Abstract

Light scattering by an evaporating water droplet several micrometers in size with spherical dielectric inclusions was investigated. The evolution of the droplet radius and the effective refractive index was determined. A deviation from predictions by standard effective-medium theories in the form of a resonance was encountered. Simple analysis of the phenomenon was conducted, and a qualitative explanation was proposed.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. I. Mishschenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).
  2. U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).
  3. Y.-l. Xu, “Scattering Mueller matrix of an ensemble of variously shaped small particles,” J. Opt. Soc. Am. A 20, 2093–2105 (2003).
    [CrossRef]
  4. Y.-l. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
    [CrossRef]
  5. V. A. Markel, “Modified spherical harmonics method for solving the radiative transport equation,” Waves Random Media 14, L13–L19 (2004).
    [CrossRef]
  6. I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
    [CrossRef]
  7. V. A. Davis, L. Schwartz, “Electromagnetic propagation in close-packed disordered suspensions,” Phys. Rev. B 31, 5155–5165 (1985).
    [CrossRef]
  8. P. Chýlek, G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
    [CrossRef]
  9. A. Doicu, T. Wriedt, “Equivalent refractive index of a sphere with multiple spherical inclusions,” J. Opt. A, Pure Appl. Opt. 3, 204–209 (2001).
    [CrossRef]
  10. D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
    [CrossRef]
  11. D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).
  12. T. Yoshiyama, I. Sogami, “Kossel images as direct manifestation of the gap structure of the dispersion surface for colloidal crystals,” Phys. Rev. Lett. 56, 1609–1612 (1986).
    [CrossRef] [PubMed]
  13. B. Steiner, B. Berge, R. Gausmann, J. Rohmann, E. Rühl, “Fast in situ sizing technique for single levitated liquid aerosols,” Appl. Opt. 38, 1523–1529 (1999).
    [CrossRef]
  14. B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
    [CrossRef]
  15. D. Stroud, F. P. Pan, “Self-consistent approach to electromagnetic wave propagation in composite media: application to model granular metals,” Phys. Rev. B 17, 1602–1610 (1978).
    [CrossRef]
  16. H. Xu, “A new method by extending Mie theory to calculate local field in outside/inside of aggregates of arbitrary spheres,” Phys. Lett. A 312, 411–419 (2003).
    [CrossRef]
  17. M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
    [CrossRef]
  18. A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
    [CrossRef] [PubMed]

2004 (1)

V. A. Markel, “Modified spherical harmonics method for solving the radiative transport equation,” Waves Random Media 14, L13–L19 (2004).
[CrossRef]

2003 (2)

Y.-l. Xu, “Scattering Mueller matrix of an ensemble of variously shaped small particles,” J. Opt. Soc. Am. A 20, 2093–2105 (2003).
[CrossRef]

H. Xu, “A new method by extending Mie theory to calculate local field in outside/inside of aggregates of arbitrary spheres,” Phys. Lett. A 312, 411–419 (2003).
[CrossRef]

2001 (3)

Y.-l. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

A. Doicu, T. Wriedt, “Equivalent refractive index of a sphere with multiple spherical inclusions,” J. Opt. A, Pure Appl. Opt. 3, 204–209 (2001).
[CrossRef]

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

2000 (1)

A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

P. Chýlek, G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

1992 (1)

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

1988 (1)

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
[CrossRef]

1986 (1)

T. Yoshiyama, I. Sogami, “Kossel images as direct manifestation of the gap structure of the dispersion surface for colloidal crystals,” Phys. Rev. Lett. 56, 1609–1612 (1986).
[CrossRef] [PubMed]

1985 (1)

V. A. Davis, L. Schwartz, “Electromagnetic propagation in close-packed disordered suspensions,” Phys. Rev. B 31, 5155–5165 (1985).
[CrossRef]

1978 (1)

D. Stroud, F. P. Pan, “Self-consistent approach to electromagnetic wave propagation in composite media: application to model granular metals,” Phys. Rev. B 17, 1602–1610 (1978).
[CrossRef]

1977 (1)

I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
[CrossRef]

Bali, S.

A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
[CrossRef] [PubMed]

Bazhan, W.

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

Berge, B.

Chýlek, P.

P. Chýlek, G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

Cohen, M. H.

I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
[CrossRef]

Davis, V. A.

V. A. Davis, L. Schwartz, “Electromagnetic propagation in close-packed disordered suspensions,” Phys. Rev. B 31, 5155–5165 (1985).
[CrossRef]

Derkachov, G.

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Doicu, A.

A. Doicu, T. Wriedt, “Equivalent refractive index of a sphere with multiple spherical inclusions,” J. Opt. A, Pure Appl. Opt. 3, 204–209 (2001).
[CrossRef]

Gausmann, R.

Gustafson, B. Å. S.

Y.-l. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Hovenier, J. W.

M. I. Mishschenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

Jakubczyk, D.

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Jortner, J.

I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
[CrossRef]

Kolwas, K.

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Kolwas, M.

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Kreibig, U.

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).

Lagendijk, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
[CrossRef]

Markel, V. A.

V. A. Markel, “Modified spherical harmonics method for solving the radiative transport equation,” Waves Random Media 14, L13–L19 (2004).
[CrossRef]

Mishschenko, M. I.

M. I. Mishschenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

Pan, F. P.

D. Stroud, F. P. Pan, “Self-consistent approach to electromagnetic wave propagation in composite media: application to model granular metals,” Phys. Rev. B 17, 1602–1610 (1978).
[CrossRef]

Rohmann, J.

Rühl, E.

Schwartz, L.

V. A. Davis, L. Schwartz, “Electromagnetic propagation in close-packed disordered suspensions,” Phys. Rev. B 31, 5155–5165 (1985).
[CrossRef]

Sogami, I.

T. Yoshiyama, I. Sogami, “Kossel images as direct manifestation of the gap structure of the dispersion surface for colloidal crystals,” Phys. Rev. Lett. 56, 1609–1612 (1986).
[CrossRef] [PubMed]

Steiner, B.

Stroud, D.

D. Stroud, F. P. Pan, “Self-consistent approach to electromagnetic wave propagation in composite media: application to model granular metals,” Phys. Rev. B 17, 1602–1610 (1978).
[CrossRef]

Thomas, J. E.

A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
[CrossRef] [PubMed]

Tip, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

Travis, L. D.

M. I. Mishschenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

van Albada, M. P.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
[CrossRef]

van der Mark, M. B.

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
[CrossRef]

van Tiggelen, B. A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

Videen, G.

P. Chýlek, G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

Vollmer, M.

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).

Wax, A.

A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
[CrossRef] [PubMed]

Webman, I.

I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
[CrossRef]

Wriedt, T.

A. Doicu, T. Wriedt, “Equivalent refractive index of a sphere with multiple spherical inclusions,” J. Opt. A, Pure Appl. Opt. 3, 204–209 (2001).
[CrossRef]

Xu, H.

H. Xu, “A new method by extending Mie theory to calculate local field in outside/inside of aggregates of arbitrary spheres,” Phys. Lett. A 312, 411–419 (2003).
[CrossRef]

Xu, Y.-l.

Y.-l. Xu, “Scattering Mueller matrix of an ensemble of variously shaped small particles,” J. Opt. Soc. Am. A 20, 2093–2105 (2003).
[CrossRef]

Y.-l. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Yoshiyama, T.

T. Yoshiyama, I. Sogami, “Kossel images as direct manifestation of the gap structure of the dispersion surface for colloidal crystals,” Phys. Rev. Lett. 56, 1609–1612 (1986).
[CrossRef] [PubMed]

Zientara, M.

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Appl. Opt. (1)

J. Opt. A, Pure Appl. Opt. (1)

A. Doicu, T. Wriedt, “Equivalent refractive index of a sphere with multiple spherical inclusions,” J. Opt. A, Pure Appl. Opt. 3, 204–209 (2001).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transf. (1)

Y.-l. Xu, B. Å. S. Gustafson, “A generalized multiparticle Mie-solution: further experimental verification,” J. Quant. Spectrosc. Radiat. Transf. 70, 395–419 (2001).
[CrossRef]

Opt. Commun. (1)

P. Chýlek, G. Videen, “Scattering by a composite sphere and effective medium approximations,” Opt. Commun. 146, 15–20 (1998).
[CrossRef]

Opto-Electron. Rev. (1)

D. Jakubczyk, M. Zientara, W. Bazhan, M. Kolwas, K. Kolwas, “A device for light scatterometry on single levitated droplets,” Opto-Electron. Rev. 9, 423–430 (2001).

Phys. Lett. A (1)

H. Xu, “A new method by extending Mie theory to calculate local field in outside/inside of aggregates of arbitrary spheres,” Phys. Lett. A 312, 411–419 (2003).
[CrossRef]

Phys. Rev. B (5)

M. B. van der Mark, M. P. van Albada, A. Lagendijk, “Light scattering in strongly scattering media: multiple scattering and weak localization,” Phys. Rev. B 37, 3575–3592 (1988); Erratum, Phys. Rev. B38, 5063 (1988).
[CrossRef]

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

D. Stroud, F. P. Pan, “Self-consistent approach to electromagnetic wave propagation in composite media: application to model granular metals,” Phys. Rev. B 17, 1602–1610 (1978).
[CrossRef]

I. Webman, J. Jortner, M. H. Cohen, “Theory of optical and microwave properties of microscopically inhomogeneous materials,” Phys. Rev. B 15, 5712–5723 (1977).
[CrossRef]

V. A. Davis, L. Schwartz, “Electromagnetic propagation in close-packed disordered suspensions,” Phys. Rev. B 31, 5155–5165 (1985).
[CrossRef]

Phys. Rev. Lett. (2)

T. Yoshiyama, I. Sogami, “Kossel images as direct manifestation of the gap structure of the dispersion surface for colloidal crystals,” Phys. Rev. Lett. 56, 1609–1612 (1986).
[CrossRef] [PubMed]

A. Wax, S. Bali, J. E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000).
[CrossRef] [PubMed]

Waves Random Media (1)

V. A. Markel, “Modified spherical harmonics method for solving the radiative transport equation,” Waves Random Media 14, L13–L19 (2004).
[CrossRef]

Other (3)

M. I. Mishschenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, San Diego, Calif., 2000).

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters (Springer, New York, 1995).

D. Jakubczyk, M. Zientara, G. Derkachov, K. Kolwas, M. Kolwas, “Investigation of the evolution of the charged water droplets in the electrodynamic trap,” in Tenth Joint International Symposium on Atmospheric and Ocean Optics/Atmospheric Physics. Part II: Laser Sensing and Atmospheric Physics, G. G. Matvienko, G. M. Krekov, eds., Proc. SPIE5397, 23–33 (2004).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Evolution of a composite droplet radius. The insets (a), (b), and (c) are scattering patterns obtained during the evaporation of water from a single compound droplet with low, medium, and high concentration of inclusions, respectively.  

Fig. 3
Fig. 3

Real part of the effective dielectric function of the composite droplet as a function of droplet radius for three sets of experimental parameters: (a) a=200 nm, polystyrene, T=294.9 K, RH=70%, Patm=1005 hPa, and ninit50 parts per million (ppm); (b) a=300 nm, silica, T=295.9 K, RH=70%, Patm=1009 hPa, and ninit200 ppm; (c) a=450 nm, silica, T=294.9 K, RH=77%, Patm=1013 hPa, and ninit200 ppm.

Fig. 4
Fig. 4

Comparison of two methods used to find the real part of the effective dielectric function. Solid circles and solid curve, averaging method; open circles and dashed curve, direct fitting. Experimental conditions are a=300 nm, silica, T=288.2 K, RH=97%, Patm=1012 hPa, and ninit400 ppm.

Equations (11)

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

Elocal=EMie+ΔE,
ΔE=P30m,
P=nαM(R)Elocal,
P=0(eff-m)EMie.
EMie=Elocal1-nαM(R)30m.
eff=nαM(R)0ElocalEMie+m.
eff=m1+[2nαM(R)]/(30m)1-[nαM(R)]/(30m).
eff-meff+2m=f -m+2m,
nα30m=f -m+2m,
eff(R)=m1+2f(R)M(R)(-m)/(+2m)1-f(R)M(R)(-m)/(+2m).
M(R)=1+P1exp{-2[(R-P2)/P3]2},

Metrics