Abstract

We use the recently extended superposition T-matrix method to study the behavior of a sharp Lorenz–Mie resonance upon filling a spherical micrometer-sized droplet with tens and hundreds of randomly positioned microscopic inclusions. We show that as the number of inclusions increases, the extinction cross-section peak and the sharp asymmetry-parameter minimum become suppressed, widen, and move toward smaller droplet size parameters, while ratios of diagonal elements of the scattering matrix exhibit sharp angular features indicative of a distinctly nonspherical particle. Our results highlight the limitedness of the concept of an effective refractive index of an inhomogeneous spherical particle.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2014 (1)

D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
[CrossRef]

2008 (1)

M. I. Mishchenko, Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

2007 (1)

2003 (2)

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

M. I. Mishchenko and A. A. Lacis, Appl. Opt. 42, 5551 (2003).
[CrossRef]

2002 (2)

P.-T. Leung, S.-W. Ng, K.-M. Pang, and K.-M. Lee, Opt. Lett. 27, 1749 (2002).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

2001 (1)

2000 (1)

1997 (2)

G. Videen, P. Pellegrino, D. Ngo, J. S. Videen, and R. G. Pinnick, Appl. Opt. 36, 6115 (1997).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

1996 (1)

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

1994 (2)

1993 (1)

1992 (2)

1985 (1)

1976 (1)

Arnold, S.

Barber, P. W.

Bartley, D.

Benner, R. E.

S. C. Hill, C. K. Rushforth, R. E. Benner, and P. R. Conwell, Appl. Opt. 24, 2380 (1985).
[CrossRef]

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, 1988), p. 3.

Bronk, B. V.

Cairns, B.

Chýlek, P.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

P. Chýlek, D. Ngo, and R. G. Pinnick, J. Opt. Soc. Am. A 9, 775 (1992).
[CrossRef]

P. Chýlek, J. Opt. Soc. Am. 66, 285 (1976).
[CrossRef]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

Conwell, P. R.

Davies, M.

Dlugach, J. M.

J. M. Dlugach and M. I. Mishchenko, “Effects of nonsphericity on the behavior of Lorenz–Mie resonances in scattering characteristics of liquid-cloud droplets,” J. Quant. Spectrosc. Radiat. Transf. (to be published).

Dobbie, J. S.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

Fu, Q.

Fuller, K. A.

Geldart, D. J. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

Greenaway, R. S.

Hill, S. C.

M. Mazumder, S. C. Hill, and P. W. Barber, J. Opt. Soc. Am. A 9, 1844 (1992).
[CrossRef]

S. C. Hill, C. K. Rushforth, R. E. Benner, and P. R. Conwell, Appl. Opt. 24, 2380 (1985).
[CrossRef]

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, 1988), p. 3.

Hirst, E.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 29.

Kahnert, F. M.

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

Kaye, P. H.

Klett, J. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko and A. A. Lacis, Appl. Opt. 42, 5551 (2003).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lee, K.-M.

Lesins, G. B.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Leung, P.-T.

Liu, L.

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, Opt. Express 15, 2822 (2007).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

Macke, A.

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

Mackowski, D. W.

Mazumder, M.

Menon, S.

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, Opt. Express 15, 2822 (2007).
[CrossRef]

M. I. Mishchenko and A. A. Lacis, Appl. Opt. 42, 5551 (2003).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 29.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

J. M. Dlugach and M. I. Mishchenko, “Effects of nonsphericity on the behavior of Lorenz–Mie resonances in scattering characteristics of liquid-cloud droplets,” J. Quant. Spectrosc. Radiat. Transf. (to be published).

Ng, S.-W.

Ngo, D.

Pang, K.-M.

Pellegrino, P.

Pinnick, R. G.

Prabhu, D. R.

Rushforth, C. K.

Secker, D. R.

Smith, M. J.

Sun, W.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 29.

Tso, H. C. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

Videen, G.

M. I. Mishchenko, L. Liu, D. W. Mackowski, B. Cairns, and G. Videen, Opt. Express 15, 2822 (2007).
[CrossRef]

D. R. Prabhu, M. Davies, and G. Videen, Opt. Express 8, 308 (2001).
[CrossRef]

G. Videen, W. Sun, Q. Fu, D. R. Secker, R. S. Greenaway, P. H. Kaye, E. Hirst, and D. Bartley, Appl. Opt. 39, 5031 (2000).
[CrossRef]

G. Videen, P. Pellegrino, D. Ngo, J. S. Videen, and R. G. Pinnick, Appl. Opt. 36, 6115 (1997).
[CrossRef]

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

Videen, J. S.

Wiscombe, W. J.

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 29.

Wong, J. G. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Appl. Opt. (4)

J. Geophys. Res. (1)

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Quant. Spectrosc. Radiat. Transfer (4)

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Rev. Geophys. (1)

M. I. Mishchenko, Rev. Geophys. 46, RG2003 (2008).
[CrossRef]

Other (5)

J. M. Dlugach and M. I. Mishchenko, “Effects of nonsphericity on the behavior of Lorenz–Mie resonances in scattering characteristics of liquid-cloud droplets,” J. Quant. Spectrosc. Radiat. Transf. (to be published).

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 273.

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, 1988), p. 3.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), p. 29.

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Figures (3)

Fig. 1.
Fig. 1.

(a), (b) Extinction cross section and asymmetry parameter for a spherical droplet with N randomly positioned inclusions. (c)–(f) As in (a), (b) but for ratios of the elements of the Stokes scattering matrix.

Fig. 2.
Fig. 2.

Asymmetry parameter computed for two different realizations of the initial configuration of 30 inclusions.

Fig. 3.
Fig. 3.

Two different realizations of the initial configuration of 30 inclusions used in Fig. 2.

Equations (3)

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

F˜(Θ)=[a1(Θ)b1(Θ)00b1(Θ)a2(Θ)0000a3(Θ)b2(Θ)00b2(Θ)a4(Θ)],
120πdΘsinΘa1(Θ)=1.
a2(Θ)/a1(Θ)1anda3(Θ)/a4(Θ)1.

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