Abstract

Nondegenerate azimuthal morphology-dependent resonances are observed for a distorted, fluorescently labeled polystyrene microsphere levitated in a quadrupole ion trap. Modeling the individual resonances by using perturbation theory allows a determination of quadrupole and octupole distortion parameters. The particle’s shape changes slowly over the course of the measurement and eventually becomes spherical. The morphological changes are facilitated by laser heating of the particle above the polystyrene glass transition temperature. We demonstrate a method of transforming a trapped particle to a sphere and rendering its azimuthal modes degenerate.

© 2006 Optical Society of America

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References

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2006 (2)

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 3 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[CrossRef]

2003 (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

2001 (1)

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

1993 (2)

1991 (1)

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, Phys. Rev. A 41, 5187 (1990).
[CrossRef] [PubMed]

Barber, P. W.

G. Chen, R. K. Chang, S. C. Hill, and P. W. Barber, Opt. Lett. 16, 1269 (1991).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, Phys. Rev. A 41, 5187 (1990).
[CrossRef] [PubMed]

Campillo, A. J.

Chang, R. K.

Chemla, Y. R.

Chen, G.

Eversole, J. D.

Gerlich, D.

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

Hill, S. C.

Huston, A. L.

Ilchenko, V. S.

A. B. Matsko and V. S. Ilchenko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 3 (2006).
[CrossRef]

Illemann, J.

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, Phys. Rev. A 41, 5187 (1990).
[CrossRef] [PubMed]

Leung, P. T.

Lin, H.-B.

Liu, S. Y.

Matsko, A. B.

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 3 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[CrossRef]

Mazumder, M. M.

Schlemmer, S.

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

Serpengüzel, A.

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Wellert, S.

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

Young, K.

IEEE J. Sel. Top. Quantum Electron. (2)

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 3 (2006).
[CrossRef]

A. B. Matsko and V. S. Ilchenko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[CrossRef]

J. Appl. Phys. (1)

S. Schlemmer, J. Illemann, S. Wellert, and D. Gerlich, J. Appl. Phys. 90, 5410 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, Phys. Rev. A 41, 5187 (1990).
[CrossRef] [PubMed]

Other (2)

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, 1996).
[CrossRef]

D.R.Lide, ed., CRC Handbook of Chemistry and Physics (CRC, 2004).

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Figures (4)

Fig. 1
Fig. 1

View of the experimental configuration.

Fig. 2
Fig. 2

A–D, Fluorescence spectra from a single polystyrene particle taken at 5 min intervals. Spectral changes are due to the particle’s relaxation from spheroidal to spherical shape. E is the predicted scattering spectrum for a sphere with a 0 = 1363 nm and m λ = 1.549 + 10,230 nm 2 λ 2 .

Fig. 3
Fig. 3

Expanded sections of spectra B and C from Fig. 1. Nondegenerate azimuthal MDRs are labeled. The m = l mode has the shortest wavelength and the m = 0 mode the longest, consistent with a prolate spheroidal particle.

Fig. 4
Fig. 4

Measured fractional frequency shifts for the TE 20 and TE 19 m modes in spectra B and C (points). Lines represent frequency shifts calculated by using Eq. (8) and the fitted Δ 2 and Δ 4 values in Table 1.

Tables (1)

Tables Icon

Table 1 Fitted Values of Quadrupole ( Δ 2 ) and Octupole ( Δ 4 ) Distortion Parameters a

Equations (10)

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r ( θ , ϕ ) = a + Δ L 4 π Y L , 0 ( θ , ϕ ) ,
δ ω ω = Δ L a F ( L , l , m ) ,
F ( L , l , m ) = A ( L , l ) f ( m ) ,
A ( L , l ) = 2 l + 1 2 L + 1 [ C ( l l L ; 000 ) ] 2 [ 1 L ( L + 1 ) 2 l ( l + 1 ) ] ,
f ( m ) = ( 1 ) m C ( l l L ; m , m , 0 ) C ( l l L ; 000 ) .
δ ω ω = Δ 2 a F ( 2 , l , m ) = Δ 2 a 5 4 [ 1 3 m 2 l ( l + 1 ) ] .
r ( θ , ϕ ) = a + Δ 2 4 π Y 2 , 0 ( θ , ϕ ) + Δ 4 4 π Y 4 , 0 ( θ , ϕ ) ,
δ ω ω = Δ 2 a F ( 2 , l , m ) Δ 4 a F ( 4 , l , m ) .
A ( 4 , l ) = 27 ( l 2 + l 10 ) ( l + 2 ) ( l 1 ) 4 ( 2 l 1 ) ( 2 l + 5 ) ( 4 l 2 9 ) ,
f ( m ) = 1 5 ( 6 l 2 + 6 l 5 ) m 2 3 l ( l 3 + 2 l 2 l 2 ) + 35 m 4 3 l ( l 3 + 2 l 2 l 2 ) .

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