Abstract

In the vicinity of a rough interface under normal illumination the speckle field has been found to be anisotropic; that is, its correlation length is much larger in the direction of polarization than in the perpendicular direction, forming stripe-shaped speckle patterns in the near-field region. Furthermore, with increasing distance from the interface, the anisotropy of the near-field speckles decays rapidly, while the speckle size increases drastically in all directions. Based on detailed analysis, it was found that the anisotropy of the near-field speckle patterns can be attributed to polarization-dependent coupling among the evanescent waves from different surface diffusers.

© 2005 Optical Society of America

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References

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  1. J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).
  2. F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
    [CrossRef]
  3. J.-J. Greffet and R. Carminati, Ultramicroscopy 61, 43 (1995).
    [CrossRef]
  4. A. V. Shchegrov, Phys. Rev. Lett. 85, 1548 (2000).
    [CrossRef] [PubMed]
  5. V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
    [CrossRef]
  6. A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
    [CrossRef]
  7. A. Apostol and A. Dogariu, Opt. Lett. 29, 235 (2004).
    [CrossRef] [PubMed]
  8. C. Cheng, C. Liu, X. Ren, M. Liu, S. Teng, and Z. Xu, Opt. Lett. 28, 1531 (2003)
    [CrossRef] [PubMed]
  9. T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
    [CrossRef]
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
    [CrossRef]
  11. G. S. Agarwal, Phys. Rev. B 14, 846 (1976).
    [CrossRef]
  12. M. Nieto-Vesperinas, J. Opt. Soc. Am. 72, 539 (1982).
    [CrossRef]
  13. A. A Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
    [CrossRef]
  14. M. Nieto-Veerpinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).
  15. M. Xiao, Opt. Commun. 136, 213 (1997).
    [CrossRef]

2004 (1)

2003 (3)

C. Cheng, C. Liu, X. Ren, M. Liu, S. Teng, and Z. Xu, Opt. Lett. 28, 1531 (2003)
[CrossRef] [PubMed]

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

2002 (1)

T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

2000 (1)

A. V. Shchegrov, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

1997 (1)

M. Xiao, Opt. Commun. 136, 213 (1997).
[CrossRef]

1995 (1)

J.-J. Greffet and R. Carminati, Ultramicroscopy 61, 43 (1995).
[CrossRef]

1994 (1)

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

1982 (1)

1976 (1)

G. S. Agarwal, Phys. Rev. B 14, 846 (1976).
[CrossRef]

1975 (1)

A. A Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
[CrossRef]

Adam, P. M.

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. B 14, 846 (1976).
[CrossRef]

Apostol, A.

A. Apostol and A. Dogariu, Opt. Lett. 29, 235 (2004).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

Carminati, R.

J.-J. Greffet and R. Carminati, Ultramicroscopy 61, 43 (1995).
[CrossRef]

Cazyous, M.

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

Cheng, C.

Colocci, M.

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

de Fornel, F.

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

Dogariu, A.

A. Apostol and A. Dogariu, Opt. Lett. 29, 235 (2004).
[CrossRef] [PubMed]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

Emiliani, V.

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

Friberg, A. T.

T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Gounner, J. P.

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet and R. Carminati, Ultramicroscopy 61, 43 (1995).
[CrossRef]

Guerin, P.

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

Intoni, F.

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

Kaivola, I. M.

T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Liu, C.

Liu, M.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

Maradudin, A. A

A. A Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
[CrossRef]

Mills, D. L.

A. A Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
[CrossRef]

Nieto-Veerpinas, M.

M. Nieto-Veerpinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).

Nieto-Vesperinas, M.

Ren, X.

Salmon, L.

F. de Fornel, P. M. Adam, L. Salmon, J. P. Gounner, and P. Guerin, Opt. Lett. 19, 14 (1994).
[CrossRef]

Setälä, T.

T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Shchegrov, A. V.

A. V. Shchegrov, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

Teng, S.

Wiersma, D. S.

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

Xiao, M.

M. Xiao, Opt. Commun. 136, 213 (1997).
[CrossRef]

Xu, Z.

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

M. Xiao, Opt. Commun. 136, 213 (1997).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (2)

A. A Maradudin and D. L. Mills, Phys. Rev. B 11, 1392 (1975).
[CrossRef]

G. S. Agarwal, Phys. Rev. B 14, 846 (1976).
[CrossRef]

Phys. Rev. Lett. (4)

T. Setälä, I. M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

A. V. Shchegrov, Phys. Rev. Lett. 85, 1548 (2000).
[CrossRef] [PubMed]

V. Emiliani, F. Intoni, M. Cazyous, D. S. Wiersma, and M. Colocci, Phys. Rev. Lett. 90, 250801 (2003).
[CrossRef]

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

Ultramicroscopy (1)

J.-J. Greffet and R. Carminati, Ultramicroscopy 61, 43 (1995).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
[CrossRef]

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984).

M. Nieto-Veerpinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic example of the scattering system. (b) Computed rough surface.

Fig. 2
Fig. 2

(a) Distribution of d y y at 30 nm from a rough surface, (b) the computed near-field intensity distribution, (c) its spatial correlation.

Fig. 3
Fig. 3

(a) Distribution of d y y at 80 nm from a rough surface, (b) the computed near-field intensity distribution, (c) its spatial correlation.

Fig. 4
Fig. 4

(a) Correlation lengths of random near fields as functions of distance and (b) spatial correlation of far-field speckle patterns.

Equations (4)

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

z = ξ ( x , y ) .
E ( r ) = E T ( 0 ) ( r ) + π ω 2 c 2 ( ϵ 1 ) + d 2 k exp ( i k r ) ξ ̂ [ k k ( 0 ) ] [ E T ( 0 ) G ( k ) + ϵ E T z ( 0 ) z ̂ G ( k ) ] ,
G ( r z = 0 , r ) = d 2 k G ( k ) exp [ i k ( r r z = 0 ) + i ( ω 2 c 2 k 2 ) 1 2 z ] .
E ( r ) = E T ( 0 ) ( r ) + π ω 2 c 2 ( ϵ 1 ) + d 2 k exp ( i k r ) ξ ̂ ( k ) [ E T ( 0 ) G ( k ) ] .

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