F. Borghese, P. Denti, R. Saija, and O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992); R. L. Armstrong, J.-G. Xie, T. Ruekgauer, J. Gu, and R. G. Pinnick, “Effects of submicrometer-sized particles on microdroplet lasing,” Opt. Lett. 18, 119–121 (1993).
We consider MDR’s of stable optical systems in the present paper; hence the imaginary part of the complex wave number of a MDR is always less than zero.
C.-T. Tai, Dyadic Functions in Electromagnetic Theory, 2nd ed. (IEEE Press, New York, 1993).
W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, New York, 1995).
J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
A. L. Fetter and J. D. Walecka, Quantum Theory of Many Body Systems (McGraw-Hill, New York, 1971).
In the present paper we assume that either the MDR’s of the unperturbed system are nondegenerate or the perturbation does not couple degenerate MDR’s by symmetry arguments. Otherwise a degenerate perturbation theory would have to be formulated, which is out of place here.
We notice that Qlml′m′ of Eq. (A12) is nonzero only if m≠ 0. Thus we concentrate on the m≠0 cases here.
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.
See, e.g., D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
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).
See, e.g., P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964).
See, e.g., M. Kerker, ed., Selected Papers on Light Scattering, Proc. SPIE 951, (1988), and references therein.
P. W. Barber and R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).
R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).