Abstract

The properties of light scattered from material systems depend on the characteristics of input optical fields. We study numerically the effect of the state of spatial coherence on the properties of scattered fields. Using a customized coupled dipole technique, we demonstrate that this influence manifests in changes of the statistics of intensities scattered at different angles.

© 2012 Optical Society of America

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References

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  1. H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
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    [CrossRef]
  4. V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
    [CrossRef]
  5. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for periodic targets: theory and tests,” J. Opt. Soc. Am. A 25, 2693–2703 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
  7. S. Sukhov, D. Haefner, and A. Dogariu, “Coupled dipole method for modeling optical properties of large-scale random media,” Phys. Rev. E 77, 066709 (2008).
    [CrossRef]
  8. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
    [CrossRef]
  9. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
    [CrossRef]
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    [CrossRef]
  11. J. W. Goodman, Statistical Optics (Wiley, 2000).
  12. Second-order field correlations are sufficient to describe phenomena such as radiation of light, propagation, diffraction, and interference. However, in general, higher-order correlations involving multiple products and powers of field variables are necessary to describe all the statistical properties of random electromagnetic fields.
  13. X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 14, 6986–6992(2006).
    [CrossRef] [PubMed]
  14. G. Gbur, “Simulating fields of arbitrary spatial and temporal coherence,” Opt. Express 14, 7567–7578 (2006).
    [CrossRef] [PubMed]
  15. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
    [CrossRef]
  16. S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic reconstruction of anisotropic polarizabilities,” J. Opt. Soc. Am. A 27, 827–831 (2010).
    [CrossRef]
  17. D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
    [CrossRef]
  18. R. Barakat, “Direct derivation of intensity and phase statistics of speckle produced by a weak scatterer from the random sinusoid model,” J. Opt. Soc. Am. 71, 86–90 (1981).
    [CrossRef]
  19. D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
    [CrossRef]
  20. J.-J. Greffet, M. De La Cruz-Gutierrez, P. V. Ignatovich, and A. Radunsky, “Influence of spatial coherence on scattering by a particle,” J. Opt. Soc. Am. A 20, 2315–2320 (2003).
    [CrossRef]
  21. A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near fields,” Phys. Rev. E 72, 0256602R (2005).
    [CrossRef]
  22. A. Apostol, A. Dogariu, and D. Carter, “Effective surface of optical coatings,” presented at the TAPPI Conference, Turku, Finland, 8–10 February 2006.
  23. A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
    [CrossRef]

2010 (3)

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
[CrossRef]

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic reconstruction of anisotropic polarizabilities,” J. Opt. Soc. Am. A 27, 827–831 (2010).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
[CrossRef]

2008 (3)

2007 (1)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

2006 (4)

V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
[CrossRef]

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 14, 6986–6992(2006).
[CrossRef] [PubMed]

G. Gbur, “Simulating fields of arbitrary spatial and temporal coherence,” Opt. Express 14, 7567–7578 (2006).
[CrossRef] [PubMed]

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
[CrossRef]

2005 (1)

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near fields,” Phys. Rev. E 72, 0256602R (2005).
[CrossRef]

2003 (1)

1998 (1)

D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
[CrossRef]

1997 (2)

1994 (1)

1981 (1)

1973 (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Apostol, A.

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
[CrossRef]

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near fields,” Phys. Rev. E 72, 0256602R (2005).
[CrossRef]

A. Apostol, A. Dogariu, and D. Carter, “Effective surface of optical coatings,” presented at the TAPPI Conference, Turku, Finland, 8–10 February 2006.

Barakat, R.

Belkebir, K.

Brouder, C.

D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
[CrossRef]

Bush, K. A.

Cabaret, D.

D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
[CrossRef]

Carter, D.

A. Apostol, A. Dogariu, and D. Carter, “Effective surface of optical coatings,” presented at the TAPPI Conference, Turku, Finland, 8–10 February 2006.

Chaumet, P. C.

De La Cruz-Gutierrez, M.

Dholakia, K.

V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
[CrossRef]

Ding, K. H.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
[CrossRef]

Dogariu, A.

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic reconstruction of anisotropic polarizabilities,” J. Opt. Soc. Am. A 27, 827–831 (2010).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
[CrossRef]

S. Sukhov, D. Haefner, and A. Dogariu, “Coupled dipole method for modeling optical properties of large-scale random media,” Phys. Rev. E 77, 066709 (2008).
[CrossRef]

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
[CrossRef]

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near fields,” Phys. Rev. E 72, 0256602R (2005).
[CrossRef]

A. Apostol, A. Dogariu, and D. Carter, “Effective surface of optical coatings,” presented at the TAPPI Conference, Turku, Finland, 8–10 February 2006.

Draine, B. T.

Flatau, P. J.

Gbur, G.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Greffet, J.-J.

Haefner, D.

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic reconstruction of anisotropic polarizabilities,” J. Opt. Soc. Am. A 27, 827–831 (2010).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
[CrossRef]

S. Sukhov, D. Haefner, and A. Dogariu, “Coupled dipole method for modeling optical properties of large-scale random media,” Phys. Rev. E 77, 066709 (2008).
[CrossRef]

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
[CrossRef]

Hirleman, E. D.

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Hyvärinen, H. J.

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
[CrossRef]

Idell, P. S.

Ignatovich, P. V.

Karasek, V.

V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
[CrossRef]

Nebeker, B. M.

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

Radunsky, A.

Rahmani, A.

Rossano, S.

D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
[CrossRef]

Schmehl, R.

Sukhov, S.

S. Sukhov, D. Haefner, and A. Dogariu, “Stochastic reconstruction of anisotropic polarizabilities,” J. Opt. Soc. Am. A 27, 827–831 (2010).
[CrossRef]

D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
[CrossRef]

S. Sukhov, D. Haefner, and A. Dogariu, “Coupled dipole method for modeling optical properties of large-scale random media,” Phys. Rev. E 77, 066709 (2008).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
[CrossRef]

Turunen, J.

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
[CrossRef]

Vahimaa, P.

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
[CrossRef]

Voelz, D.

Voelz, D. G.

Xiao, X.

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Zemanek, P.

V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

H. J. Hyvärinen, J. Turunen, and P. Vahimaa, “Elementary-field modeling of surface-plasmon excitation with partially coherent light,” Appl. Phys. B 101, 273–282 (2010).
[CrossRef]

V. Karasek, K. Dholakia, and P. Zemanek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156(2006).
[CrossRef]

Astrophys. J. (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

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

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Opt. Commun. (1)

D. Cabaret, S. Rossano, and C. Brouder, “Mie scattering of a partially coherent beam,” Opt. Commun. 150, 239–250 (1998).
[CrossRef]

Opt. Express (3)

Phys. Rev. E (4)

D. Haefner, S. Sukhov, and A. Dogariu, “Scale-dependent anisotropic polarizability in mesoscopic structures,” Phys. Rev. E 81, 016609 (2010).
[CrossRef]

S. Sukhov, D. Haefner, and A. Dogariu, “Coupled dipole method for modeling optical properties of large-scale random media,” Phys. Rev. E 77, 066709 (2008).
[CrossRef]

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near fields,” Phys. Rev. E 72, 0256602R (2005).
[CrossRef]

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 066603(2006).
[CrossRef]

Other (4)

A. Apostol, A. Dogariu, and D. Carter, “Effective surface of optical coatings,” presented at the TAPPI Conference, Turku, Finland, 8–10 February 2006.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley-Interscience, 2001).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, 2000).

Second-order field correlations are sufficient to describe phenomena such as radiation of light, propagation, diffraction, and interference. However, in general, higher-order correlations involving multiple products and powers of field variables are necessary to describe all the statistical properties of random electromagnetic fields.

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Figures (3)

Fig. 1
Fig. 1

(a) Coherent Gaussian beam with 0.7 μm waist and (b) one realization of a PCB profile having a random phase variation within ( 2 π / 3 , 2 π / 3 ) and generated using the plane wave decomposition described in text.

Fig. 2
Fig. 2

Probability density functions of scattered intensities corresponding to different illumination conditions and different detection geometries: (a) coherent beam and normal detection, (b) PCB normal detection, (c) coherent beam and specular detection, and (d) PCB and specular detection. The angular width of both coherent and PCBs is π / 22 . A random phase variation within ( 2 π / 3 , 2 π / 3 ) was used to model the PCB.

Fig. 3
Fig. 3

Directions along which the intensity of scattered light was collected in numerical simulations.

Tables (1)

Tables Icon

Table 1 Relative Scattered Intensities Along the Directions Indicated in Fig. 3 a

Equations (2)

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E ( r j ) = E inc ( r j ) + k = 1 N E k dip ( r j ) .
γ ( r 1 , r 2 , t 1 , t 2 ) = E * ( r 1 , t 1 ) E ( r 2 , t 2 ) e I ( r 1 , t 1 ) e · I ( r 2 , t 2 ) e .

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