Abstract

The coupled dipole model of scattering by an arbitrary particle has been reformulated in terms of internal scattering processes of all orders. This formalism readily permits physical interpretation of observables and provides a rational basis for making computations more efficient. The calculation of scattering parameters can be simplified by appropriately terminating the infinite series at any order as well as by restricting the summations over the dipolar interaction terms within each order. Large particles can be partitioned into segments so that the scattered field is a superposition of the fields from the segments together with fields due to interactions among dipoles in different segments.

© 1987 Optical Society of America

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References

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  1. E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973)
    [CrossRef]
  2. S. D. Druger, M. Kerker, D.-S. Wang, D. D. Cooke, Appl. Opt. 18, 3888 (1979).
    [CrossRef] [PubMed]
  3. S. B. Singham, G. C. Salzman, J. Chem. Phys. 84, 2658 (1986).
    [CrossRef]
  4. M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
    [CrossRef]
  5. Y. L. Yung, Appl. Opt. 17, 3707 (1978).
    [CrossRef] [PubMed]
  6. M. Bôcher, An Introduction to the Study of Integral Equations (Hafner, New York, 1909), p. 13.
  7. C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
    [CrossRef]
  8. See, for example, A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, p. 254.
  9. V. Twersky, J. Opt. Soc. Am. 52, 145 (1962).
    [CrossRef] [PubMed]
  10. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 65.
  11. S. B. Singham, Chem. Phys. Lett. 130, 139 (1986).
    [CrossRef]

1986 (3)

S. B. Singham, G. C. Salzman, J. Chem. Phys. 84, 2658 (1986).
[CrossRef]

M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
[CrossRef]

S. B. Singham, Chem. Phys. Lett. 130, 139 (1986).
[CrossRef]

1984 (1)

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

1979 (1)

1978 (1)

1973 (1)

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973)
[CrossRef]

1962 (1)

Bôcher, M.

M. Bôcher, An Introduction to the Study of Integral Equations (Hafner, New York, 1909), p. 13.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 65.

Bustamante, C.

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

Cooke, D. D.

Druger, S. D.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 65.

Ishimaru, A.

See, for example, A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, p. 254.

Keller, D.

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

Kerker, M.

Maestre, M. F.

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

Pennypacker, C. R.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973)
[CrossRef]

Purcell, E. M.

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973)
[CrossRef]

Salzman, G. C.

S. B. Singham, G. C. Salzman, J. Chem. Phys. 84, 2658 (1986).
[CrossRef]

M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
[CrossRef]

Singham, M. K.

M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
[CrossRef]

Singham, S. B.

M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
[CrossRef]

S. B. Singham, G. C. Salzman, J. Chem. Phys. 84, 2658 (1986).
[CrossRef]

S. B. Singham, Chem. Phys. Lett. 130, 139 (1986).
[CrossRef]

Tinoco, I.

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

Twersky, V.

Wang, D.-S.

Yung, Y. L.

Appl. Opt. (2)

Astrophys. J. (1)

E. M. Purcell, C. R. Pennypacker, Astrophys. J. 186, 705 (1973)
[CrossRef]

Chem. Phys. Lett. (1)

S. B. Singham, Chem. Phys. Lett. 130, 139 (1986).
[CrossRef]

J. Chem. Phys. (3)

S. B. Singham, G. C. Salzman, J. Chem. Phys. 84, 2658 (1986).
[CrossRef]

M. K. Singham, S. B. Singham, G. C. Salzman, J. Chem. Phys. 85, 3807 (1986).
[CrossRef]

C. Bustamante, M. F. Maestre, D. Keller, I. Tinoco, J. Chem. Phys. 80, 4817 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (3)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 65.

See, for example, A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, p. 254.

M. Bôcher, An Introduction to the Study of Integral Equations (Hafner, New York, 1909), p. 13.

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Figures (2)

Fig. 1
Fig. 1

S11 versus scattering angle for a sphere of size parameter (2πa/λ) 2.2 and refractive index 1.33 in vacuum. Solid line, Mie calculation. Dashed line, calculation for a sphere modeled by 925 dipoles with inclusion of all first-order internal scattering contributions. Chain-dashed line, calculation for the dipolar sphere model with neglect of interactions.

Fig. 2
Fig. 2

S14 versus scattering angle for two turns of a right-handed cylindrical helix (radius = pitch = 250 nm) of refractive index 1.4 in vacuum. The helical axis is along the direction of incident light (λ = 500 nm), and the structure is modeled by 64 spherical dipoles. The azimuthal angle of the detector is 0°. Solid line, self-consistently coupled dipole calculation. Chain-dashed line, calculation using the self-consistently coupled dipole field for one turn with neglect of interactions between the turns. Dashed line, same as chain-dashed line with interactions to second order between turns.

Equations (4)

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E i = E i 0 + j i N [ A i j α ˜ j E j + B i j ( α ˜ j E j · n j i ) n j i ]             ( i = 1 , 2 , , N ) ,
A i j = ( k 2 - 1 r i j 2 + i k r i j ) exp ( i k r i j ) r i j , B i j = ( 3 r i j 2 - k 2 - 3 i k r i j ) exp ( i k r i j ) r i j ,
E i = E i 0 + j i C ˜ i j E j ,
E i = E i 0 + j i C ˜ i j E j 0 + j i k j C ˜ i j C ˜ j k E k 0 + j i k j m k C ˜ i j C ˜ j k C ˜ k m E m 0 + .

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