Abstract

The order-of-scattering approach developed earlier [Opt. Lett. 13, 90 (1988)] and applied there to the case of linear chains of spheres is extended to the more difficult problem of scattering by clusters of spheres, the centers of which no longer need lie on a common axis. To help establish the validity of this most general calculation, comparisons are made between theoretical and experimental results for triangular and tetrahedral arrays of spheres. We also perform calculations based on an older method that requires the inversion of matrices, and we find that for the cases considered here the order-of-scattering method is substantially faster.

© 1988 Optical Society of America

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References

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  1. K. A. Fuller, G. W. Kattawar, Opt. Lett. 13, 90 (1988).
    [Crossref] [PubMed]
  2. C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).
  3. J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
    [Crossref]
  4. K. A. Fuller, Ph.D. dissertation (Department of Physics, Texas A&M University, 1987).

1988 (1)

1971 (1)

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[Crossref]

1967 (1)

C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).

Bruning, J. H.

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[Crossref]

Fuller, K. A.

K. A. Fuller, G. W. Kattawar, Opt. Lett. 13, 90 (1988).
[Crossref] [PubMed]

K. A. Fuller, Ph.D. dissertation (Department of Physics, Texas A&M University, 1987).

Kattawar, G. W.

Liang, C.

C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).

Lo, Y. T.

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[Crossref]

C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).

IEEE Trans. Antennas Propag. (1)

J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
[Crossref]

Opt. Lett. (1)

Radio Sci. (1)

C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).

Other (1)

K. A. Fuller, Ph.D. dissertation (Department of Physics, Texas A&M University, 1987).

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Figures (3)

Fig. 1
Fig. 1

Intensity of radiation scattered into the angle β = 50° by a close-packed triangular cluster of spheres as a function of particle orientation for the particle characteristics and scattering geometry shown. Intensity distributions of this nature are called sparkle functions. The solid curve indicates the converged solution, the dashed curve indicates the case of noninteracting spheres, and the dotted curve indicates the result of first-order interactions between a sphere and a bisphere. The bisphere is illuminated at broadside incidence when az = 0°. The diamonds indicate the experimental measurements by R. T. Wang (Space Astronomy Laboratory, University of Florida, Gainesville, Florida).

Fig. 2
Fig. 2

Sparkle function of a close-packed tetrahedral cluster at β = 30°. The solid, dotted, short-dashed, and dashed curves correspond to exact, first- plus second-order, first-order, and zeroth-order interactions, respectively. (The scattered fields of noninteracting spheres are produced by zeroth-order multiple scattering.) The diamonds indicate the values measured by R. T. Wang (Space Astronomy Laboratory, University of Florida, Gainesville, Florida).

Fig. 3
Fig. 3

Same function as Fig. 2, except that the cluster is now a hexahedron, with the fifth sphere located opposite the fourth sphere and invisible from the aspect shown in the inset. (No experimental data are available.)

Equations (3)

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E l ( j ) = n = 1 m = - n n [ a l m n ( j ) N l m n ( 3 ) + b l m n ( j ) + M l m n ( 3 ) ] ,
M i m n ( 3 ) = ν = 1 μ = - ν ν [ M l μ ν ( 1 ) A μ ν m n ( k d i l ) + N l μ ν ( 1 ) B μ ν m n ( k d i l ) ] , N i m n ( 3 ) = ν = 1 μ = - ν ν [ N l μ ν ( 1 ) A μ ν m n ( k d i l ) + M l μ ν ( 1 ) B μ ν m n ( k d i l ) ] ,
a l m n ( j ) = ν = 1 μ = - ν ν [ a i μ ν ( j - 1 ) A m n μ ν ( k d i l ) + b i μ ν ( j - 1 ) B m n μ ν ( k d i l ) ] , b l m n ( j ) = ν = 1 μ = - ν ν [ a i μ ν ( j - 1 ) B m n μ ν ( k d i l ) + b i μ ν ( j - 1 ) A m n μ ν ( k d i l ) ] ,

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