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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 16, Iss. 9 — Sep. 1, 1999
  • pp: 1418–1430

Dyadic formulation of morphology-dependent resonances. II. Perturbation theory

K. M. Lee, P. T. Leung, and K. M. Pang  »View Author Affiliations

JOSA B, Vol. 16, Issue 9, pp. 1418-1430 (1999)

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A generic perturbation theory for the morphology-dependent resonances (MDR’s) of dielectric spheres is developed based on the dyadic formulation of a completeness relation established previously [J. Opt. Soc. Am. B 16, 1409 (1999)]. Unlike other perturbation methods proposed previously, the formulation presented here takes full account of the vector nature of MDR’s and hence does not limit its validity to perturbations that preserve spherical symmetry. However, the second-order frequency correction obtained directly from the theory, which is expressed as a sum of contributions from individual MDR’s, converges slowly. An efficient scheme, based on the dyadic form of the completeness relation, is thus constructed to accelerate the rate of convergence. As an example illustrating our theory, we apply the perturbation method to study MDR’s of a dielectric sphere that contains another smaller spherical inclusion and compare the results with those obtained from an exact diagonalization method.

© 1999 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

K. M. Lee, P. T. Leung, and K. M. Pang, "Dyadic formulation of morphology-dependent resonances. II. Perturbation theory," J. Opt. Soc. Am. B 16, 1418-1430 (1999)

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  28. We notice that Qlmlm of Eq. (A12) is nonzero only if m≠ 0. Thus we concentrate on the m≠0 cases here.
  29. By mode order we mean, for TE modes, that the mode with the smallest positive Re(ωa) is of mode order 1, the second smallest is of mode order 2, and so on. The TM modes are similarly defined, except that the mode on the imaginary frequency axis is of mode order 0.
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  31. K. M. Pang, “Completeness and perturbation of morphology-dependent resonances in dielectric spheres,” Ph.D. thesis dissertation (Chinese University of Hong Kong, Hong Kong, 1999).

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