Abstract

We derive and examine the general expression for the scattering asymmetry parameter g. For aggregate particles, the asymmetry parameter is made up of two terms. One term accounts for interference effects of the electromagnetic fields radiating from the individual subsystems. The other term contains the effects of the interaction of the electromagnetic fields between these subsystems. Enhanced backscatter is one phenomenon resulting from these interactions. Numerical results demonstrate that interference effects play a dominant role when the separation distance between two-sphere aggregates is smaller than half the incident wavelength. As the separation distance becomes large, both interference and interaction effects drop off and the asymmetry parameter approaches that of the individual particle constituents.

© 1998 Optical Society of America

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References

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  1. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
    [CrossRef]
  2. K.-N. Liou, Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).
  3. Y. Takano, K.-N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 45, 3–19 (1989).
    [CrossRef]
  4. G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
    [CrossRef]
  5. Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
    [CrossRef]
  6. K.-N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
    [CrossRef]
  7. P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
    [CrossRef]
  8. S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
    [CrossRef]
  9. B. T. N. Evans, G. R. Fournier, “Approximations of polydispersed extinction,” Appl. Opt. 35, 3281–3285 (1996).
    [CrossRef] [PubMed]
  10. P. Chýlek, J. D. Klett, “Extinction cross sections of nonspherical particles in the anomalous diffraction approximation,” J. Opt. Soc. Am. A 8, 274–281 (1991).
    [CrossRef]
  11. P. Chýlek, J. D. Klett, “Absorption and scattering of electromagnetic radiation by prismatic columns: anomalous diffraction approximation,” J. Opt. Soc. Am. A 8, 1713–1720 (1991).
    [CrossRef]
  12. P. Chýlek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystals,” J. Atmos. Sci. 51, 175–190 (1994).
    [CrossRef]
  13. C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).
  14. J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres parts I and II,” IEEE Trans. Antennas Propag. AP-19, 378–400 (1971).
    [CrossRef]
  15. A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
    [CrossRef]
  16. J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations: the long wavelength limit,” Phys. Rev. B 22, 4950–4959 (1980).
    [CrossRef]
  17. F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
    [CrossRef]
  18. K. A. Fuller, G. W. Kattawar, “Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I: Clusters of arbitrary configuration,” Opt. Lett. 13, 1063–1065 (1988).
    [CrossRef] [PubMed]
  19. M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
    [CrossRef] [PubMed]
  20. D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
    [CrossRef]
  21. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
    [CrossRef]
  22. J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
    [CrossRef]
  23. M. I. Mishchenko, D. W. Mackowski, “Light scattering by randomly oriented bispheres,” Opt. Lett. 19, 1604–1606 (1994).
    [CrossRef] [PubMed]
  24. D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
    [CrossRef]
  25. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994).
    [CrossRef]
  26. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A 12, 881–892 (1995).
    [CrossRef]
  27. S. C. Hill, H. I. Saleheen, K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneously perturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
    [CrossRef]
  28. G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
    [CrossRef]
  29. J. G. Fikioris, N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. 69, 1359–1366 (1979).
    [CrossRef]
  30. F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
    [CrossRef]
  31. F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–493 (1994).
    [CrossRef] [PubMed]
  32. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995).
    [CrossRef]
  33. M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
    [CrossRef]
  34. N. C. Skaropoulos, M. P. Ioannidow, D. P. Chrissoulidis, “Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion,” J. Opt. Soc. Am. A 11, 1859–1866 (1994).
    [CrossRef]
  35. G. Videen, D. Ngo, P. Chýlek, “Effective-medium predictions of absorption by graphitic carbon in water droplets,” Opt. Lett. 19, 1675–1677 (1994).
    [CrossRef] [PubMed]
  36. G. Videen, D. Ngo, P. Chýlek, R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
    [CrossRef]
  37. S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).
  38. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).

1996 (3)

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[CrossRef]

B. T. N. Evans, G. R. Fournier, “Approximations of polydispersed extinction,” Appl. Opt. 35, 3281–3285 (1996).
[CrossRef] [PubMed]

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

1995 (4)

1994 (8)

1992 (3)

1991 (4)

1990 (1)

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

1989 (2)

Y. Takano, K.-N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 45, 3–19 (1989).
[CrossRef]

M. F. Iskander, H. Y. Chen, J. E. Penner, “Optical scattering and absorption by branched chains of aerosols,” Appl. Opt. 28, 3083–3091 (1989).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

1986 (1)

K.-N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

1984 (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

1980 (1)

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations: the long wavelength limit,” Phys. Rev. B 22, 4950–4959 (1980).
[CrossRef]

1979 (2)

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

J. G. Fikioris, N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. 69, 1359–1366 (1979).
[CrossRef]

1971 (1)

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres parts I and II,” IEEE Trans. Antennas Propag. AP-19, 378–400 (1971).
[CrossRef]

1967 (1)

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

1961 (1)

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

Ackerman, S. A.

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Ausloos, M.

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations: the long wavelength limit,” Phys. Rev. B 22, 4950–4959 (1980).
[CrossRef]

Barber, P. W.

Borghese, F.

Bruning, J. H.

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres parts I and II,” IEEE Trans. Antennas Propag. AP-19, 378–400 (1971).
[CrossRef]

Chen, H. Y.

Chrissoulidis, D. P.

Chýlek, P.

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

Denti, P.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).

Evans, B. T. N.

Fikioris, J. G.

Flatau, P. J.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Fournier, G. R.

Francis, P. N.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Fu, Q.

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[CrossRef]

Fuller, K. A.

Gérardy, J. M.

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations: the long wavelength limit,” Phys. Rev. B 22, 4950–4959 (1980).
[CrossRef]

Hart, M. B.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Hill, S. C.

Ioannidow, M. P.

Iskander, M. F.

Jones, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Jones, A. R.

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

Kattawar, G. W.

Klett, J. D.

Ku, J. C.

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Liang, C.

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Liou, K.-N.

Y. Takano, K.-N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 45, 3–19 (1989).
[CrossRef]

K.-N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

K.-N. Liou, Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

Lo, Y. T.

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres parts I and II,” IEEE Trans. Antennas Propag. AP-19, 378–400 (1971).
[CrossRef]

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Mackowski, D. W.

Mazumder, M. M.

Mishchenko, M. I.

Ngo, D.

Penner, J. E.

Pinnick, R. G.

Saija, R.

Saleheen, H. I.

Saunders, R. W.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Shim, K.-H.

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Shine, K. P.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Sindoni, O. I.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Skaropoulos, N. C.

Slingo, A.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Stackhouse, P. W.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stein, S.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Stephens, G. L.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Sun, Z.

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Takano, Y.

Y. Takano, K.-N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 45, 3–19 (1989).
[CrossRef]

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Tsay, S. C.

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Uzunoglu, N. K.

Videen, G.

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

G. Videen, D. Ngo, P. Chýlek, R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
[CrossRef]

G. Videen, D. Ngo, P. Chýlek, “Effective-medium predictions of absorption by graphitic carbon in water droplets,” Opt. Lett. 19, 1675–1677 (1994).
[CrossRef] [PubMed]

P. Chýlek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystals,” J. Atmos. Sci. 51, 175–190 (1994).
[CrossRef]

Aerosol Sci. Technol. (1)

F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984).
[CrossRef]

Ann. Phys. (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Antennas Propag. (1)

J. H. Bruning, Y. T. Lo, “Multiple scattering of EM waves by spheres parts I and II,” IEEE Trans. Antennas Propag. AP-19, 378–400 (1971).
[CrossRef]

J. Atmos. Sci. (4)

P. Chýlek, G. Videen, “Longwave radiative properties of polydispersed hexagonal ice crystals,” J. Atmos. Sci. 51, 175–190 (1994).
[CrossRef]

S. A. Ackerman, G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Y. Takano, K.-N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 45, 3–19 (1989).
[CrossRef]

G. L. Stephens, S. C. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

J. Climate (1)

Q. Fu, “An accurate parameterization of the solar radiative properties of cirrus clouds for climate models,” J. Climate 9, 2058–2082 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (12)

F. Borghese, P. Denti, R. Saija, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
[CrossRef]

G. Videen, D. Ngo, P. Chýlek, R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922–928 (1995).
[CrossRef]

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995).
[CrossRef]

M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of the layered T-matrix method and the time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[CrossRef]

N. C. Skaropoulos, M. P. Ioannidow, D. P. Chrissoulidis, “Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion,” J. Opt. Soc. Am. A 11, 1859–1866 (1994).
[CrossRef]

M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
[CrossRef]

D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994).
[CrossRef]

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994).
[CrossRef]

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A 12, 881–892 (1995).
[CrossRef]

S. C. Hill, H. I. Saleheen, K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneously perturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
[CrossRef]

P. Chýlek, J. D. Klett, “Extinction cross sections of nonspherical particles in the anomalous diffraction approximation,” J. Opt. Soc. Am. A 8, 274–281 (1991).
[CrossRef]

P. Chýlek, J. D. Klett, “Absorption and scattering of electromagnetic radiation by prismatic columns: anomalous diffraction approximation,” J. Opt. Soc. Am. A 8, 1713–1720 (1991).
[CrossRef]

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

J. C. Ku, K.-H. Shim, “A comparison of solutions for light scattering and absorption by agglomerated or arbitrarily-shaped particles,” J. Quant. Spectrosc. Radiat. Transfer 47, 201–220 (1992).
[CrossRef]

Mon. Weather Rev. (1)

K.-N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

Opt. Commun. (1)

G. Videen, D. Ngo, M. B. Hart, “Light scattering from a pair of conducting, osculating spheres,” Opt. Commun. 125, 275–287 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (1)

J. M. Gérardy, M. Ausloos, “Absorption spectrum of clusters of spheres from the general solution of Maxwell’s equations: the long wavelength limit,” Phys. Rev. B 22, 4950–4959 (1980).
[CrossRef]

Proc. R. Soc. London Ser. A (2)

A. R. Jones, “Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation,” Proc. R. Soc. London Ser. A 366, 111–127 (1979).
[CrossRef]

D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc. R. Soc. London Ser. A 433, 599–614 (1991).
[CrossRef]

Q. Appl. Math. (1)

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Q. J. R. Meteorol. Soc. (1)

P. N. Francis, A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, Z. Sun, “An observational and theoretical study of the radiative properties of cirrus: some results from ICE’89,” Q. J. R. Meteorol. Soc. 120, 809–848 (1994).
[CrossRef]

Radio Sci. (1)

C. Liang, Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481–1495 (1967).

Other (2)

K.-N. Liou, Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957).

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Figures (4)

Fig. 1
Fig. 1

Asymmetry parameter of water (n = 1.33) and carbon (n = 1.75 + 0.44i) spheres as a function of sphere radius.

Fig. 2
Fig. 2

Asymmetry parameter as a function of separation distance d for two carbon spheres (a) r = λ/2 and (b) r = λ/10 averaged over all orientations. For plotting purposes, the interference term was multiplied by 10 in Fig. 2(a), and the interaction term was multiplied by -10 in both figures.

Fig. 3
Fig. 3

Intensity as a function of scattering angle for an r = λ/4 carbon (n = 1.75 + 0.44i) spheres at two different separation distances (d = λ/2, d = λ) illuminated at broadside incidence. Scatter from an isolated sphere is shown for comparison.

Fig. 4
Fig. 4

(a) Components of the asymmetry parameter as a function of component radius r for two carbon spheres in contact averaged over all orientations. For plotting purposes, the interaction term was multiplied by -1. (b) Asymmetry parameter for the two-sphere aggregate compared with equivalent single carbon spheres.

Equations (25)

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E sca = n = 0 m = - n n   a nm j M nm + b nm j N nm ,
M nm = θ ˆ im sin   θ   h n ( 1 ) ( kr ) P ˜ n m ( cos   θ ) exp ( im φ ) - φ ˆ h n ( 1 ) ( kr ) d d θ   P ˜ n m ( cos   θ ) exp ( im φ ) ,
N nm = r ˆ 1 kr   h n ( 1 ) ( kr ) n ( n + 1 ) P ˜ n m ( cos   θ ) exp ( im φ ) + θ ˆ 1 kr d d r [ rh n ( 1 ) ( kr ) ] d d θ   P ˜ n m ( cos   θ ) exp ( im φ ) + φ ˆ 1 kr d d r [ rh n ( 1 ) ( kr ) ] im sin   θ   P ˜ n m ( cos   θ ) exp ( im φ ) ,
P ˜ n m ( cos   θ ) = ( 2 n + 1 ) ( n - m ) ! 2 ( n + m ) ! 1 / 2 P n m ( cos   θ ) .
E θ sca E ϕ sca =   exp ikr - ikr S 2 S 4 S 3 S 1 E x inc E y inc ,
S 1 = n = 0 m = - n n ( - i ) n exp ( im φ ) b nm ( 2 ) π ˜ n m + a nm ( 2 ) τ ˜ n m ,
S 2 = - i   n = 0 m = - n n ( - i ) n exp ( im φ ) a nm ( 1 ) π ˜ n m + b nm ( 1 ) τ ˜ n m ,
S 3 = - i   n = 0 m = - n n ( - i ) n exp ( im φ ) a nm ( 2 ) π ˜ n m + b nm ( 2 ) τ ˜ n m ,
S 4 = n = 0 m = - n n ( - i ) n exp ( im φ ) b nm ( 1 ) π ˜ n m + a nm ( 1 ) τ ˜ n m ,
π ˜ n m = m sin   θ   P ˜ n m ( cos   θ ) ,
τ ˜ n m = θ   P ˜ n m ( cos   θ ) .
g = 1 2 k 2 C sca 0 2 π 0 π ( | S 1 | 2 + | S 2 | 2 + | S 3 | 2 + | S 4 | 2 ) × cos   θ   sin   θ   d θ d ϕ ,
C sca = 1 2 k 2 0 2 π 0 π ( | S 1 | 2 + | S 2 | 2 + | S 3 | 2 + | S 4 | 2 ) × sin   θ   d θ d ϕ ,
C sca = 2 π k 2 n = 1   n ( n + 1 ) m = - n n ( | a nm ( 1 ) | 2 + | b nm ( 1 ) | 2 + | a nm ( 2 ) | 2 + | b nm ( 2 ) | 2 ) .
g = 4 π k 2 C sca Re n , m   m [ a nm 1   b nm 1 * + a nm 2 b nm 2 * ] + in n + 2 n - m + 1 n + m + 1 2 n + 1 2 n + 3 1 / 2 × [ a nm 1 a n + 1 m 1 * + b nm 1 b n + 1 m 1 * + a nm 2 a n + 1 m 2 * + b nm 2 b n + 1 m 2 * ] .
a nm j a n + 1 m j * = b nm j b n + 1 m j * = a nm j b nm j * = 0 ,
f nm 1 , j = a nm 1 , j + k j n m   f n m 1 , k A nm jkn m + f n m 2 , k B nm jkn m ,
f nm 2 , j = a nm 2 , j + k j n m   f n m 1 , k C nm jkn m + f n m 2 , k D nm jkn m ,
g = j k 0 2 π 0 π   E sca j * · E sca k cos   θ   sin   θ   d θ d ϕ 0 2 π 0 π   E sca * · E sca   sin   θ   d θ d ϕ + j 0 2 π 0 π   E sca j * · E sca j cos   θ   sin   θ   d θ d ϕ 0 2 π 0 π   E sca * · E sca   sin   θ   d θ d ϕ .
g 0 = j   g j C sca , j C sca ,
M nm 3 = m   D m n , m M nm 3 ,
N nm 3 = m   D m n , m N nm 3 ,
D m n , m = exp i m α + m γ n + m ! n - m ! n + m ! n - m ! 1 / 2 × σ n + m n - m - σ n - m σ × - 1 n + m - σ cos β / 2 2 σ + m + m × sin β / 2 2 n - 2 σ - m - m ,
a nm = m   D m n , m c nm ,
b nm = m   D m n , m d nm .

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