Abstract

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 Wigner’s semicircular theorem.

© 2002 Optical Society of America

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References

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  1. M. Kerker, ed., Selected Papers on Light Scattering, Proc. SPIE951 (1988).
  2. P. W. Barber and R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).
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  5. K. M. Lee, P. T. Leung, and K. M. Pang, J. Opt. Soc. Am. B 16, 1418 (1999).
    [CrossRef]
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    [CrossRef]
  7. H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).
  8. J. Gu, T. E. Ruekgauer, J. G. Xie, and R. L. Armstrong, Opt. Lett. 18, 1293 (1993).
    [CrossRef]
  9. H. Taniguchi, M. Nishiya, S. Tanosaki, and H. Inaba, Opt. Lett. 21, 263 (1996).
    [CrossRef] [PubMed]
  10. D. Ngo and R. G. Pinnick, J. Opt. Soc. Am. B 11, 1352 (1994).
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  11. See, e.g., G. Gouesbet and G. Gréhan, J. Mod. Opt. 47, 821 (2000).
    [CrossRef]
  12. S. W. Ng, P. T. Leung, and K. M. Lee, J. Opt. Soc. Am. B 19, 154 (2002).
    [CrossRef]
  13. M. L. Mehta, Random Matrices, 2nd ed. (Academic, San Diego, Calif., 1999).
  14. 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).
    [CrossRef]

2002 (1)

2000 (1)

See, e.g., G. Gouesbet and G. Gréhan, J. Mod. Opt. 47, 821 (2000).
[CrossRef]

1999 (2)

1996 (1)

1994 (1)

D. Ngo and R. G. Pinnick, J. Opt. Soc. Am. B 11, 1352 (1994).
[CrossRef]

1993 (2)

J. Gu, T. E. Ruekgauer, J. G. Xie, and R. L. Armstrong, Opt. Lett. 18, 1293 (1993).
[CrossRef]

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

1992 (1)

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Armstrong, R. L.

Brune, M.

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Campillo, A. J.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Chýlek, P.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Collot, L.

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Eversole, J. D.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Gouesbet, G.

See, e.g., G. Gouesbet and G. Gréhan, J. Mod. Opt. 47, 821 (2000).
[CrossRef]

Gréhan, G.

See, e.g., G. Gouesbet and G. Gréhan, J. Mod. Opt. 47, 821 (2000).
[CrossRef]

Gu, J.

Haroche, S.

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Huston, A. L.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Inaba, H.

Khersonskii, V. K.

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).
[CrossRef]

Lee, K. M.

Lefevre-Seguin, V.

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Leung, P. T.

Lin, H.-B.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, and P. Chýlek, Opt. Lett. 17, 960 (1992).

Mehta, M. L.

M. L. Mehta, Random Matrices, 2nd ed. (Academic, San Diego, Calif., 1999).

Moskalev, A. N.

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).
[CrossRef]

Ng, S. W.

Ngo, D.

D. Ngo and R. G. Pinnick, J. Opt. Soc. Am. B 11, 1352 (1994).
[CrossRef]

Nishiya, M.

Pang, K. M.

Pinnick, R. G.

D. Ngo and R. G. Pinnick, J. Opt. Soc. Am. B 11, 1352 (1994).
[CrossRef]

Raimond, J. M.

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Ruekgauer, T. E.

Taniguchi, H.

Tanosaki, S.

Varshalovich, D. A.

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).
[CrossRef]

Xie, J. G.

Europhys. Lett. (1)

See, e.g., L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

J. Mod. Opt. (1)

See, e.g., G. Gouesbet and G. Gréhan, J. Mod. Opt. 47, 821 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Lett. (3)

Other (5)

M. Kerker, ed., Selected Papers on Light Scattering, Proc. SPIE951 (1988).

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).

M. L. Mehta, Random Matrices, 2nd ed. (Academic, San Diego, Calif., 1999).

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).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Shifts in the MDR frequency δωδωγp for a TE MDR [l=50 and ωγ0=42.0497-6.9830×10-4i] of a water droplet nI=1.33 after the addition of inclusions nII=1.50 with a fixed volume ratio of 3% and (a) N=105 and (b) N=106. Note that the MDR frequency shifts for both cases lie on a common straight line.

Fig. 2
Fig. 2

Normalized distribution function ρn2σcρx plotted versus xnx/2σc for TE MDRs with l=50, N=105 (circles); l=50, N=106 (squares); l=75, N=105 (triangles); l=75, N=106 (pluses). nI=1.33, nII=1.50, and the volume ratio of the inclusions is 3% for all the cases. The data all lie on a universal (solid) curve as predicted by Eq. (4).

Fig. 3
Fig. 3

Dashed and solid curves, respectively, show the TE501 TCS as functions of the size parameter ka for a pure water droplet and a doped water droplet with l=50,nI=1.33,nII=1.50,N=105, and a volume ratio of the inclusions of 3%.

Equations (6)

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ϱdrjlnIωrdrr=a=jnIωahl1ωadrhl1ωrdrr=a,
Tmn=-ωγ02II-Ii=1Nvid3reγmr·eγnr,
Tmm=-ωγ02Nb3II-II2a3N1lj2,
ρx=2πσc2-14σc2-x2if x<2σc0otherwise.
σc2=m,mTmm2-Tmm2/2l+1,
σcTmm=1N2l+1a3I46I22-11/2,

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