## Dyadic formulation of morphology-dependent resonances. III. Degenerate perturbation theory

JOSA B, Vol. 19, Issue 1, pp. 154-164 (2002)

http://dx.doi.org/10.1364/JOSAB.19.000154

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### Abstract

Based on the completeness of morphology-dependent resonances (MDRs) in a dielectric sphere and the associated MDR expansion of the transverse dyadic Green’s function, a generic perturbation theory is formulated. The method is capable of handling cases with degeneracies in the MDR frequencies, which are ubiquitous in systems with a specific symmetry. One then applies the perturbation scheme to locate the MDRs of a dielectric sphere that contains several smaller spherical inclusions. To gauge the accuracy and efficiency of the perturbation scheme, we also use a transfer-matrix method to obtain an eigenvalue equation for MDRs in these systems. The results obtained from these two methods are compared, and good agreement is found.

© 2002 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

(260.2110) Physical optics : Electromagnetic optics

(260.5740) Physical optics : Resonance

(290.0290) Scattering : Scattering

(290.4020) Scattering : Mie theory

**Citation**

Sheung-wah Ng, Pui-tang Leung, and Kai-ming Lee, "Dyadic formulation of morphology-dependent resonances. III. Degenerate perturbation theory," J. Opt. Soc. Am. B **19**, 154-164 (2002)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-1-154

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### References

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- Our definition for the transverse dyadic Green’s function is slightly different from the conventional one, which is related to ours through direct differentiation. In addition to yielding the magnetic field of a localized current source, the Green’s function defined by us is symmetric for the transposition of the field and source points and can be expanded in terms of the tensor products of relevant MDR fields.
- In general, both G and Δ are non-Hermitian and sometimes cannot be diagonalized. However, it is always possible to transform these matrices into a triangular form, and our derivation in this paper still holds.
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- S. W. Ng, “Mie’s scattering: a morphology-dependent resonance approach,” M. Phil. thesis (Chinese University of Hong Kong, Shatin, Hong Kong, China, 2000).

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