Abstract

The angular variations of scattering-matrix elements of coated cylindrical particles are presented. The sensitivity of different elements for a number of physical parameters are discussed, including size parameter, real and imaginary parts of the refractive index of the outer coat, and the inner core. The numerical predictions are presented for typical index-of-refraction values of cotton fibers. These results show that the physical structure of coated cylinders can be determined from carefully conducted light-scattering experiments.

© 1998 Optical Society of America

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References

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  1. H. G. Barth, R. B. Flippen, “Particle size analysis,” Anal. Chem. 67, 257R–272R (1995).
    [CrossRef]
  2. M. P. Mengüç, S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. (to be published).
  3. S. Manickavasagam, M. P. Mengüç, “Scattering matrix elements of fractal-like soot agglomerates,” App. Opt. 36, 1337–1351 (1997).
    [CrossRef]
  4. D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
    [CrossRef]
  5. C. F. Bohren, D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).
  6. S. C. Lee, “Scattering by closely-spaced radially-stratified parallel cylinders,” J. Quant. Spectrosc. Radiat. Transfer 48, 119–130 (1992).
    [CrossRef]
  7. S. C. Lee, “Scattering of polarized radiation by an arbitrary collection of closely spaced parallel nonhomogeneous tilted cylinders,” J. Opt. Soc. Am. A 13, 2256–2265 (1996).
    [CrossRef]
  8. S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
    [CrossRef]
  9. J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
    [CrossRef]
  10. M. Barabas, “Scattering of a plane wave by a radially stratified tilted cylinder,” J. Opt. Soc. Am. A 4, 2240–2248 (1987).
    [CrossRef]
  11. P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
    [CrossRef]
  12. L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 34, 5520–5530 (1995).
    [CrossRef] [PubMed]
  13. IMSL Reference Manual (International Mathematical & Statistical Library, Houston, Tex., 1982).
  14. M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
    [CrossRef]
  15. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  16. J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).
  17. R. Govindan, S. Manickavasagam, M. P. Mengüç, “Measuring the Mueller matrix elements of soot agglomerates,” in Radiative Transfer 1: Proceedings of the International Symposium on Radiative Heat Transfer, M. P. Mengüç, ed. (Begell House, New York, 1996), pp. 280–295.
  18. S. Manickavasagam, R. Govindan, M. P. Mengüç, “Estimating the morphology of agglomerates from scattering experiments,” in Proceedings of the ASME Heat Transfer Division, HTD Vol. 352 (American Society of Mechanical Engineers, New York1997), pp. 29–38.

1997 (1)

S. Manickavasagam, M. P. Mengüç, “Scattering matrix elements of fractal-like soot agglomerates,” App. Opt. 36, 1337–1351 (1997).
[CrossRef]

1996 (2)

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
[CrossRef]

S. C. Lee, “Scattering of polarized radiation by an arbitrary collection of closely spaced parallel nonhomogeneous tilted cylinders,” J. Opt. Soc. Am. A 13, 2256–2265 (1996).
[CrossRef]

1995 (3)

L. Kai, A. D’Alessio, “Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves,” Appl. Opt. 34, 5520–5530 (1995).
[CrossRef] [PubMed]

J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).

H. G. Barth, R. B. Flippen, “Particle size analysis,” Anal. Chem. 67, 257R–272R (1995).
[CrossRef]

1992 (1)

S. C. Lee, “Scattering by closely-spaced radially-stratified parallel cylinders,” J. Quant. Spectrosc. Radiat. Transfer 48, 119–130 (1992).
[CrossRef]

1991 (1)

P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
[CrossRef]

1987 (1)

1986 (2)

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

1970 (1)

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

Barabas, M.

Barth, H. G.

H. G. Barth, R. B. Flippen, “Particle size analysis,” Anal. Chem. 67, 257R–272R (1995).
[CrossRef]

Bhanti, D.

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).

Cunnington, G. R.

P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
[CrossRef]

D’Alessio, A.

Flippen, R. B.

H. G. Barth, R. B. Flippen, “Particle size analysis,” Anal. Chem. 67, 257R–272R (1995).
[CrossRef]

Govindan, R.

S. Manickavasagam, R. Govindan, M. P. Mengüç, “Estimating the morphology of agglomerates from scattering experiments,” in Proceedings of the ASME Heat Transfer Division, HTD Vol. 352 (American Society of Mechanical Engineers, New York1997), pp. 29–38.

R. Govindan, S. Manickavasagam, M. P. Mengüç, “Measuring the Mueller matrix elements of soot agglomerates,” in Radiative Transfer 1: Proceedings of the International Symposium on Radiative Heat Transfer, M. P. Mengüç, ed. (Begell House, New York, 1996), pp. 280–295.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).

Kai, L.

Lee, S. C.

S. C. Lee, “Scattering of polarized radiation by an arbitrary collection of closely spaced parallel nonhomogeneous tilted cylinders,” J. Opt. Soc. Am. A 13, 2256–2265 (1996).
[CrossRef]

S. C. Lee, “Scattering by closely-spaced radially-stratified parallel cylinders,” J. Quant. Spectrosc. Radiat. Transfer 48, 119–130 (1992).
[CrossRef]

Manickavasagam, S.

S. Manickavasagam, M. P. Mengüç, “Scattering matrix elements of fractal-like soot agglomerates,” App. Opt. 36, 1337–1351 (1997).
[CrossRef]

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
[CrossRef]

S. Manickavasagam, R. Govindan, M. P. Mengüç, “Estimating the morphology of agglomerates from scattering experiments,” in Proceedings of the ASME Heat Transfer Division, HTD Vol. 352 (American Society of Mechanical Engineers, New York1997), pp. 29–38.

R. Govindan, S. Manickavasagam, M. P. Mengüç, “Measuring the Mueller matrix elements of soot agglomerates,” in Radiative Transfer 1: Proceedings of the International Symposium on Radiative Heat Transfer, M. P. Mengüç, ed. (Begell House, New York, 1996), pp. 280–295.

M. P. Mengüç, S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. (to be published).

Mengüç, M. P.

S. Manickavasagam, M. P. Mengüç, “Scattering matrix elements of fractal-like soot agglomerates,” App. Opt. 36, 1337–1351 (1997).
[CrossRef]

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
[CrossRef]

J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).

S. Manickavasagam, R. Govindan, M. P. Mengüç, “Estimating the morphology of agglomerates from scattering experiments,” in Proceedings of the ASME Heat Transfer Division, HTD Vol. 352 (American Society of Mechanical Engineers, New York1997), pp. 29–38.

M. P. Mengüç, S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. (to be published).

R. Govindan, S. Manickavasagam, M. P. Mengüç, “Measuring the Mueller matrix elements of soot agglomerates,” in Radiative Transfer 1: Proceedings of the International Symposium on Radiative Heat Transfer, M. P. Mengüç, ed. (Begell House, New York, 1996), pp. 280–295.

Salzman, G. C.

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Samaddar, S. N.

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

Shearer, S. A.

J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).

Singham, M. K.

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Singham, S. B.

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

Swathi, P. S.

P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
[CrossRef]

Thomasson, J. A.

J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).

Tong, T. W.

P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wait, J. R.

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

Anal. Chem. (1)

H. G. Barth, R. B. Flippen, “Particle size analysis,” Anal. Chem. 67, 257R–272R (1995).
[CrossRef]

App. Opt. (1)

S. Manickavasagam, M. P. Mengüç, “Scattering matrix elements of fractal-like soot agglomerates,” App. Opt. 36, 1337–1351 (1997).
[CrossRef]

Appl. Opt. (1)

J. Chem. Phys. (1)

M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (3)

D. Bhanti, S. Manickavasagam, M. P. Mengüç, “Identification of non-homogeneous spherical particles from their scattering matrix elements,” J. Quant. Spectrosc. Radiat. Transfer 56, 591–608 (1996).
[CrossRef]

S. C. Lee, “Scattering by closely-spaced radially-stratified parallel cylinders,” J. Quant. Spectrosc. Radiat. Transfer 48, 119–130 (1992).
[CrossRef]

P. S. Swathi, T. W. Tong, G. R. Cunnington, “Scattering of electromagnetic waves by cylinders coated with a radially-inhomogeneous layer,” J. Quant. Spectrosc. Radiat. Transfer 46, 281–292 (1991).
[CrossRef]

Nuovo Cimento B (1)

S. N. Samaddar, “Scattering of plane electromagnetic waves by radially inhomogeneous infinite cylinders,” Nuovo Cimento B 66, 33–50 (1970).
[CrossRef]

Radio Sci. (1)

J. R. Wait, “Impedance conditions for a coated cylindrical conductor,” Radio Sci. 21, 623–626 (1986).
[CrossRef]

Trans. ASAE (1)

J. A. Thomasson, M. P. Mengüç, S. A. Shearer, “A radiative transfer model for relating near-infrared spectroscopy and miconaire measurements of cotton fibers,” Trans. ASAE 38, 367–377 (1995).

Other (6)

R. Govindan, S. Manickavasagam, M. P. Mengüç, “Measuring the Mueller matrix elements of soot agglomerates,” in Radiative Transfer 1: Proceedings of the International Symposium on Radiative Heat Transfer, M. P. Mengüç, ed. (Begell House, New York, 1996), pp. 280–295.

S. Manickavasagam, R. Govindan, M. P. Mengüç, “Estimating the morphology of agglomerates from scattering experiments,” in Proceedings of the ASME Heat Transfer Division, HTD Vol. 352 (American Society of Mechanical Engineers, New York1997), pp. 29–38.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

IMSL Reference Manual (International Mathematical & Statistical Library, Houston, Tex., 1982).

C. F. Bohren, D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1983).

M. P. Mengüç, S. Manickavasagam, “Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light,” Int. J. Eng. Sci. (to be published).

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Figures (12)

Fig. 1
Fig. 1

Normalized intensity value for two different angles of incidence: (a) ϕ = 0° and (b) ϕ = 45° (compare with Fig. 5 of Ref. 10) for TE (⊥) and TM (∥) incident polarizations.

Fig. 2
Fig. 2

Effect of f on angular profiles of S ij . Refractive index of inner core, m 1 = 1.1-i0.05 and outer coat, m 2 = 1.4-i0.1.

Fig. 3
Fig. 3

Effect of f on angular profiles of normalized S ij . Refractive index of inner core, m 1 = 1.1-i0.05 and the outer coat, m 2 = 1.4-i0.1.

Fig. 4
Fig. 4

Effect of g on angular profiles of S ij . Refractive index of inner core, m 1 = 1.1-i0.05 and the outer coat, m 2 = 1.4-i0.1.

Fig. 5
Fig. 5

Effect of n 1 on angular profiles of S 11 for k 1 = i0.05 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 6
Fig. 6

Effect of n 1 on angular profiles of S 12 for k 1 = i0.05 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 7
Fig. 7

Effect of n 1 on angular profiles of S 33 for k 1 = i0.05 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 8
Fig. 8

Effect of n 1 on angular profiles of S 34 for k 1 = i0.05 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 9
Fig. 9

Effect of k 1 on angular profiles of S 11 for n 1 = 1.1 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 10
Fig. 10

Effect of k 1 on angular profiles of S 12 for n 1 = 1.1 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 11
Fig. 11

Effect of k 1 on angular profiles of S 33 for n 1 = 1.1 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Fig. 12
Fig. 12

Effect of k 1 on angular profiles of S 34 for n 1 = 1.1 and m 2 = 1.4-i0.1: (a) f = 0.91, (b) f = 0.95, (c) f = 0.99.

Equations (17)

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E n , z , l = A n , l J n γ l r + a n , l H n γ l r ,   l = 2 N ,
H n , z , l = B n , l J n γ l r + b n , l H n γ l r ,   l = 2 N ,
F l x l = G l x l + 1 ,
F l = J n μ l H n μ l 0 0 nhJ n μ l γ l μ l nhH n μ l γ l μ l ikJ n μ l γ l ikH n μ l γ l 0 0 J n μ l H n μ l - ikm l 2 J n μ l γ l - ikm l 2 H n μ l γ l nhJ n μ l γ l μ l nhH n μ l γ l μ l ,
G l = J n β l H n β l 0 0 nhJ n β l γ l + 1 β l nhH n β l γ l + 1 β l ikJ n β l γ l + 1 ikH n β l γ l + 1 0 0 J n β l H n β l - ikm l + 1 2 J n β l γ l + 1 - ikm l + 1 2 H n β l γ l + 1 nhJ n β l γ l + 1 β l nhH n β l γ l + 1 β l ,
x l = A n , l   a n , l   B n , l   b n , l T ,
K A n , 1 B n , 1 T = G 1 x 2 ,
K = J n μ 1 0 nhJ n μ 1 γ 1 μ 1 ikJ n μ 1 γ 1 0 J n μ 1 - ikm l 2 J n μ 1 γ 1 nhJ n μ 1 γ 1 μ 1 .
F N x N = L a n , s b n , s T + M ,
L = H n ψ N 0 nhH n ψ N c ψ N ikH n ψ N c 0 H n ψ N - ikm l + 1 2 H n ψ N c nhH n c c ψ N ,
M = J N ψ N   nhJ N ψ N / c ψ N   0   - ikJ N ψ N / c T ,
M = 0   - ikJ N ψ N / c   J N ψ N   nhJ N ψ N / c ψ N T .
E s E s = exp ik L - z - ikL S 2 S 3 S 4 S 1 E i E i ,
I s Q s U s V s = 1 k 2 L 2 S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 I i Q i U i V i
K s = 1 k 2 L 2 S K i .
S θ = 1 k 2 r 2 S 11 S 12 0 0 S 12 S 22 0 0 0 0 S 33 S 34 0 0 - S 34 S 44 .
g = r o r i - 1 = 1 f - 1 .

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