## Evolutions of speckles on rough glass/silver surfaces with film thickness |

Optics Express, Vol. 21, Issue 7, pp. 8831-8842 (2013)

http://dx.doi.org/10.1364/OE.21.008831

Acrobat PDF (1901 KB)

### Abstract

This paper reports experimental studies on speckles produced by the rough silver films. The speckles on the rough glass/silver surfaces are measured with a microscopic imaging system. The structures of speckle patterns have the characteristics of fractals and multi-scaled sizes. We find that with the increase of the silver film thickness, the contrast of the speckles increases, and the intensity probability density functions gradually transit to exponential decay. We calculate the global and the local correlation functions of the speckle patterns, and find that both the fractal exponent and correlation length of the small-sized speckles decrease with the thickness of the silver films. We use the mechanisms of rough dielectric interface scattering and random surface plasmon waves to give the preliminary explanations for the evolutions of the speckles.

© 2013 OSA

## 1. Introduction

1. D. Han, M. Wang, and J. Zhou, “Fractal analysis of self-mixing speckle signal in velocity sensing,” Opt. Express **16**(5), 3204–3211 (2008). [CrossRef] [PubMed]

3. B. Wiesner, O. Hybl, and G. Häusler, “Improved white-light interferometry on rough surfaces by statistically independent speckle patterns,” Appl. Opt. **51**(6), 751–757 (2012). [CrossRef] [PubMed]

5. J. W. Goodman, “Speckle with a finite number of steps,” Appl. Opt. **47**(4), A111–A118 (2008). [CrossRef] [PubMed]

6. R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A **75**(5), 053815 (2007). [CrossRef]

8. A. Gatti, D. Magatti, and F. Ferri, “Three-dimensional coherence of light speckles: Theory,” Phys. Rev. A **78**(6), 063806 (2008). [CrossRef]

10. Z. W. Liu, Y. Wang, J. Yao, H. Lee, W. Srituravanich, and X. Zhang, “Broad band two-dimensional manipulation of surface plasmons,” Nano Lett. **9**(1), 462–466 (2009). [CrossRef] [PubMed]

12. Z. Y. Fan and A. O. Govorov, “Plasmonic circular dichroism of chiral metal nanoparticle assemblies,” Nano Lett. **10**(7), 2580–2587 (2010). [CrossRef] [PubMed]

13. J. A. Sánchez-Gil and M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B Condens. Mater. **45**(15), 8623–8633 (1992). [CrossRef] [PubMed]

14. J. Laverdant, S. Buil, B. Berini, and X. Quelin, “Polarization dependent near-field speckle of random gold films,” Phys. Rev. B **77**(16), 165406 (2008). [CrossRef]

15. Z. Q. Tian, B. Ren, and D. Y. Wu, “Surface-enhanced Raman scattering: from noble to transition metals and from rough surfaces to ordered nanostructures,” J. Phys. Chem. B **106**(37), 9463–9483 (2002). [CrossRef]

16. C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, and Z. Z. Xu, “M. Liu1, N. Y. Zhang, S. Y. Teng, H. S. Song and Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. **65**(6), 779–784 (2004). [CrossRef]

## 2. Experiments for surface plasmon speckle acquisitions

### 2.1 *Experimental setup*

### 2.2. The sample fabrication and the fractal description of rough surfaces

20. O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, and S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt. **40**(31), 5693–5707 (2001). [CrossRef] [PubMed]

## 3. Analysis of speckle evolution with thickness of silver film

### 3.1 The basic characteristics of the speckles on the sample surfaces

*P*is the superposition of the waves scattered from a small area on rough surface neighboring to point

*P*. The incident light illuminating the neighboring small area is indicated by three parallel shorter blue arrows, and the three smallest blue arrows on the right side of the surface indicate the scattered waves contributing to intensity at

*P*. The pink arrows indicate the waves scattered to other points on the observation plane. According to the diffraction theory of Kirchhoff approximation, the scattered wave field for the ground glass sample is expressed in the form of Green’s integral:where

*m*the reflective index of the sample,

20. O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, and S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt. **40**(31), 5693–5707 (2001). [CrossRef] [PubMed]

*P*

^{’}.

### 3.2 The contrast and the intensity probability density of speckles

21. E. Jakeman, “Speckle statistics with a small number of scatters,” Opt. Eng. **23**(4), 234453 (1984). [CrossRef]

5. J. W. Goodman, “Speckle with a finite number of steps,” Appl. Opt. **47**(4), A111–A118 (2008). [CrossRef] [PubMed]

22. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express **18**(14), 14519–14534 (2010). [CrossRef] [PubMed]

23. J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. **34**(16), 2429–2431 (2009). [CrossRef] [PubMed]

## 4. Evolution of the autocorrelation function

7. M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. **85**(7), 1416–1419 (2000). [CrossRef] [PubMed]

### 4.1 The global autocorrelation function

*d*and finally obtain the

*d*. Since the calculation is performed over a whole image, we call

*d*; the thicker the silver film of sample is, the more quickly the curve descends. This corresponds to facts that small-sized speckle grains are smaller for thicker silver film samples, as shown in Figs. 3 and Figs. 4. While

### 4.2 The local autocorrelation function

## 5. Discussion and conclusion

## Acknowledgment

## References and links

1. | D. Han, M. Wang, and J. Zhou, “Fractal analysis of self-mixing speckle signal in velocity sensing,” Opt. Express |

2. | A. S. Ulyanov, “Application of laser speckles for identification of tissues with pathological changes,” Quant. Elec. |

3. | B. Wiesner, O. Hybl, and G. Häusler, “Improved white-light interferometry on rough surfaces by statistically independent speckle patterns,” Appl. Opt. |

4. | J. W. Goodman, |

5. | J. W. Goodman, “Speckle with a finite number of steps,” Appl. Opt. |

6. | R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A |

7. | M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. |

8. | A. Gatti, D. Magatti, and F. Ferri, “Three-dimensional coherence of light speckles: Theory,” Phys. Rev. A |

9. | H. Raether, |

10. | Z. W. Liu, Y. Wang, J. Yao, H. Lee, W. Srituravanich, and X. Zhang, “Broad band two-dimensional manipulation of surface plasmons,” Nano Lett. |

11. | J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. |

12. | Z. Y. Fan and A. O. Govorov, “Plasmonic circular dichroism of chiral metal nanoparticle assemblies,” Nano Lett. |

13. | J. A. Sánchez-Gil and M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B Condens. Mater. |

14. | J. Laverdant, S. Buil, B. Berini, and X. Quelin, “Polarization dependent near-field speckle of random gold films,” Phys. Rev. B |

15. | Z. Q. Tian, B. Ren, and D. Y. Wu, “Surface-enhanced Raman scattering: from noble to transition metals and from rough surfaces to ordered nanostructures,” J. Phys. Chem. B |

16. | C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, and Z. Z. Xu, “M. Liu1, N. Y. Zhang, S. Y. Teng, H. S. Song and Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett. |

17. | Y. P. Zhao, G. C. Wang, and T. M. Lu, |

18. | D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, and C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin. |

19. | S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B Condens. Matter |

20. | O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, and S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt. |

21. | E. Jakeman, “Speckle statistics with a small number of scatters,” Opt. Eng. |

22. | S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express |

23. | J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett. |

**OCIS Codes**

(030.6140) Coherence and statistical optics : Speckle

(240.6680) Optics at surfaces : Surface plasmons

(290.0290) Scattering : Scattering

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: February 8, 2013

Revised Manuscript: March 21, 2013

Manuscript Accepted: March 21, 2013

Published: April 3, 2013

**Virtual Issues**

Vol. 8, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Meina Zhang, Zhenhua Li, Xiaoyi Chen, Guotao Liang, Shuyun Wang, Shuyun Teng, and Chuanfu Cheng, "Evolutions of speckles on rough glass/silver surfaces with film thickness," Opt. Express **21**, 8831-8842 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-7-8831

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### References

- D. Han, M. Wang, and J. Zhou, “Fractal analysis of self-mixing speckle signal in velocity sensing,” Opt. Express16(5), 3204–3211 (2008). [CrossRef] [PubMed]
- A. S. Ulyanov, “Application of laser speckles for identification of tissues with pathological changes,” Quant. Elec.38(6), 557–562 (2008). [CrossRef]
- B. Wiesner, O. Hybl, and G. Häusler, “Improved white-light interferometry on rough surfaces by statistically independent speckle patterns,” Appl. Opt.51(6), 751–757 (2012). [CrossRef] [PubMed]
- J. W. Goodman, Speckle Phenonmena in Optics: Theory and Applications (Ben Robert & Company, 2007).
- J. W. Goodman, “Speckle with a finite number of steps,” Appl. Opt.47(4), A111–A118 (2008). [CrossRef] [PubMed]
- R. Cerbino, “Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem,” Phys. Rev. A75(5), 053815 (2007). [CrossRef]
- M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett.85(7), 1416–1419 (2000). [CrossRef] [PubMed]
- A. Gatti, D. Magatti, and F. Ferri, “Three-dimensional coherence of light speckles: Theory,” Phys. Rev. A78(6), 063806 (2008). [CrossRef]
- H. Raether, Surface Plasmons on Smooth and Rrough Surfaces and on Gratings (Springer, 1988).
- Z. W. Liu, Y. Wang, J. Yao, H. Lee, W. Srituravanich, and X. Zhang, “Broad band two-dimensional manipulation of surface plasmons,” Nano Lett.9(1), 462–466 (2009). [CrossRef] [PubMed]
- J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010). [CrossRef] [PubMed]
- Z. Y. Fan and A. O. Govorov, “Plasmonic circular dichroism of chiral metal nanoparticle assemblies,” Nano Lett.10(7), 2580–2587 (2010). [CrossRef] [PubMed]
- J. A. Sánchez-Gil and M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B Condens. Mater.45(15), 8623–8633 (1992). [CrossRef] [PubMed]
- J. Laverdant, S. Buil, B. Berini, and X. Quelin, “Polarization dependent near-field speckle of random gold films,” Phys. Rev. B77(16), 165406 (2008). [CrossRef]
- Z. Q. Tian, B. Ren, and D. Y. Wu, “Surface-enhanced Raman scattering: from noble to transition metals and from rough surfaces to ordered nanostructures,” J. Phys. Chem. B106(37), 9463–9483 (2002). [CrossRef]
- C. F. Cheng, M. Liu, N. Y. Zhang, S. Y. Teng, H. S. Song, and Z. Z. Xu, “M. Liu1, N. Y. Zhang, S. Y. Teng, H. S. Song and Z. Z. Xu, “Speckle intensity correlation in the diffraction region near rough surfaces and simulational experiments for extraction of surface parameters,” Europhys. Lett.65(6), 779–784 (2004). [CrossRef]
- Y. P. Zhao, G. C. Wang, and T. M. Lu, Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications, (Academic Press, 2001).
- D. P. Qi, D. L. Liu, S. Y. Teng, N. Y. Zhang, and C. F. Cheng, “Morphology analysis atomic force microscope and light scattering study for random scattering screens,” Acta Phys. Sin.49(7), 1260–1266 (2000) (in Chinese).
- S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B Condens. Matter38(4), 2297–2311 (1988). [CrossRef] [PubMed]
- O. V. Angelsky, P. P. Maksimyak, V. V. Ryukhtin, and S. G. Hanson, “New feasibilities for characterizing rough surfaces by optical-correlation techniques,” Appl. Opt.40(31), 5693–5707 (2001). [CrossRef] [PubMed]
- E. Jakeman, “Speckle statistics with a small number of scatters,” Opt. Eng.23(4), 234453 (1984). [CrossRef]
- S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express18(14), 14519–14534 (2010). [CrossRef] [PubMed]
- J. Sorrentini, M. Zerrad, and C. Amra, “Statistical signatures of random media and their correlation to polarization properties,” Opt. Lett.34(16), 2429–2431 (2009). [CrossRef] [PubMed]

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