Abstract

We have compared radiative transfer theory with analytical solutions of the Maxwell equations for light scattering by multiple infinitely long parallel cylinders at perpendicular incidence. The calculated scattering cross sections for both methods show large differences, but the angle-dependent differential scattering cross-section results are very similar for small cylinder densities, except close to the forward direction. In contrast to recently published results, it is shown that the radiative transfer equation is a useful approximation for small cylinder concentrations.

© 2008 Optical Society of America

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References

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  1. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).
  2. S. H. Tseng, J. H. Greene, A. Taflove, D. Maitland, V. Backman, and J. T. Walsh, Jr., Opt. Lett. 29, 1393 (2004).
    [CrossRef] [PubMed]
  3. A. Kienle, F. K. Forster, and R. Hibst, Opt. Lett. 29, 2617 (2004).
    [CrossRef] [PubMed]
  4. A. Kienle and R. Hibst, Phys. Rev. Lett. 97, 018104 (2006).
    [CrossRef] [PubMed]
  5. S. H. Tseng and B. Huang, Appl. Phys. Lett. 91, 051114 (2007).
    [CrossRef]
  6. S.-C. Lee, J. Appl. Phys. 68, 4952 (1990).
    [CrossRef]
  7. H. A. Yousif and S. Köhler, Comput. Phys. Commun. 59, 371 (1990).
    [CrossRef]
  8. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).
    [CrossRef]

2007

S. H. Tseng and B. Huang, Appl. Phys. Lett. 91, 051114 (2007).
[CrossRef]

2006

A. Kienle and R. Hibst, Phys. Rev. Lett. 97, 018104 (2006).
[CrossRef] [PubMed]

2004

1990

S.-C. Lee, J. Appl. Phys. 68, 4952 (1990).
[CrossRef]

H. A. Yousif and S. Köhler, Comput. Phys. Commun. 59, 371 (1990).
[CrossRef]

Backman, V.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).
[CrossRef]

Forster, F. K.

Greene, J. H.

Hibst, R.

Huang, B.

S. H. Tseng and B. Huang, Appl. Phys. Lett. 91, 051114 (2007).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).
[CrossRef]

Kienle, A.

Köhler, S.

H. A. Yousif and S. Köhler, Comput. Phys. Commun. 59, 371 (1990).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Lee, S.-C.

S.-C. Lee, J. Appl. Phys. 68, 4952 (1990).
[CrossRef]

Maitland, D.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Taflove, A.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Tseng, S. H.

Walsh, J. T.

Yousif, H. A.

H. A. Yousif and S. Köhler, Comput. Phys. Commun. 59, 371 (1990).
[CrossRef]

Appl. Phys. Lett.

S. H. Tseng and B. Huang, Appl. Phys. Lett. 91, 051114 (2007).
[CrossRef]

Comput. Phys. Commun.

H. A. Yousif and S. Köhler, Comput. Phys. Commun. 59, 371 (1990).
[CrossRef]

J. Appl. Phys.

S.-C. Lee, J. Appl. Phys. 68, 4952 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

A. Kienle and R. Hibst, Phys. Rev. Lett. 97, 018104 (2006).
[CrossRef] [PubMed]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

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Figures (4)

Fig. 1
Fig. 1

Simulation results of the scattering cross section for different numbers of cylinders.

Fig. 2
Fig. 2

Differential scattering cross section versus scattering angle for different numbers of cylinders.

Fig. 3
Fig. 3

Differential scattering cross section versus scattering angle for different numbers of cylinders in forward-scattering direction.

Fig. 4
Fig. 4

Simulation results of the anisotropy factor for different numbers of cylinders.

Equations (7)

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

{ T 1 ( θ ) T 2 ( θ ) } = j = 1 N n = M M e i n θ e i k R 1 j cos ( γ 1 j θ ) { b j n a j n } ,
l = 1 N s = M M ( δ l j δ n s + ( 1 δ l j ) G l s j n { b j n 0 a j n 0 } ) { b k s a k s } = ϵ j { b j n 0 a j n 0 } ,
G l s j n = ( 1 ) s n H s n ( k R l j ) e i ( s n ) γ l j .
σ ( θ ) = 1 π k ( T 1 ( θ ) 2 + T 2 ( θ ) 2 ) ,
C sca = 0 2 π σ ( θ ) d θ ,
g = 1 C sca 0 2 π σ ( θ ) cos ( θ ) d θ .
μ s = N C sca d A .

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