Abstract

An outline is provided of the derivation of an order-of-scattering technique that we apply here for the first reported time to the study of light scattering by two or more interacting spheres. This new method provides what is to our knowledge the first complete physical description of the classical processes involved in cooperative EM scattering by an aggregate of spheres. In addition, the algorithms that it employs are often more efficient than those used in an already established method. Comparisons between selected calculations and experimental results are made for linear chains of three and five spheres, and effects of particle orientation are investigated theoretically.

© 1988 Optical Society of America

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References

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  1. C. Liang, Y. T. Lo, Radio Sci. 2, 1481 (1967).
  2. J. H. Bruning, Y. T. Lo, IEEE Trans. Antennas Propag. AP-19, 378 (1971).
    [CrossRef]
  3. B. Friedman, J. Russek, Q. Appl. Math. 12, 13 (1954).
  4. S. Stein, Q. Appl. Math. 19, 15 (1961).
  5. O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).
  6. G. W. Kattawar, C. E. Dean, Opt. Lett. 8, 48 (1983).
    [CrossRef] [PubMed]
  7. K. A. Fuller, G. W. Kattawar, Appl. Opt. 25, 2521 (1986).
    [CrossRef] [PubMed]

1986 (1)

1983 (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).

1962 (1)

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

1961 (1)

S. Stein, Q. Appl. Math. 19, 15 (1961).

1954 (1)

B. Friedman, J. Russek, Q. Appl. Math. 12, 13 (1954).

Bruning, J. H.

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

Cruzan, O. R.

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

Dean, C. E.

Friedman, B.

B. Friedman, J. Russek, Q. Appl. Math. 12, 13 (1954).

Fuller, K. A.

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).

Russek, J.

B. Friedman, J. Russek, Q. Appl. Math. 12, 13 (1954).

Stein, S.

S. Stein, Q. Appl. Math. 19, 15 (1961).

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

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

Opt. Lett. (1)

Q. Appl. Math. (3)

B. Friedman, J. Russek, Q. Appl. Math. 12, 13 (1954).

S. Stein, Q. Appl. Math. 19, 15 (1961).

O. R. Cruzan, Q. Appl. Math. 20, 33 (1962).

Radio Sci. (1)

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

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Figures (3)

Fig. 1
Fig. 1

Scattering-ladder representation of the OS process. A term of the form idk(j) is understood to be the wave vector of the jth-order multiply scattered field, or the jth-order partial field, emanating from the idth sphere, and idθ is the angle between the wave vectors idk(j) and the z axis. This theory applies equally well to the calculation of far, near, and internal fields, and this is why 1θ2θ.

Fig. 2
Fig. 2

Comparison of calculated and measured values of the intensity distribution of light scattered by a chain of three spheres for the scattering geometry shown. The diamonds mark the experimental values provided by Wang. The dashed line corresponds to the fictitious case of noninteracting spheres.

Fig. 3
Fig. 3

OS development of the scattered intensity (at a scattering angle of β = 90°) for varying target orientations. The curve made up of long dashes is for the case of a nonin-teracting sphere and a bisphere, i.e., I(j=0) = |(1E + 2E)(0) + 3E(0)|2 ≡ |bE(0) + 3E(0)|2, where b stands for bisphere. The evenly dashed curve, the dotted curve, and the solid curve represent the cases j = 1, 2, and ∞, respectively. The convergence is almost complete at j = 3. To avoid confusion, the scattering geometry is included.

Equations (4)

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E s = i d = 1 L n = 1 m = n n [ id A E m n id N m n ( 3 ) + id A H m n id M m n ( 3 ) ] ,
k M m n ( 3 ) = ν = m a x ( 1 , m ) g n v [ i M m ν ( 1 ) A m ν m n ± i N m ν ( 1 ) B m ν m n ] , k N m n ( 3 ) = ν = m a x ( 1 , m ) g n v [ i N m ν ( 1 ) A m ν m n ± i M m ν ( 1 ) B m ν m n ] .
k E ( j ) = n , m [ k a m n ( j ) k N m n ( 3 ) + k b m n ( j ) k M m n ( 3 ) ] ,
1 a m n ( j ) = 1 υ n ν [ 2 a m ν ( j 1 ) A m v m n + 2 b m ν ( j 1 ) B m ν m n ] , 1 b m n ( j ) = 1 u n ν [ 2 b m ν ( j 1 ) A m v m n + 2 a m ν ( j 1 ) B m ν m n ] , 2 a m n ( j ) = 2 υ n ν ( ) n + ν [ 1 a m ν ( j 1 ) A m v m n 1 b m ν ( j 1 ) B m ν m n ] , 2 b m n ( j ) = 2 u n ν ( ) n + ν [ 1 b m ν ( j 1 ) A m v m n 1 a m ν ( j 1 ) B m ν m n ] ,

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