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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 16, Iss. 9 — Sep. 1, 1999
  • pp: 1409–1417

Dyadic formulation of morphology-dependent resonances. I. Completeness relation

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


JOSA B, Vol. 16, Issue 9, pp. 1409-1417 (1999)
http://dx.doi.org/10.1364/JOSAB.16.001409


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Abstract

The magnetic (or electric) fields of morphology-dependent resonances of a dielectric sphere are shown to form an orthogonal complete set for expanding divergence-free vectorial functions inside the dielectric sphere, provided that there is a spatial discontinuity in its refractive index, say, at the edge of the sphere. A transverse projection dyad that picks up the divergence-free part (or its generalization) of a vector is defined and shown to be expandable in terms of the magnetic (or electric) fields of these morphology-dependent resonances. Moreover, the transverse dyadic Green’s function in these dielectric spheres is in turn expressed as a sum of tensor products of relevant morphology-dependent resonance fields. Each term in the sum manifests itself as a resonant response to external perturbations. Thus the morphology-dependent resonance expansion provides a powerful tool to analyze various optical phenomena in dielectric spheres.

© 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

Citation
K. M. Lee, P. T. Leung, and K. M. Pang, "Dyadic formulation of morphology-dependent resonances. I. Completeness relation," J. Opt. Soc. Am. B 16, 1409-1417 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-9-1409


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  23. 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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