Abstract

Splitting of low-Q Mie resonances in high-density alumina spheres with dielectric constant 9.6 is observed. The spheres have a shape distortion parameter value that ranges over 2 orders of magnitude, i.e., from 8×10-5 to 10×10-3. Splitting is observed at the (magnetic or TE) b4,1 (Q425), b5,1 (Q1700), and b6,1 (Q5650) resonances. No splitting of the b3,1 or (electric or TM) a4,1 and a5,1 resonances is observed. The b5,1 resonance is studied extensively. The expected broadening or reduced Q of the resonances that is due to overlapping of the lines split by shape distortion is generally not observed. It is also found that it is easier to observe splitting in the spheres with the smallest shape distortion. This suggests that the mechanism responsible for the observed splitting competes with the shape splitting in such a way that destructive interference results.

© 1998 Optical Society of America

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References

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    [CrossRef]
  2. P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
    [CrossRef]
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  5. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 9, Sec. 25, p. 563.
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    [CrossRef]
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    [CrossRef] [PubMed]
  27. H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
    [CrossRef]
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1995 (4)

1994 (2)

1992 (3)

1991 (2)

1990 (2)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

P. Chylek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
[CrossRef]

1989 (1)

1988 (1)

1985 (1)

1984 (2)

1982 (1)

J. Qwen, R. K. Chang, P. W. Barber, “Morphology dependent resonances in Raman scattering, fluorescence emission, and elastic scattering from microparticles,” Aerosol. Sci. Technol. 1, 293–302 (1982).
[CrossRef]

1981 (1)

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

1978 (1)

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

1909 (1)

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

1908 (1)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Armstrong, R. L.

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Barber, P. W.

M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
[CrossRef]

J. Qwen, R. K. Chang, P. W. Barber, “Morphology dependent resonances in Raman scattering, fluorescence emission, and elastic scattering from microparticles,” Aerosol. Sci. Technol. 1, 293–302 (1982).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Box, M. A.

Chang, R. K.

Chang, R. W.

Chen, G.

Chylek, P.

Chýlek, P.

Conwell, P. R.

Debye, P.

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Essien, M.

Fuller, K. A.

Gillespie, J. B.

Gustafson, B. A.

Hare, J.

Haroche, S.

Hill, S. C.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hunter, B. A.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 8, Sec. 8.8, p. 357.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 16, Sec. 9, p. 769.

Kaiser, T.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kiehl, J. T.

Ko, M. K. W.

Lai, H. M.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Lam, C. C.

Lange, S.

LeFevre-Sequin, V.

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Li, J.

Long, M. B.

Maier, B.

Mazumder, M. M.

Mie, G.

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Ngo, D.

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Pinnick, R. G.

Qian, S.

Qwen, J.

J. Qwen, R. K. Chang, P. W. Barber, “Morphology dependent resonances in Raman scattering, fluorescence emission, and elastic scattering from microparticles,” Aerosol. Sci. Technol. 1, 293–302 (1982).
[CrossRef]

Raimond, J. M.

Rushforth, C. K.

Saleheen, H. I.

Sandoghdar, V.

Schaefer, R. W.

Schuerman, D. W.

Schweiger, G.

Snow, J. B.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 9, Sec. 25, p. 563.

Tzeng, H. M.

Videen, G.

Wall, K. F.

Wang, R. T.

Weiss, D. S.

Young, K.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[CrossRef]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

K. Young, Department of Physics, The Chinese University of Hong Kong, Hong Kong (personal communication, 1997).

Zhang, J. Z.

Aerosol. Sci. Technol. (1)

J. Qwen, R. K. Chang, P. W. Barber, “Morphology dependent resonances in Raman scattering, fluorescence emission, and elastic scattering from microparticles,” Aerosol. Sci. Technol. 1, 293–302 (1982).
[CrossRef]

Ann. Phys. (Leipzig) (2)

G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. A (9)

J. Opt. Soc. Am. B (2)

Opt. Lett. (4)

Phys. Rev. A (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Other (6)

K. Young, Department of Physics, The Chinese University of Hong Kong, Hong Kong (personal communication, 1997).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 8, Sec. 8.8, p. 357.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 9, Sec. 25, p. 563.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), Chap. 16, Sec. 9, p. 769.

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Figures (8)

Fig. 1
Fig. 1

(a) Scattering efficiency Qs versus size parameter x=ka for a dielectric sphere with =9.6, (b) same as (a) but restricted to the range from x=2.0 to 3.5.

Fig. 2
Fig. 2

Schematic diagram of the experiment.

Fig. 3
Fig. 3

(a) The upper plot is scattered power versus frequency at the angles θ=100° and ϕ=90° from a dielectric sphere with e8×10-5. The lower plot is the calculated scattered power at the same angles from a sphere with =9.55. (b) Scattered power versus frequency at the angles θ=100° and ϕ=90° for the same sphere as that used in (a). For this plot the sphere has been rotated 90° about the x axis.

Fig. 4
Fig. 4

(a) Scattered power at the b5,1 resonance from a dielectric sphere with e=2.9×10-3. The detector is at θ=100° and ϕ=90°. (b) Scattered power when the sphere in (a) is rotated a small angle about the x axis. (c) Scattered power when the sphere in (a) is rotated an additional small angle about the x axis.

Fig. 5
Fig. 5

Same as Fig. 4 but for e=10×10-3.

Fig. 6
Fig. 6

(a) Scattered power at the b5,1 resonance from a second dielectric sphere with e=8×10-5. The detector is at θ=100° and ϕ=90°. (b) Scattered power when the sphere in (a) is rotated approximately 45° about the x axis.

Fig. 7
Fig. 7

Scattered power at the b4,1 resonance from a dielectric sphere with e=1.1×10-4. The detector is at θ=100° and ϕ=90°.

Fig. 8
Fig. 8

Scattered power at the b3,1 resonance from a dielectric sphere with e=2.4×10-4. The detector is at θ=100° and ϕ=90°.

Tables (1)

Tables Icon

Table 1 Details of the High-Density Alumina Spheres Used in This Study and a Selection of Some of the Experimental Results: Measured and Calculated Q’s and Spacing of the Split Resonance Lines

Equations (11)

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r(θ, ϕ)=a+Δ4πYL,M(θ, ϕ),
erp-rea=35/4 Δa.
Δωω=-e61-3m2l(l+1),
U=U0 exp(-ω0t/Q),
E(t)=E0 exp(-ω0t/2Q)exp[-i(ω0+δω)t],
E(t)=12π-+E(ω)exp(-iωt)dω,
E(ω)=12π0E0 exp(-ω0t/Q)×exp[i(ω-ω0-δω)t]dt.
[E(ω)]2=E022π1(ω-ω0-δω)2-(ω0/2Q)2.
Ep(ω)=2/π E0Qω0.
[Ep(ω)]2
=n=1Nω0n2Ep24Qn21(ω-ω0n-δωn)2-(ω0n/2Qn)2.

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