morphology-dependent resonances observed in the scattering of electromagnetic waves from dielectric spheres have recently been investigated intensively, and a second-order perturbative expansion for these resonances has also been derived. Nevertheless, it is still desirable to obtain higher-order corrections to their eigenfrequencies, which will become important for strong enough perturbations. Conventional explicit expressions for higher-order corrections inevitably involve multiple sums over intermediate states, which are computationally cumbersome. In this analysis an efficient iterative scheme is developed to evaluate the higher-order perturbation results. This scheme, together with the optimal truncation rule and the Pade resummation, yields accurate numerical results for eigenfrequencies of morphology-dependent resonances even if the dielectric sphere in consideration deviates strongly from a uniform one. It is also interesting to find that a spatial discontinuity in the refractive index, say, at the edge of the dielectric sphere, is crucial to the validity of the perturbative expansion.

Two-component wave formalism in spherical open systems

We study wave evolution in open dielectric spheres by expanding the wave field and its conjugate momentum?the two components?in terms of relevant quasi-normal modes (QNMs), which are complete under appropriate conditions. We first establish a novel outgoing boundary condition at the surface of a sphere for waves emanating from its interior. A proper definition of inner product for two-component outgoing wavefunctions, involving only the waves inside the sphere and a surface term, can then be defined in general. The orthogonality relation of QNMs and hence a unique expansion in terms of the QNM basis are found, which can be applied to solve for the evolution of waves inside open dielectric cavities. Furthermore, a time-independent perturbation for QNMs can also be developed.