Abstract

Analytic solutions are developed for the single-scattering properties of an infinite dielectric cylinder embedded in an absorbing medium with normal incidence, which include extinction, scattering and absorption efficiencies, the scattering phase function, and the asymmetry factor. The extinction and scattering efficiencies are derived by the near-field solutions at the surface of the particle. The normalized scattering phase function is obtained by use of the far-field approximation. Computational results show that, although the absorbing medium significantly reduces the scattering efficiency, it has little effect on absorption efficiency. The absorbing medium can significantly change the conventional phase function. The absorbing medium also strongly affects the polarization of the scattered light. However, for large absorbing particles the degrees of polarization change little with the medium’s absorption. This implies that, if the transmitting lights are strongly weakened inside the particle, the scattered polarized lights can be used to identify objects even when the absorption property of the host medium is unknown, which is important for both active and passive remote sensing.

© 2005 Optical Society of America

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References

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    [CrossRef]
  3. C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
    [CrossRef]
  4. M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
    [CrossRef]
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  6. W. Sun, “Light scattering by nonspherical particles: numerical simulation and applications,” Ph.D. dissertation (Dalhousie University, Halifax, Nova Scotia, Canada, 2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  15. M. I. Mischenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
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    [CrossRef]
  17. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

2003 (1)

2002 (2)

2001 (3)

1999 (1)

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

1996 (2)

M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

M. I. Mischenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef]

1979 (1)

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

1977 (1)

1974 (1)

1972 (1)

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

1918 (1)

Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Baum, B. A.

Bohren, C. F.

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Chylek, P.

Fu, Q.

Gao, B.

Gartz, M.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

Gilra, D. P.

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

Hu, Y.

Huang, H.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kreibig, U.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

Lebedev, A. N.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

Liou, K. N.

Macke, A.

Mischenko, M. I.

Mishchenko, M. I.

Mundy, W. C.

Park, S. K.

Ping, Y.

Platnick, S. E.

Quinten, M.

M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Rayleigh,

Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Rostalski, J.

M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Roux, J. A.

Ruppin, R.

R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
[CrossRef]

Smith, A. M.

Stenzel, O.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

Sudiarta, I. W.

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

I. W. Sudiarta, P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
[CrossRef]

Sun, W.

Travis, L. D.

Tsay, S.

Videen, G.

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Winker, D. M.

Wiscombe, W. J.

Appl. Opt. (5)

Can. J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Eur. Phys. J. (1)

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. 6, 365–373 (1999).

J. Colloid Interface Sci. (1)

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

Opt. Commun. (1)

R. Ruppin, “Extinction by a circular cylinder in an absorbing medium,” Opt. Commun. 211, 335–340 (2002).
[CrossRef]

Part. Part. Syst. Charact. (1)

M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Philos. Mag. (1)

Rayleigh, “The dispersal of light by a dielectric cylinder,” Philos. Mag. 36, 365–376 (1918).
[CrossRef]

Other (2)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

W. Sun, “Light scattering by nonspherical particles: numerical simulation and applications,” Ph.D. dissertation (Dalhousie University, Halifax, Nova Scotia, Canada, 2000).

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Figures (5)

Fig. 1
Fig. 1

Geometry of light scattering by a circular cylinder embedded in an absorbing medium.

Fig. 2
Fig. 2

Single-scattering properties of a cylinder embedded in a medium as functions of the size parameter in free space (2πra0), which include extinction, scattering and absorption efficiencies, and the asymmetry factor. The refractive index of the cylinder is mt= 1.4 + i0.05 and the refractive index of the medium is m= 1.2 + imi, where mi = 0.0, 0.001, 0.01, and 0.05, respectively.

Fig. 3
Fig. 3

Normalized nonzero phase-matrix elements of a cylinder embedded in a medium as functions of scattering angle. The refractive index of the cylinder is mt = 1.4 + i0.05 and the refractive index of the medium is m = 1.2 + imi, where mi = 0.0, 0.001, 0.01, and 0.05, respectively. The size parameter of the cylinder in free space (2πa0) is 5.

Fig. 4
Fig. 4

Same as Fig. 3, but the size parameter of the cylinder in free space (2πa0) is 25.

Fig. 5
Fig. 5

Same as Fig. 3, but the size parameter of the cylinder in free space (2πa0) is 100.

Equations (19)

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E i = n = E n N n ( 1 ) ,
H i = i k ω μ n = E n M n ( 1 ) ,
E s = n = E n b n N n ( 3 ) ,
H s = i k ω μ n = E n b n M n ( 3 ) ,
M n = k exp ( i n φ ) [ i n z n ( ρ ) ρ e r z n ( ρ ) e φ ] ,
N n = k exp ( i n φ ) z n ( ρ ) e ,
b n = m J n ( m t x ) J n ( m x ) m t J n ( m t x ) J n ( m x ) m J n ( m t x ) H n ( 1 ) ( m x ) m t J n ( m t x ) H n ( 1 ) ( m x ) ,
W s = 1 2 Re [ 0 2 π ( E s × H s * ) r a d φ ] = 2 a I 0 Im { π ( 1 i m i m r ) [ b 0 b 0 * H 0 ( 1 ) ( m x ) H 0 ( 1 ) * ( m x ) + 2 n = 1 b n b n * H n ( 1 ) ( m x ) H n ( 1 ) * ( m x ) ] } ,
W e = 1 2 Re [ 0 2 π ( E i × H i * + E i × H s * + E s × H i * ) r a d φ ] = 2 a I 0 Im { π ( 1 i m i m r ) [ J 0 ( m x ) J 0 * ( m x ) b 0 * J 0 ( m x ) H 0 ( 1 ) * ( m x ) b 0 J 0 * ( m x ) H 0 ( 1 ) ( m x ) + 2 n = 1 ( J n ( m x ) J n * ( m x ) b n * J n ( m x ) H n ( 1 ) * ( m x ) b n J n * ( m x ) H n ( 1 ) ( m x ) ) ] } ,
E i = i n = E n M n ( 1 ) ,
H i = i k ω μ n = E n N n ( 1 ) ,
E s = i n = E n a n M n ( 3 ) ,
H s = i k ω μ n = E n a n N n ( 3 ) .
a n = m t J n ( m t x ) J n ( m x ) m J n ( m t x ) J n ( m x ) m t J n ( m t x ) H n ( 1 ) ( m x ) m J n ( m t x ) H n ( 1 ) ( m x ) .
W s = 1 2 Re [ 0 2 π ( E s × H s * ) r a d φ ] = 2 a I 0 Im { π ( 1 i m i m r ) [ a 0 a 0 * H 0 ( 1 ) ( m x ) H 0 ( 1 ) * ( m x ) + 2 n = 1 a n a n * H n ( 1 ) ( m x ) H n ( 1 ) * ( m x ) ] } ,
W e = 1 2 Re [ 0 2 π ( E i × H i * + E i × H s * + E s × H i * ) r a d φ ] = 2 a I 0 Im { π ( 1 i m i m r ) [ J 0 ( m x ) J 0 * ( m x ) a 0 * J 0 ( m x ) H 0 ( 1 ) * ( m x ) a 0 J 0 * ( m x ) H n ( 1 ) ( m x ) + 2 n = 1 ( J n ( m x ) J n * ( m x ) a n * J n ( m x ) H n ( 1 ) * ( m x ) a n J n * ( m x ) H n ( 1 ) ( m x ) ) ] } .
f = 2 a I 0 0 π / 2 exp ( 2 m i x cos α ) cos α d α .
s 1 ( θ ) = b 0 + 2 n = 1 b n cos ( n θ ) ,
s 2 ( θ ) = a 0 + 2 n = 1 a n cos ( n θ ) ,

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