Abstract

A formula of considerable generality is derived for the spectrum of light produced by static scattering of polychromatic light on a system of particles. It applies to deterministic as well as to random distributions of monodispersed or polydispersed particles. We illustrate it by examples. It is suggested that spectral changes produced by scattering could be used for determining the structure of some scattering systems.

© 1998 Optical Society of America

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  1. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  2. For a review of these investigations see E. Wolf and D. F. V. James, Rep. Progr. Phys. 59, 771 (1996).
    [CrossRef]
  3. D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
    [CrossRef]
  4. H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
    [CrossRef]
  5. S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
    [CrossRef]
  6. E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).
  7. T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
    [CrossRef]
  8. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989); erratum,  7, 173 (1990).
    [CrossRef]
  9. T. Shirai and T. Asakura, J. Opt. Soc. Am. 12, 1354 (1995).
    [CrossRef]
  10. T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
    [CrossRef]
  11. T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
    [CrossRef]
  12. J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
    [CrossRef] [PubMed]
  13. E. Wolf, Phys. Rev. Lett. 63, 2220 (1989).
    [CrossRef] [PubMed]
  14. D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
    [CrossRef]
  15. D. F. V. James and E. Wolf, Phys. Lett. A 146, 167 (1990).
    [CrossRef]
  16. D. F. V. James and E. Wolf, Phys. Lett. A 188, 239 (1994).
    [CrossRef]
  17. M. ?er?anský, Phys. Stat. Sol. (b) 114, 365 (1982).
    [CrossRef]
  18. In this connection see also M. Dušek, Phys. Rev. E 52, 6833 (1995).
    [CrossRef]
  19. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap.??7.
  20. N. W. Ashcroft and D. C. Langreth, Phys. Rev. 159, 500 (1967).
    [CrossRef]
  21. A. Dogariu, K. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 585 (1997).
    [CrossRef] [PubMed]
  22. M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
    [CrossRef]

1998 (1)

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

1997 (3)

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

A. Dogariu, K. Kutsche, P. Likamwa, G. Boreman, and B. Moudgil, Opt. Lett. 22, 585 (1997).
[CrossRef] [PubMed]

1996 (3)

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

For a review of these investigations see E. Wolf and D. F. V. James, Rep. Progr. Phys. 59, 771 (1996).
[CrossRef]

S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
[CrossRef]

1995 (4)

D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

T. Shirai and T. Asakura, J. Opt. Soc. Am. 12, 1354 (1995).
[CrossRef]

In this connection see also M. Dušek, Phys. Rev. E 52, 6833 (1995).
[CrossRef]

1994 (1)

D. F. V. James and E. Wolf, Phys. Lett. A 188, 239 (1994).
[CrossRef]

1990 (2)

D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 146, 167 (1990).
[CrossRef]

1989 (3)

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 63, 2220 (1989).
[CrossRef] [PubMed]

E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989); erratum,  7, 173 (1990).
[CrossRef]

1986 (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

1982 (1)

M. ?er?anský, Phys. Stat. Sol. (b) 114, 365 (1982).
[CrossRef]

1967 (2)

N. W. Ashcroft and D. C. Langreth, Phys. Rev. 159, 500 (1967).
[CrossRef]

M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
[CrossRef]

Asakura, T.

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

T. Shirai and T. Asakura, J. Opt. Soc. Am. 12, 1354 (1995).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and D. C. Langreth, Phys. Rev. 159, 500 (1967).
[CrossRef]

Boreman, G.

Burford, R. J.

M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
[CrossRef]

Cernanský, M.

M. ?er?anský, Phys. Stat. Sol. (b) 114, 365 (1982).
[CrossRef]

Chen, H.

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

Dogariu, A.

Dušek, M.

In this connection see also M. Dušek, Phys. Rev. E 52, 6833 (1995).
[CrossRef]

Fisher, M. E.

M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
[CrossRef]

Foley, J. T.

Gori, F.

James, D. F. V.

For a review of these investigations see E. Wolf and D. F. V. James, Rep. Progr. Phys. 59, 771 (1996).
[CrossRef]

D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 188, 239 (1994).
[CrossRef]

D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 146, 167 (1990).
[CrossRef]

Joshi, K. C.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

Kandpal, H. C.

D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
[CrossRef]

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

Kutsche, K.

Langreth, D. C.

N. W. Ashcroft and D. C. Langreth, Phys. Rev. 159, 500 (1967).
[CrossRef]

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

Likamwa, P.

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

Mehta, D. S.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

Méndez, E. R.

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

Moudgil, B.

Santarsiero, M.

S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
[CrossRef]

Savedoff, M. P.

D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
[CrossRef]

Saxena, K.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

Shchegrov, A. V.

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

Shirai, T.

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

T. Shirai and T. Asakura, J. Opt. Soc. Am. 12, 1354 (1995).
[CrossRef]

Shirripa Spagnolo, G.

S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
[CrossRef]

Vaishya, J. S.

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap.??7.

Vicalvi, S.

S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
[CrossRef]

Wang, W.

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

Wolf, E.

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

For a review of these investigations see E. Wolf and D. F. V. James, Rep. Progr. Phys. 59, 771 (1996).
[CrossRef]

D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 188, 239 (1994).
[CrossRef]

D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 146, 167 (1990).
[CrossRef]

E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989); erratum,  7, 173 (1990).
[CrossRef]

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 63, 2220 (1989).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Astrophys. J. (2)

D. F. V. James, H. C. Kandpal, and E. Wolf, Astrophys. J. 445, 406 (1995).
[CrossRef]

D. F. V. James, M. P. Savedoff, and E. Wolf, Astrophys. J. 359, 67 (1990).
[CrossRef]

J. Mod. Opt. (3)

H. C. Kandpal, K. Saxena, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, J. Mod. Opt. 42, 447 (1995).
[CrossRef]

E. Wolf, T. Shirai, H. Chen, and W. Wang, J. Mod. Opt. 44, 1345 (1997).

T. Shirai, E. Wolf, H. Chen, and W. Wang, J. Mod. Opt. 45, 799 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

T. Shirai and T. Asakura, J. Opt. Soc. Am. 12, 1354 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

T. Shirai and T. Asakura, Opt. Commun. 123, 234 (1996).
[CrossRef]

S. Vicalvi, G. Shirripa Spagnolo, and M. Santarsiero, Opt. Commun. 130, 241 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (2)

D. F. V. James and E. Wolf, Phys. Lett. A 146, 167 (1990).
[CrossRef]

D. F. V. James and E. Wolf, Phys. Lett. A 188, 239 (1994).
[CrossRef]

Phys. Rev. (2)

N. W. Ashcroft and D. C. Langreth, Phys. Rev. 159, 500 (1967).
[CrossRef]

M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
[CrossRef]

Phys. Rev. A (1)

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (1)

In this connection see also M. Dušek, Phys. Rev. E 52, 6833 (1995).
[CrossRef]

Phys. Rev. Lett. (3)

E. Wolf, Phys. Rev. Lett. 63, 2220 (1989).
[CrossRef] [PubMed]

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

T. A. Leskova, A. A. Maradudin, A. V. Shchegrov, and E. R. Méndez, Phys. Rev. Lett. 79, 1010 (1997).
[CrossRef]

Phys. Stat. Sol. (b) (1)

M. ?er?anský, Phys. Stat. Sol. (b) 114, 365 (1982).
[CrossRef]

Rep. Progr. Phys. (1)

For a review of these investigations see E. Wolf and D. F. V. James, Rep. Progr. Phys. 59, 771 (1996).
[CrossRef]

Other (1)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap.??7.

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Figures (2)

Fig. 1
Fig. 1

Spectrum of the scattered light in the far field at different angles of scattering, calculated for monodispersed systems of spherical particles with radius a=150 nm and volume fraction 45%. The spectrum of the incident field has a Gaussian shape with 70-nm FWHM, centered at λ=500 nm.

Fig. 2
Fig. 2

(a) Relative wavelength shifts z=λ0-λ0/λ0 for scattering on fractal aggregates with increasing number of monomers and different fractal dimension. (b) Relative wavelength shifts for scattering from a cluster containing 1000 particles and different fractal dimensions. The spectrum of the incident light is the same as that shown in Fig.  1a, and the relative wavelength shifts are calculated for scattering angle θ=π/6.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Fr,ω=ωc2ηr,ω=14πωc2n2r,ω-1.
CFr1,r2,ω=F*r1,ωFr2,ω
Sru,ω=1r2C˜F-ku-u0,ku-u0,ωSiω,
C˜FK1,K2,ω=VVCFr1,r2,ω×exp-iK1·r1+K2·r2d3r1d3r2
C˜FK1,K2,ω=F˜*-K1,ωF˜K2,ω,
F̃K,ω=VFr,ωexp-iK·rd3r
Fr,ω=l=1LmlUlr-rlm,ω.
F˜K,ω=l=1LmlVUlr-rlm,ωexp-iK·rd3r.
F˜K,ω=l=1LmlU˜lK,ωexp-iK·rlm,
F̃K,ω2=l=1Ll=1LŨl*K,ωŨlK,ωSllK,
SllK=mlml exp-iK·rml-rml
Sru,ω=1r2l=1Ll=1LŨl*ku-u0,ω×Ũlku-u0,ωSllku-u0Siω.
SK=1+DΓD-11+KR-21-D/2KaD×sinD-1tanKa,

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