Abstract

Structural resonances have been found in the Raman spectra of optically levitated liquid droplets of mixtures of water and glycerol. The observed resonances could be assigned by using the well-known Lorenz-Mie formalism. It was found that for the particular droplet under investigation quite high-order numbers (l = 8,9) of the natural modes of oscillation of a sphere play a dominant role. We describe the intensities of the resonances in the Raman spectrum particularly through the volume averaged internal field intensity. We show further that the internal angle-averaged electric field intensity is localized near, but not confined to, the sphere surface.

© 1985 Optical Society of America

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References

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  1. A. B. Pluchino, “Surface Waves and the Radiative Properties of Micron-sized Particles,” Appl. Opt. 20, 2986 (1981).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. J. F. Owen, P. W. Barber, B. J. Messinger, R. R. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
    [CrossRef] [PubMed]
  4. A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
    [CrossRef] [PubMed]
  5. A. Ashkin, J. M. Dziedzic, “Observation of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
    [CrossRef]
  6. A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  7. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  8. J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
    [CrossRef]
  9. S. C. Hill, R. E. Benner, C. K. Rushforth, D. R. Conwell, “Structural Resonances Observed in the Fluorescence Emission from Small Spheres on Substrates,” Appl. Opt. 23, 1680 (1984).
    [CrossRef] [PubMed]
  10. J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
    [CrossRef]
  11. J. F. Owen, P. W. Barber, R. K. Chang, “Morphology Dependent Raman Spectra from Microparticles,” in Microbeam Analysis 1982, K. F. J. Heinrich, Ed. (San Francisco Press, San Francisco, 1982), p. 255.
  12. R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
    [CrossRef]
  13. R. Thurn, W. Kiefer, “Observation of Resonance Structure in the Raman Spectra of Optically Levitated Microspheres,” in Proceedings Ninth International Conference on Raman Spectroscopy (1984), p. 860.
  14. R. Thurn, W. Kiefer, “Observations of Structural Resonances in the Raman Spectra of Optically Levitated Dielectric Microspheres,” J. Raman Spectrosc. 15, 411 (1984).
    [CrossRef]
  15. A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
    [CrossRef]
  16. A. Ashkin, J. M. Dziedzic, “Optical Levitation of Liquid Drops by Radiation Pressure,” Science 187, 1073 (1975).
    [CrossRef] [PubMed]
  17. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  18. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc.Am. A12, 62 (1984).
    [CrossRef]
  19. P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-wave Resonances,” Phys. Rev. A 18, 2229 (1978).
    [CrossRef]
  20. J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
    [CrossRef] [PubMed]

1984 (5)

R. Thurn, W. Kiefer, “Observation of Resonance Structure in the Raman Spectra of Optically Levitated Microspheres,” in Proceedings Ninth International Conference on Raman Spectroscopy (1984), p. 860.

R. Thurn, W. Kiefer, “Observations of Structural Resonances in the Raman Spectra of Optically Levitated Dielectric Microspheres,” J. Raman Spectrosc. 15, 411 (1984).
[CrossRef]

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc.Am. A12, 62 (1984).
[CrossRef]

S. C. Hill, R. E. Benner, C. K. Rushforth, D. R. Conwell, “Structural Resonances Observed in the Fluorescence Emission from Small Spheres on Substrates,” Appl. Opt. 23, 1680 (1984).
[CrossRef] [PubMed]

R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
[CrossRef]

1982 (1)

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
[CrossRef]

1981 (6)

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

1978 (2)

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

1975 (1)

A. Ashkin, J. M. Dziedzic, “Optical Levitation of Liquid Drops by Radiation Pressure,” Science 187, 1073 (1975).
[CrossRef] [PubMed]

1970 (1)

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical Levitation of Liquid Drops by Radiation Pressure,” Science 187, 1073 (1975).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Barber, P. W.

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc.Am. A12, 62 (1984).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
[CrossRef]

J. F. Owen, P. W. Barber, B. J. Messinger, R. R. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

J. F. Owen, P. W. Barber, R. K. Chang, “Morphology Dependent Raman Spectra from Microparticles,” in Microbeam Analysis 1982, K. F. J. Heinrich, Ed. (San Francisco Press, San Francisco, 1982), p. 255.

Benner, R. E.

S. C. Hill, R. E. Benner, C. K. Rushforth, D. R. Conwell, “Structural Resonances Observed in the Fluorescence Emission from Small Spheres on Substrates,” Appl. Opt. 23, 1680 (1984).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Bennett, H. S.

Chang, R. K.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

J. F. Owen, P. W. Barber, R. K. Chang, “Morphology Dependent Raman Spectra from Microparticles,” in Microbeam Analysis 1982, K. F. J. Heinrich, Ed. (San Francisco Press, San Francisco, 1982), p. 255.

Chang, R. R.

Chýlek, P.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Conwell, D. R.

Conwell, P. R.

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc.Am. A12, 62 (1984).
[CrossRef]

Dorain, P. B.

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Optical Levitation of Liquid Drops by Radiation Pressure,” Science 187, 1073 (1975).
[CrossRef] [PubMed]

Hill, S. C.

Kerker, M.

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

Kiefer, W.

R. Thurn, W. Kiefer, “Observations of Structural Resonances in the Raman Spectra of Optically Levitated Dielectric Microspheres,” J. Raman Spectrosc. 15, 411 (1984).
[CrossRef]

R. Thurn, W. Kiefer, “Observation of Resonance Structure in the Raman Spectra of Optically Levitated Microspheres,” in Proceedings Ninth International Conference on Raman Spectroscopy (1984), p. 860.

R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
[CrossRef]

Kiehl, J. T.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Ko, M. K. W.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Messinger, B. J.

Owen, J. F.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal Electric Field Distributions of a Dielectric Cylinder at Resonance Wavelengths,” Opt. Lett. 6, 540 (1981).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, B. J. Messinger, R. R. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

J. F. Owen, P. W. Barber, R. K. Chang, “Morphology Dependent Raman Spectra from Microparticles,” in Microbeam Analysis 1982, K. F. J. Heinrich, Ed. (San Francisco Press, San Francisco, 1982), p. 255.

Pluchino, A. B.

Rosasco, G. J.

Rushforth, C. K.

Stolen, R. H.

Thurn, R.

R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
[CrossRef]

R. Thurn, W. Kiefer, “Observations of Structural Resonances in the Raman Spectra of Optically Levitated Dielectric Microspheres,” J. Raman Spectrosc. 15, 411 (1984).
[CrossRef]

R. Thurn, W. Kiefer, “Observation of Resonance Structure in the Raman Spectra of Optically Levitated Microspheres,” in Proceedings Ninth International Conference on Raman Spectroscopy (1984), p. 860.

Aerosol Sci. Tech. J. (1)

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Tech. J. 1, 293 (1982).
[CrossRef]

Appl. Opt. (4)

Appl. Spectrosc. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc.Am. (1)

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc.Am. A12, 62 (1984).
[CrossRef]

J. Raman Spectrosc. (1)

R. Thurn, W. Kiefer, “Observations of Structural Resonances in the Raman Spectra of Optically Levitated Dielectric Microspheres,” J. Raman Spectrosc. 15, 411 (1984).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Phys. Rev. Lett. (4)

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Observation of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structural Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of Fluorescence Induced by Microstructure Resonances of a Dielectric Fiber,” Phys. Rev. Lett. 47, 1075 (1981).
[CrossRef]

Proceedings Ninth International Conference on Raman Spectroscopy (1)

R. Thurn, W. Kiefer, “Observation of Resonance Structure in the Raman Spectra of Optically Levitated Microspheres,” in Proceedings Ninth International Conference on Raman Spectroscopy (1984), p. 860.

Science (1)

A. Ashkin, J. M. Dziedzic, “Optical Levitation of Liquid Drops by Radiation Pressure,” Science 187, 1073 (1975).
[CrossRef] [PubMed]

Other (2)

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

J. F. Owen, P. W. Barber, R. K. Chang, “Morphology Dependent Raman Spectra from Microparticles,” in Microbeam Analysis 1982, K. F. J. Heinrich, Ed. (San Francisco Press, San Francisco, 1982), p. 255.

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Figures (5)

Fig. 1
Fig. 1

Sketch of the experimental apparatus for optical levitation of liquid drops by radiation pressure.

Fig. 2
Fig. 2

Raman spectrum of a 1:6 mixture of water and glycerol (refractive index m = 1.45).

Fig. 3
Fig. 3

A, O–H stretching region of the Raman spectrum of a liquid 1:6 water–glycerol mixture (refractive index m = 1.45); B, observed Raman spectrum of an optically levitated liquid drop of the same mixture as for A (radius of sphere a ≈ 15 μm; resolution = 7 cm−1); C, theoretical curve obtained by multiplication of curve A in Fig. 3 with curve C of Fig. 4.

Fig. 4
Fig. 4

Calculated structural resonances for a sphere of radius a = 14.422 μm, refractive index m = 1.45, and incident field strength E0 = 1 V/m. A,B, averaged internal field intensity vs Mie size parameter and Raman shift (from 530.9 nm). A and B differ only in vertical scale. C, this calculated spectrum was obtained by integration over the peaks in spectrum A, respectively, B, and convolution with a Gaussian slit function (for further explanation see text).

Fig. 5
Fig. 5

Calculated angle averaged field intensity within a lossless dielectric sphere as a function of the fraction of radius. Calculations are shown for m = 1.45 and x satisfying resonance conditions for TE154 modes.

Tables (1)

Tables Icon

Table I Mie Size Parameters, Halfwidths of Resonance, and Volume Averaged Internal Electric Field Intensity for the TE154 Mode of a Dielectric Sphere with Refractive Index m = 1.450 as a Function of Resonance Order I

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I total ( x ) = 3 a 3 0 a d r r 2 I ( r ) ,
I ( r ) = 1 4 π 0 2 π d φ 0 π sin θ d θ E i ( r , θ , φ ) E i * ( r , θ , φ ) = E 0 2 2 n = 1 { ( 2 n + 1 ) j n 2 ( m 2 π r / λ ) | d n | 2 + [ ( n + 1 ) j n 1 2 ( m 2 π r / λ ) + n j n + 1 2 ( m 2 π r / λ ) ] | c n | 2 }
c n = m i / x h n ( 2 ) ( x ) [ m x j n ( m x ) ] m 2 j n ( m x ) [ x h n ( 2 ) ( x ) ] ,
d n = i / x h n ( 2 ) ( x ) [ m x j n ( m x ) ] j n ( m x ) [ x h n ( 2 ) ( x ) ] ,

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