Abstract

We study the intensity spatial correlation function of optical speckle patterns above a disordered dielectric medium in the multiple scattering regime. The intensity distributions are recorded by scanning near-field optical microscopy (SNOM) with sub-wavelength spatial resolution at variable distances from the surface in a range which spans continuously from the near-field (distance ≪ λ) to the far-field regime (distance ≫ λ). The non-universal behavior at sub-wavelength distances reveals the connection between the near-field speckle pattern and the internal structure of the medium.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Anisotropy of near-field speckle patterns

Cheng Liu and Seung-Han Park
Opt. Lett. 30(13) 1602-1604 (2005)

Near-field speckles produced by random self-affine surfaces and their contrast transitions

Chuanfu Cheng, Chunxiang Liu, Xiaorong Ren, Man Liu, Shuyun Teng, and Zhizhan Xu
Opt. Lett. 28(17) 1531-1533 (2003)

First- and second-order statistics of optical near fields

Adela Apostol and Aristide Dogariu
Opt. Lett. 29(3) 235-237 (2004)

References

  • View by:
  • |
  • |
  • |

  1. L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2006).
    [Crossref]
  2. D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
    [Crossref]
  3. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2010).
  4. A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
    [Crossref]
  5. J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18(19), 20105–20113 (2010).
    [Crossref] [PubMed]
  6. R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
    [Crossref]
  7. R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
    [Crossref]
  8. A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
    [Crossref] [PubMed]
  9. A. Apostol and A. Dogariu, “First- and second-order statistics of optical near fields,” Opt. Lett. 29, 235–237 (2004).
    [Crossref] [PubMed]
  10. V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
    [Crossref] [PubMed]
  11. A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near-fields,” Phys. Rev. E 72, 025602 (2005).
    [Crossref]
  12. R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
    [Crossref] [PubMed]
  13. A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
    [Crossref] [PubMed]
  14. G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
    [Crossref] [PubMed]
  15. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309 (2007).
    [Crossref] [PubMed]
  16. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [Crossref] [PubMed]

2015 (2)

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

2010 (3)

J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18(19), 20105–20113 (2010).
[Crossref] [PubMed]

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

2007 (2)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309 (2007).
[Crossref] [PubMed]

2005 (1)

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near-fields,” Phys. Rev. E 72, 025602 (2005).
[Crossref]

2004 (1)

2003 (2)

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref] [PubMed]

2002 (1)

A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
[Crossref] [PubMed]

2001 (1)

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[Crossref] [PubMed]

1984 (1)

D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Aliev, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Apostol, A.

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near-fields,” Phys. Rev. E 72, 025602 (2005).
[Crossref]

A. Apostol and A. Dogariu, “First- and second-order statistics of optical near fields,” Opt. Lett. 29, 235–237 (2004).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref] [PubMed]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Broky, J.

Carminati, R.

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Cazayous, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Colocci, M.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Cwilich, G.

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

Denk, W.

D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Derode, A.

A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
[Crossref] [PubMed]

Dogariu, A.

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

J. Broky and A. Dogariu, “Complex degree of mutual polarization in randomly scattered fields,” Opt. Express 18(19), 20105–20113 (2010).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near-fields,” Phys. Rev. E 72, 025602 (2005).
[Crossref]

A. Apostol and A. Dogariu, “First- and second-order statistics of optical near fields,” Opt. Lett. 29, 235–237 (2004).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref] [PubMed]

Emiliani, V.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
[Crossref] [PubMed]

Froufe-Pérez, L. S.

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2010).

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2006).
[Crossref]

Intonti, F.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Lagendijk, A.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Lanz, M.

D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

Lobkis, O. I.

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[Crossref] [PubMed]

Mosk, A. P.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2006).
[Crossref]

Pohl, D.

D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Sáenz, J. J.

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

Tourin, A.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
[Crossref] [PubMed]

Vellekoop, I. M.

Weaver, R. L.

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[Crossref] [PubMed]

Wiersma, D. S.

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

D. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rep. (1)

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

Phys. Rev. A (2)

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

R. Carminati, G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Speckle fluctuations resolve the interdistance between incoherent point sources in complex media,” Phys. Rev. A 91, 023807 (2015).
[Crossref]

Phys. Rev. E (1)

A. Apostol and A. Dogariu, “Non-Gaussian statistics of optical near-fields,” Phys. Rev. E 72, 025602 (2005).
[Crossref]

Phys. Rev. Lett. (4)

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[Crossref] [PubMed]

V. Emiliani, F. Intonti, M. Cazayous, D. S. Wiersma, M. Colocci, F. Aliev, and A. Lagendijk, “Near-field short range correlation in optical waves transmitted through random media,” Phys. Rev. Lett. 90, 250801 (2003).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref] [PubMed]

Science (1)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315, 1120 (2007).
[Crossref] [PubMed]

Ultrasonics (1)

A. Derode, A. Tourin, and M. Fink, “Time reversal versus phase conjugation in a multiple scattering environment,” Ultrasonics 40, 275 (2002).
[Crossref] [PubMed]

Other (2)

L. Novotny and B. Hecht, Principles of Nano-Optics, 2nd ed. (Cambridge University, 2006).
[Crossref]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company Publishers, 2010).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

a) Scheme of the setup. The laser beam is focused on the sample down to a diameter of ∼40 μm. The sample is placed on a three-axis stage which allows scanning in the x–y plane during the acquisition. The z-stage is used in contact mode to follow the surface topography with the pyramid when the electronic feedback is in operation. The light above the sample surface passing through the ∼ 150 nm wide hole in the pyramid is collected by the confocal microscope (objective 20X, NA 0.4). It is injected by means of the microscope tube lens (TL, focal distance 200 mm) into a multimode fiber (MMF) connected to a photomultiplier (PM) which measures the light intensity. The z distance between the pyramid and the sample surface is controlled by the sample-stage unit up to 8 μm and then by jointly moving the cantilever and the objective. b) Scanning electron microscope images of the surfaces of the two analyzed samples.

Fig. 2
Fig. 2

Scans in contact mode for the two samples. a) Topography, and b) intensity images measured in one zone of sample A. c) and d) the same for sample B. The vertical and horizontal scales units are μm. Colorbars are in nm for a), c) and PM counts for b), d).

Fig. 3
Fig. 3

Evaluation of speckle grain size. a) On upper part left: typical intensity speckles pattern. Bottom: its autocorrelation with a zoom of the central region (upper right). b) The autocorrelation is cut with a plane at a height of 0.2. c) The surface resulting from the cut: the speckle size δ is obtained as the average radius of the surface. Scales units are μm.

Fig. 4
Fig. 4

a) Series of intensity speckle patterns in one zone of the sample B at different distances from the surface ranging from the near-field to the far-field regime. The vertical and horizontal scales units are μm, while the values on the colorbar are number of counts of the PM. b) Sections along the x direction of the autocorrelation function obtained from the five patterns.

Fig. 5
Fig. 5

Measurement of autocorrelation size from the near-field to the far-field regime in the case of sample A (red points) and sample B (black) points. The curves are composed by several series of measurements varying z in different zones of the samples.

Fig. 6
Fig. 6

a) Near-field subset of data in Fig. 5. The two points at z = 0 result from averaging over 9 measurements in the case of sample A (red) and over 3 measurements in case of sample B (black). b) Section along the x direction of the autocorrelation functions for z = 0. Red curve: average over the measurements of sample A, black curve: average over the measurements of sample B, yellow curves: the 9 measurements for sample A at z = 0.

Metrics