Abstract

We present results of simulation of light scattering by randomly irregular particles that have dimensions larger than the wavelength of incident light. We apply the discontinuous Galerkin time domain method and compare the accurate solution with that obtained using an approximate geometric-optics model. A qualitative agreement is observed for scattering angle curves of intensity at the size parameter of X=60, whereas angular dependence of polarization appears to be more sensitive to the wave effects and requires larger sizes for application of geometrical optics.

© 2013 Optical Society of America

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  1. G. Videen, Y. Yatskiv, and M. Mishchenko, eds. Photopolarimetry in Remote Sensing (Kluwer Academic, 2004).
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    [CrossRef]
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    [CrossRef]
  4. A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
    [CrossRef]
  5. Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 78, 319 (2003).
    [CrossRef]
  6. Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 106, 56 (2007).
    [CrossRef]
  7. Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
    [CrossRef]
  8. Y. Shkuratov and Y. Grynko, Icarus 173, 16 (2005).
    [CrossRef]
  9. Y. Grynko and Y. Shkuratov, in Light Scattering Reviews, A. Kokhanovsky, ed. (Springer, 2008), Vol. III, pp. 329–382.
  10. O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
    [CrossRef]
  11. A. Macke, M. Mishchenko, K. Muinonen, and B. E. Carlson, Opt. Lett. 20, 1934 (1995).
    [CrossRef]
  12. D. J. Wielaard, M. I. Mishchenko, A. Macke, and B. E. Carlson, Appl. Opt. 36, 4305 (1997).
    [CrossRef]
  13. C. Liu, R. Lee Panetta, and P. Yang, J. Quant. Spectrosc. Radiat. Transfer 113, 1728 (2012).
    [CrossRef]
  14. J. S. Hesthaven and T. Warburton, J. Comput. Phys. 181, 186 (2002).
    [CrossRef]
  15. K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
    [CrossRef]
  16. G. Tang, R. L. Panetta, and P. Yang, Appl. Opt. 49, 2827 (2010).
    [CrossRef]
  17. P. Yang and K. N. Liou, Appl. Opt. 35, 6568 (1996).
    [CrossRef]
  18. P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
    [CrossRef]
  19. T. Warburton, www.nudg.org .
  20. P. W. Zhai, Y. K. Lee, G. W. Kattawar, and P. Yang, Appl. Opt. 43, 3738 (2004).
    [CrossRef]
  21. J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
    [CrossRef]
  22. C. Liu, R. L. Panetta, P. Yang, A. Macke, and A. J. Baran, Appl. Opt. 52, 640 (2013).
    [CrossRef]
  23. J. Um and G. M. McFarquhar, J. Quantum Spectrosc. Radiat. Transfer 127, 207 (2013).
    [CrossRef]
  24. H. Si, tetgen.org .
  25. A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
    [CrossRef]

2013

C. Liu, R. L. Panetta, P. Yang, A. Macke, and A. J. Baran, Appl. Opt. 52, 640 (2013).
[CrossRef]

J. Um and G. M. McFarquhar, J. Quantum Spectrosc. Radiat. Transfer 127, 207 (2013).
[CrossRef]

2012

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, Opt. Express 20, 16763 (2012).
[CrossRef]

C. Liu, R. Lee Panetta, and P. Yang, J. Quant. Spectrosc. Radiat. Transfer 113, 1728 (2012).
[CrossRef]

2011

K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
[CrossRef]

2010

2009

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

2007

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 106, 56 (2007).
[CrossRef]

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

2006

Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
[CrossRef]

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

2005

Y. Shkuratov and Y. Grynko, Icarus 173, 16 (2005).
[CrossRef]

2004

2003

M. Kahnert, J. Quantum Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 78, 319 (2003).
[CrossRef]

2002

J. S. Hesthaven and T. Warburton, J. Comput. Phys. 181, 186 (2002).
[CrossRef]

1997

1996

P. Yang and K. N. Liou, Appl. Opt. 35, 6568 (1996).
[CrossRef]

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

1995

Baran, A. J.

Bi, L.

Busch, K.

K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
[CrossRef]

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

Carlson, B. E.

Clarke, A. J. M.

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

Dubovik, O.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Feng, Q.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Grynko, Y.

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 106, 56 (2007).
[CrossRef]

Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
[CrossRef]

Y. Shkuratov and Y. Grynko, Icarus 173, 16 (2005).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 78, 319 (2003).
[CrossRef]

Y. Grynko and Y. Shkuratov, in Light Scattering Reviews, A. Kokhanovsky, ed. (Springer, 2008), Vol. III, pp. 329–382.

Guirado, D.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Hesse, E.

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

Hesthaven, J. S.

J. S. Hesthaven and T. Warburton, J. Comput. Phys. 181, 186 (2002).
[CrossRef]

Hong, G.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Hovenier, J. W.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Kahnert, M.

M. Kahnert, J. Quantum Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

Kattawar, G. W.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

P. W. Zhai, Y. K. Lee, G. W. Kattawar, and P. Yang, Appl. Opt. 43, 3738 (2004).
[CrossRef]

Kaye, P. H.

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

König, M.

K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
[CrossRef]

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

Laszlo, I.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Lee, Y. K.

Lee Panetta, R.

C. Liu, R. Lee Panetta, and P. Yang, J. Quant. Spectrosc. Radiat. Transfer 113, 1728 (2012).
[CrossRef]

Liou, K. N.

Liu, C.

Macke, A.

McFarquhar, G. M.

J. Um and G. M. McFarquhar, J. Quantum Spectrosc. Radiat. Transfer 127, 207 (2013).
[CrossRef]

Mishchenko, M.

Mishchenko, M. I.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

D. J. Wielaard, M. I. Mishchenko, A. Macke, and B. E. Carlson, Appl. Opt. 36, 4305 (1997).
[CrossRef]

Moreno, F.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Mueller, J.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Muinonen, K.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

A. Macke, M. Mishchenko, K. Muinonen, and B. E. Carlson, Opt. Lett. 20, 1934 (1995).
[CrossRef]

Muñoz, O.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Niegemann, J.

K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
[CrossRef]

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

Nousiainen, T.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Panetta, R. L.

Raschke, E.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

Shkuratov, Y.

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 106, 56 (2007).
[CrossRef]

Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
[CrossRef]

Y. Shkuratov and Y. Grynko, Icarus 173, 16 (2005).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 78, 319 (2003).
[CrossRef]

Y. Grynko and Y. Shkuratov, in Light Scattering Reviews, A. Kokhanovsky, ed. (Springer, 2008), Vol. III, pp. 329–382.

Sokolik, I. N.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Stannigel, K.

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

Tang, G.

Ulanowski, Z.

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

Um, J.

J. Um and G. M. McFarquhar, J. Quantum Spectrosc. Radiat. Transfer 127, 207 (2013).
[CrossRef]

Videen, G.

Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
[CrossRef]

Volten, H.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Warburton, T.

J. S. Hesthaven and T. Warburton, J. Comput. Phys. 181, 186 (2002).
[CrossRef]

Waters, L. B. F. M.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

Wielaard, D. J.

Wiscombe, W. J.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

Yang, P.

Yurkin, M. A.

Zhai, P. W.

Appl. Opt.

Icarus

Y. Shkuratov and Y. Grynko, Icarus 173, 16 (2005).
[CrossRef]

J. Aerosol Sci.

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, J. Aerosol Sci. 38, 995 (2007).
[CrossRef]

J. Atmos. Sci.

A. Macke, J. Mueller, and E. Raschke, J. Atmos. Sci. 53, 2813 (1996).
[CrossRef]

J. Comput. Phys.

J. S. Hesthaven and T. Warburton, J. Comput. Phys. 181, 186 (2002).
[CrossRef]

J. Geophys. Res.

O. Muñoz, H. Volten, J. W. Hovenier, T. Nousiainen, K. Muinonen, D. Guirado, F. Moreno, and L. B. F. M. Waters, J. Geophys. Res. 112, D13215 (2007).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

C. Liu, R. Lee Panetta, and P. Yang, J. Quant. Spectrosc. Radiat. Transfer 113, 1728 (2012).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 78, 319 (2003).
[CrossRef]

Y. Grynko and Y. Shkuratov, J. Quant. Spectrosc. Radiat. Transfer 106, 56 (2007).
[CrossRef]

J. Quantum Spectrosc. Radiat. Transfer

Y. Grynko, Y. Shkuratov, and G. Videen, J. Quantum Spectrosc. Radiat. Transfer 101, 522 (2006).
[CrossRef]

M. Kahnert, J. Quantum Spectrosc. Radiat. Transfer 79, 775 (2003).
[CrossRef]

J. Um and G. M. McFarquhar, J. Quantum Spectrosc. Radiat. Transfer 127, 207 (2013).
[CrossRef]

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, J. Quantum Spectrosc. Radiat. Transfer 100, 103 (2006).
[CrossRef]

Laser Photon. Rev.

K. Busch, M. König, and J. Niegemann, Laser Photon. Rev. 5, 773 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Photon. Nanostr. Fundam. Appl.

J. Niegemann, M. König, K. Stannigel, and K. Busch, Photon. Nanostr. Fundam. Appl. 7, 2 (2009).
[CrossRef]

Other

G. Videen, Y. Yatskiv, and M. Mishchenko, eds. Photopolarimetry in Remote Sensing (Kluwer Academic, 2004).

H. Si, tetgen.org .

T. Warburton, www.nudg.org .

Y. Grynko and Y. Shkuratov, in Light Scattering Reviews, A. Kokhanovsky, ed. (Springer, 2008), Vol. III, pp. 329–382.

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Figures (4)

Fig. 1.
Fig. 1.

Scattering angle curves of intensity (F11, left) and degree of linear polarization (F12/F11, right) for three arbitrary samples of GRF particles calculated with the DGTD method (m=1.5+0.0i) (thick solid lines), GO model (thin solid lines), and an average over 100 samples (dashed lines) also calculated with the GO model. The size parameter along the largest dimension is X=60. The result is averaged over 80 orientations including 180 scattering planes per orientation.

Fig. 2.
Fig. 2.

Scattering angle curves of intensity (F11, left) and degree of linear polarization (F12/F11, right) calculated with the DGTD method (solid lines) and GO model (dashed lines) for sample 1 for two complex refractive indices m=1.313+0.0i and m=1.5+0.005i. Orientation averaging is equivalent to that in Fig. 1.

Fig. 3.
Fig. 3.

Nonzero elements of scattering matrix calculated for five samples (all averaged over orientations) of GRF particles with the DGTD method (solid lines) and GO model (dashed lines) at X=60, m=1.5+0i.

Fig. 4.
Fig. 4.

Scattering components explaining the formation of GO scattering angle curves of intensity (F11) and degree of linear polarization (F12/F11) at m=1.5+0i. (a) Contributions of the first four orders of scattering compared with the total sum of all orders. (b) Linear polarization as a result of summation of the main components.

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