Abstract

The single-scattering properties of concave fractal polyhedra are investigated, with particle size parameters ranging from the Rayleigh to geometric-optics regimes. Two fractal shape parameters, irregularity and aspect ratio, are used to iteratively construct “generations” of irregular fractal particles. The pseudospectral time-domain (PSTD) method and the improved geometric-optics method (IGOM) are combined to compute the single-scattering properties of fractal particles over the range of size parameters. The effects of fractal generation, irregularity, and aspect ratio on the single-scattering properties of fractals are investigated. The extinction efficiency, absorption efficiency, and asymmetry factor, calculated by the PSTD method for fractal particles, with small-to-moderate size parameters, smoothly bridges the gap between those size parameters and size parameters for which solutions given by the IGOM may be used. Somewhat surprisingly, excellent agreement between values of the phase function of randomly oriented fractal particles calculated by the two numerical methods is found, not only for large particles, but in fact extends as far down in equivalent-projected-area size parameters as 25. The agreement in the case of other nonzero phase matrix elements is not as good at so small a size. Furthermore, the numerical results of ensemble-averaged phase matrix elements of a single fractal realization are compared with dust particle measurements, and good agreement is found by using the fractal particle model to represent data from a study of feldspar aerosols.

© 2013 Optical Society of America

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  28. L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
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    [CrossRef]
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    [CrossRef]
  48. M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17902–17911(2007).
    [CrossRef]
  49. C. L. McConnell, P. Formenti, E. J. Highwood, and M. A. J. Harrison, “Using aircraft measurements to determine the refractive index of Saharan dust during the DODO experiments,” Atmos. Chem. Phys. 10, 3081–3098 (2010).
    [CrossRef]
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  51. D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
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  52. D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. A 240, 206–213 (1957).
    [CrossRef]
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    [CrossRef]

2012

C. Liu, R. L. Panetta, and P. Yang, “The influence of water coating on the optical scattering properties of fractal soot aggregates,” Aerosol Sci. Technol. 46, 31–43 (2012).
[CrossRef]

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transfer 113, 1728–1740(2012).
[CrossRef]

A. J. Baran, “From the single-scattering properties of ice crystals to climate prediction: a way forward,” Atmos. Res. 112, 45–69 (2012).
[CrossRef]

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20, 16763–16776 (2012).
[CrossRef]

2011

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete-dipole-approximation code ADDA: capabilities and known limitations,” J. Quant. Spectrosc. Radiat. Transfer 112, 2234–2247 (2011).
[CrossRef]

S. Merikallio, H. Lindqvist, T. Nousiainen, and M. Kahnert, “Modeling light scattering by mineral dust using spheroids: assessment of applicability,” Atmos. Chem. Phys. 11, 5347–5363 (2011).
[CrossRef]

S. R. Osborne, A. J. Baran, B. T. Johnson, J. M. Haywood, E. Hesse, and S. Newman, “Short-wave and long-wave radiative properties of Saharan dust aerosol,” Q. J. R. Meteorol. Soc. 137, 1149–1167 (2011).
[CrossRef]

J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

B. Yi, C. N. Hsu, P. Yang, and S.-C. Tsay, “Radiative transfer simulation of dust-like aerosols: uncertainties from particle shape and refractive index,” J. Aerosol Sci. 42, 631–644(2011).
[CrossRef]

2010

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef]

C. L. McConnell, P. Formenti, E. J. Highwood, and M. A. J. Harrison, “Using aircraft measurements to determine the refractive index of Saharan dust during the DODO experiments,” Atmos. Chem. Phys. 10, 3081–3098 (2010).
[CrossRef]

2009

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at wavelengths of 0.532 and 1.064 μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[CrossRef]

T. Nousiainen, “Optical modeling of mineral dust particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 1261–1279 (2009).
[CrossRef]

2008

S. R. Osborne, B. T. Johnson, J. M. Haywood, A. J. Baran, M. A. J. Harrison, and C. L. McConnell, “Physical and optical properties of mineral dust aerosol during the dust and biomass-burning experiment,” J. Geophys. Res. 113, D00C03(2008).
[CrossRef]

G. Chen, P. Yang, and G. W. Kattawar, “Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles,” J. Opt. Soc. Am. A 25, 785–790 (2008).
[CrossRef]

E. Hesse, “Modeling diffraction during ray-tracing using the concept of energy flow lines,” J. Quant. Spectrosc. Radiat. Transfer 109, 1374–1383 (2008).
[CrossRef]

2007

M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17902–17911(2007).
[CrossRef]

E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
[CrossRef]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of nonspherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014 (2007).
[CrossRef]

2006

H. Volten, O. Muæoz, J. W. Hovenier, and L. B. F. M. Waters, “An update of the Amsterdam light scattering database,” J. Quant. Spectrosc. Radiat. Transfer 100, 437–443 (2006).
[CrossRef]

T. Nousiainen, M. Kahnert, and B. Veihelmann, “Light scattering modeling of small feldspar aerosol particles using polyhedral; prims and spheroids,” J. Quant. Spectrosc. Radiat. Transfer 101, 471–487 (2006).
[CrossRef]

A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, “A 3D implementation of ray-tracing with diffraction on facets: verification and a potential application,” J. Quant. Spectrosc. Radiat. Transfer 100, 103–114 (2006).
[CrossRef]

2005

M. Kahnert, T. Nousiainen, and B. Veihelmann, “Spherical and spheroidal model particles as an error source in aerosol climate forcing and radiance computations: a case study for feldspar aerosols,” J. Geophys. Res. 110, D18S13 (2005).
[CrossRef]

L. Liu and M. I. Mishchenko, “Effects of aggregation on scattering and radiative properties of soot aerosols,” J. Geophys. Res. 110, D11211 (2005).
[CrossRef]

P. Yang, H. Wie, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[CrossRef]

2001

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
[CrossRef]

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, “Aerosols, climate, and the hydrological cycle,” Science 294, 2119–2124 (2001).
[CrossRef]

1998

P. Yang and K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contr. Atmos. Phys. 71, 223–248 (1998).

1997

P. Yang, K. N. Liou, and W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

Q. H. Liu, “The PSTD algorithm: a time-domain method requiring only two cells per wavelength,” Microw. Opt. Technol. Lett. 15, 158–165 (1997).
[CrossRef]

1996

P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
[CrossRef]

A. Macke, J. Mueller, and E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

P. Yang and K. N. Liou, “Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals,” Appl. Opt. 35, 6568–6584 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

1995

M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
[CrossRef]

1992

A. Macke and F. Tzschichholz, “Scattering of light by two-dimensional deterministic Koch islands,” Phys. A 191, 545–548 (1992).
[CrossRef]

1991

G. R. Fournier and B. T. N. Evans, “Approximation to extinction efficiency for randomly oriented spheroids,” Appl. Opt. 30, 2042–2048 (1991).
[CrossRef]

1989

K. Muinonen, “Scattering of light by crystals: a modified Kirchhoff approximation,” Appl. Opt. 28, 3044–3050(1989).
[CrossRef]

1975

W. B. Gordon, “Far-field approximations to the Kirchhoff–Helmholtz representations of scattered fields,” IEEE Trans. Antennas Propag. 23, 590–592 (1975).
[CrossRef]

1974

P. Chýlek and J. A. Coakley, “Aerosols and climate,” Science 183, 75–77 (1974).
[CrossRef]

1973

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

1971

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

1957

D. S. Jones, “Approximate methods in high-frequency scattering,” Proc. R. Soc. A 239, 338–348 (1957).
[CrossRef]

D. S. Jones, “High-frequency scattering of electromagnetic waves,” Proc. R. Soc. A 240, 206–213 (1957).
[CrossRef]

Allan, R. P.

J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

Arnott, W. P.

P. Yang, K. N. Liou, and W. P. Arnott, “Extinction efficiency and single-scattering albedo for laboratory and natural cirrus clouds,” J. Geophys. Res. 102, 21825–21835 (1997).
[CrossRef]

Baran, A. J.

A. J. Baran, “From the single-scattering properties of ice crystals to climate prediction: a way forward,” Atmos. Res. 112, 45–69 (2012).
[CrossRef]

J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

S. R. Osborne, A. J. Baran, B. T. Johnson, J. M. Haywood, E. Hesse, and S. Newman, “Short-wave and long-wave radiative properties of Saharan dust aerosol,” Q. J. R. Meteorol. Soc. 137, 1149–1167 (2011).
[CrossRef]

S. R. Osborne, B. T. Johnson, J. M. Haywood, A. J. Baran, M. A. J. Harrison, and C. L. McConnell, “Physical and optical properties of mineral dust aerosol during the dust and biomass-burning experiment,” J. Geophys. Res. 113, D00C03(2008).
[CrossRef]

Baum, B. A.

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at wavelengths of 0.532 and 1.064 μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

P. Yang, H. Wie, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
[CrossRef]

Bi, L.

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20, 16763–16776 (2012).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at wavelengths of 0.532 and 1.064 μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

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S. Merikallio, H. Lindqvist, T. Nousiainen, and M. Kahnert, “Modeling light scattering by mineral dust using spheroids: assessment of applicability,” Atmos. Chem. Phys. 11, 5347–5363 (2011).
[CrossRef]

T. Nousiainen, “Optical modeling of mineral dust particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 110, 1261–1279 (2009).
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E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
[CrossRef]

T. Nousiainen, M. Kahnert, and B. Veihelmann, “Light scattering modeling of small feldspar aerosol particles using polyhedral; prims and spheroids,” J. Quant. Spectrosc. Radiat. Transfer 101, 471–487 (2006).
[CrossRef]

M. Kahnert, T. Nousiainen, and B. Veihelmann, “Spherical and spheroidal model particles as an error source in aerosol climate forcing and radiance computations: a case study for feldspar aerosols,” J. Geophys. Res. 110, D18S13 (2005).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
[CrossRef]

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J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

S. R. Osborne, A. J. Baran, B. T. Johnson, J. M. Haywood, E. Hesse, and S. Newman, “Short-wave and long-wave radiative properties of Saharan dust aerosol,” Q. J. R. Meteorol. Soc. 137, 1149–1167 (2011).
[CrossRef]

S. R. Osborne, B. T. Johnson, J. M. Haywood, A. J. Baran, M. A. J. Harrison, and C. L. McConnell, “Physical and optical properties of mineral dust aerosol during the dust and biomass-burning experiment,” J. Geophys. Res. 113, D00C03(2008).
[CrossRef]

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C. Liu, R. L. Panetta, and P. Yang, “The influence of water coating on the optical scattering properties of fractal soot aggregates,” Aerosol Sci. Technol. 46, 31–43 (2012).
[CrossRef]

C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transfer 113, 1728–1740(2012).
[CrossRef]

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20, 16763–16776 (2012).
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E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
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E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
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H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
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E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
[CrossRef]

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P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of nonspherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014 (2007).
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M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
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M. I. Mishchenko, A. A. Lacis, B. E. Carlson, and L. D. Travis, “Nonsphericity of dust-like tropospheric aerosols: implications for aerosol remote sensing and climate modeling,” Geophys. Res. Lett. 22, 1077–1080 (1995).
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B. Yi, C. N. Hsu, P. Yang, and S.-C. Tsay, “Radiative transfer simulation of dust-like aerosols: uncertainties from particle shape and refractive index,” J. Aerosol Sci. 42, 631–644(2011).
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A. Macke and F. Tzschichholz, “Scattering of light by two-dimensional deterministic Koch islands,” Phys. A 191, 545–548 (1992).
[CrossRef]

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A. J. M. Clarke, E. Hesse, Z. Ulanowski, and P. H. Kaye, “A 3D implementation of ray-tracing with diffraction on facets: verification and a potential application,” J. Quant. Spectrosc. Radiat. Transfer 100, 103–114 (2006).
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H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
[CrossRef]

Veihelmann, B.

T. Nousiainen, M. Kahnert, and B. Veihelmann, “Light scattering modeling of small feldspar aerosol particles using polyhedral; prims and spheroids,” J. Quant. Spectrosc. Radiat. Transfer 101, 471–487 (2006).
[CrossRef]

M. Kahnert, T. Nousiainen, and B. Veihelmann, “Spherical and spheroidal model particles as an error source in aerosol climate forcing and radiance computations: a case study for feldspar aerosols,” J. Geophys. Res. 110, D18S13 (2005).
[CrossRef]

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E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
[CrossRef]

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H. Volten, O. Muæoz, J. W. Hovenier, and L. B. F. M. Waters, “An update of the Amsterdam light scattering database,” J. Quant. Spectrosc. Radiat. Transfer 100, 437–443 (2006).
[CrossRef]

H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
[CrossRef]

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J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
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H. Volten, O. Muæoz, J. W. Hovenier, and L. B. F. M. Waters, “An update of the Amsterdam light scattering database,” J. Quant. Spectrosc. Radiat. Transfer 100, 437–443 (2006).
[CrossRef]

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P. Yang, H. Wie, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
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L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at wavelengths of 0.532 and 1.064 μm,” J. Geophys. Res. 114, D00H08 (2009).
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P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of nonspherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014 (2007).
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J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

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C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transfer 113, 1728–1740(2012).
[CrossRef]

C. Liu, R. L. Panetta, and P. Yang, “The influence of water coating on the optical scattering properties of fractal soot aggregates,” Aerosol Sci. Technol. 46, 31–43 (2012).
[CrossRef]

C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20, 16763–16776 (2012).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, “Scattering and absorption of light by ice particles: solution by a new physical-geometric optics hybrid method,” J. Quant. Spectrosc. Radiat. Transfer 112, 1492–1508 (2011).
[CrossRef]

B. Yi, C. N. Hsu, P. Yang, and S.-C. Tsay, “Radiative transfer simulation of dust-like aerosols: uncertainties from particle shape and refractive index,” J. Aerosol Sci. 42, 631–644(2011).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometric-optics regimes,” Appl. Opt. 48, 114–126 (2009).
[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, B. A. Baum, Y. X. Hu, D. M. Winker, R. S. Brock, and J. Q. Lu, “Simulation of the color ratio associated with the backscattering of radiation by ice particles at wavelengths of 0.532 and 1.064 μm,” J. Geophys. Res. 114, D00H08 (2009).
[CrossRef]

G. Chen, P. Yang, and G. W. Kattawar, “Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles,” J. Opt. Soc. Am. A 25, 785–790 (2008).
[CrossRef]

P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of nonspherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014 (2007).
[CrossRef]

P. Yang, H. Wie, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
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K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).

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B. Yi, C. N. Hsu, P. Yang, and S.-C. Tsay, “Radiative transfer simulation of dust-like aerosols: uncertainties from particle shape and refractive index,” J. Aerosol Sci. 42, 631–644(2011).
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C. Liu, L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, “Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations,” Opt. Express 20, 16763–16776 (2012).
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M. A. Yurkin, A. G. Hoekstra, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers,” Opt. Express 15, 17902–17911(2007).
[CrossRef]

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E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
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[CrossRef]

L. Bi, P. Yang, G. W. Kattawar, and R. Kahn, “Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra,” Appl. Opt. 49, 334–342 (2010).
[CrossRef]

P. Yang, H. Wie, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, “Scattering and absorption property database for nonspherical ice particles in the near- through far-infrared spectral region,” Appl. Opt. 44, 5512–5523 (2005).
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P. Yang, Q. Feng, G. Hong, G. W. Kattawar, W. J. Wiscombe, M. I. Mishchenko, O. Dubovik, I. Laszlo, and I. N. Sokolik, “Modeling of the scattering and radiative properties of nonspherical dust-like aerosols,” J. Aerosol Sci. 38, 995–1014 (2007).
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S. R. Osborne, B. T. Johnson, J. M. Haywood, A. J. Baran, M. A. J. Harrison, and C. L. McConnell, “Physical and optical properties of mineral dust aerosol during the dust and biomass-burning experiment,” J. Geophys. Res. 113, D00C03(2008).
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H. Volten, O. Muñoz, E. Rol, J. F. de Haan, W. Vassen, J. W. Hovenier, K. Muinonen, and T. Nousiainen, “Scattering matrices of mineral aerosol particles at 441.6 nm and 632.8 nm,” J. Geophys. Res. 106, 17375–17401 (2001).
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C. Liu, R. L. Panetta, and P. Yang, “Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200,” J. Quant. Spectrosc. Radiat. Transfer 113, 1728–1740(2012).
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E. Zubko, K. Muinonen, Y. Shkuratov, G. Videen, and T. Nousiainen, “Scattering of light by roughened Gaussian random particles,” J. Quant. Spectrosc. Radiat. Transfer 106, 604–615 (2007).
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J. M. Haywood, B. T. Johnson, S. R. Osborne, A. J. Baran, M. Brooks, S. F. Milton, J. Mulcahy, D. Walters, R. P. Allan, M. J. Woodage, A. Klaver, P. Formenti, H. E. Brindley, S. Christopher, and P. Gupta, “Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign,” Q. J. R. Meteorol. Soc. 137, 1106–1116 (2011).
[CrossRef]

Science

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[CrossRef]

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H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, 1983).

K. J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, 2003).

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

A. A. Kokhanovsky, Polarization Optics of Random Media (Springer, 2003).

A. A. Kokhanovsky, Light Scattering Media Optics: Problems and Solutions (Springer, 2004).

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Figures (9)

Fig. 1.
Fig. 1.

(a) First step in construction of a regular fractal particle. A0B0C0D0 is the initial tetrahedron, and A1B1C1D1 is one first-generation added tetrahedron. The dotted–dashed line (D0D1) is the height of the fractal particle, and the dotted–dashed curve gives the circumscribed circle of triangle A0B0C0 with O0 its center. (b) Modification to first step in construction of irregular fractal particle: the side B1C1 of the first-generation regular tetrahedron, used to locate the vertex of the irregular first-generation tetrahedron as described in the text, is made parallel to the side B0C0 of the previous (zeroth)-generation face.

Fig. 2.
Fig. 2.

(a)–(d) Regular fractal particles from the zero to the third generations and (e)–(h) the second-generation irregular particles [the irregular ratios of (e)– (h) are 0.1, 0.2, 0.3, and 0.3, respectively, and the aspect ratio of (h) is 1.7].

Fig. 3.
Fig. 3.

Comparison of the nonzero phase matrix elements of the zero- to fourth-generation regular fractal particles given by the IGOM. The length of the initial tetrahedron’s side is 100 μm.

Fig. 4.
Fig. 4.

Comparison of the nonzero phase matrix elements of the second-generation regular and irregular fractal particles having different values of the irregularity parameter β. Computations use the IGOM, and the length of the initial tetrahedron’s side is 100 μm.

Fig. 5.
Fig. 5.

Comparison of results for the nonzero phase matrix elements of the second-generation irregular fractal particles, with different realizations of fractal particles all having β=0.3 and AR=1.06. Computations use the IGOM, and the length of the initial tetrahedron’s side is 100 μm.

Fig. 6.
Fig. 6.

Comparison of the nonzero phase matrix elements of second-generation regular particles with different aspect ratios. Computations use the IGOM, and the length of the initial tetrahedron’s side is 100 μm.

Fig. 7.
Fig. 7.

Integral scattering properties of randomly oriented second-generation fractal particles given by the PSTD method and the IGOM. The irregularity parameter and aspect ratio of the fractal particles are 0.3 and 1.7, respectively.

Fig. 8.
Fig. 8.

Comparison of the nonzero phase matrix elements of a random second-generation fractal given by the PSTD method and the IGOM. The same particle realization as that of Fig. 5 is used, and the equivalent-projected-area size parameter of the particle is 25.

Fig. 9.
Fig. 9.

Comparison between results of the bulk phase matrix elements of numerically simulated fractal and spherical particles and the laboratory measurements for feldspar particles at the 0.6328 μm wavelength.

Equations (7)

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AspectRatio=HW=heightwidth.
AspectRatio(F1)=3241.06.
z=AR1.06z.
Adif=k22πIs((cosθs+cos2θs)/200(1+cosθs)/2),
Is=ik|w⃗|2Lexp(ikw⃗·l⃗)(w⃗×dl⃗)n⃗inc.
Qext,edge=fextx2/3,
Qabs,edge=fabsx2/3.

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