Abstract

The frequencies of the normal azimuthal modes of a slightly deformed droplet that is axisymmetric about its flow direction are no longer degenerate but vary with position along the droplet rim. We measured the wavelength variation along the entire rim of a dye-lasing droplet with a spectrograph and a CCD array. We determined the amplitude and the shape of the droplet deformation from the observed and predicted parabolic dependence of wavelength variation with distance along the spectrograph slit.

© 1993 Optical Society of America

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References

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  1. S. C. Hill, R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.
  3. H.-M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, Phys. Rev. A 41, 5187 (1990).
    [CrossRef] [PubMed]
  4. S. Arnold, D. E. Spock, L. M. Folan, Opt. Lett. 15, 1111 (1990).
    [CrossRef] [PubMed]
  5. H.-M. Tzeng, M. B. Long, R. K. Chang, P. W. Barber, Opt. Lett. 10, 20 (1985).
    [CrossRef]
  6. G. Chen, R. K. Chang, S. C. Hill, P. W. Barber, Opt. Lett. 16, 1269 (1991).
    [CrossRef] [PubMed]
  7. J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, Opt. Lett. 18, 191 (1993).
    [CrossRef] [PubMed]
  8. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, pp. 79–185.
    [CrossRef]

1993

1991

1990

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

S. Arnold, D. E. Spock, L. M. Folan, Opt. Lett. 15, 1111 (1990).
[CrossRef] [PubMed]

1985

H.-M. Tzeng, M. B. Long, R. K. Chang, P. W. Barber, Opt. Lett. 10, 20 (1985).
[CrossRef]

Arnold, S.

Barber, P. W.

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

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

H.-M. Tzeng, M. B. Long, R. K. Chang, P. W. Barber, Opt. Lett. 10, 20 (1985).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, pp. 79–185.
[CrossRef]

Benner, R. E.

S. C. Hill, R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

Chang, R. K.

Chen, G.

Folan, L. M.

Hill, S. C.

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

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

S. C. Hill, R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, pp. 79–185.
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

Lai, H.-M.

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

Leach, D. H.

Leung, P. T.

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

Long, M. B.

H.-M. Tzeng, M. B. Long, R. K. Chang, P. W. Barber, Opt. Lett. 10, 20 (1985).
[CrossRef]

Spock, D. E.

Swindal, J. C.

Tzeng, H.-M.

H.-M. Tzeng, M. B. Long, R. K. Chang, P. W. Barber, Opt. Lett. 10, 20 (1985).
[CrossRef]

Young, K.

J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, Opt. Lett. 18, 191 (1993).
[CrossRef] [PubMed]

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

Opt. Lett.

Phys. Rev. A

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

Other

S. C. Hill, R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), Chap. 1, pp. 3–61.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 3, pp. 79–185.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

CCD images of the orange-dye-lasing droplets as they appear at the entrance slit of a spectrograph (left-hand column). The droplets in (a) are less magnified than those in (b) and (c). For (b) the right-half rim and for (c) the left-half rim is imaged onto the slit. The spatially preserved wavelength-dispersed data captured by the CCD are shown on the right-hand side. Note the ⊃- and ⊂-shaped λz) curves. The distance z below the orifice is indicated for each CCD image.

Fig. 2
Fig. 2

Wavelength dependence of the light from different positions (with different θ and Δz) on the deformed droplet rim; various parts of the parabolic λz) curve can be related to different m-mode MDR’s. (b) Actual CCD data recorded from a single droplet (with the right semicircle imaged onto the entrance slit) located at z = 10 mm downstream from the orifice. The ⊃-shaped λz) curve can be observed from four n-mode MDR’s (both TE and TM) of the same radial mode order l.

Fig. 3
Fig. 3

Image-corrected λz) data (+ symbols): the CCD data shown in Fig. 2(b) are corrected for the semicircular image that is measured with the grating turned to its zeroth order. The solid curve is the second-order polynomial fit λz) = C0 + C2z/a)2. For the least-squares error, C0 = 591.8 nm and C2 = −1.16 nm. By using Eq. (2) and the values of C0 and C2, we obtain λ0 = 591 nm and e = −4 × 10−3.

Equations (2)

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ω ( m ) = ω 0 { 1 e 6 [ 1 3 m 2 n ( n + 1 ) ] } ,
λ ( Δ z ) = λ 0 [ 1 e 3 + e 2 ( Δ z a ) 2 ] ,

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