Abstract
Long- and infinite range correlations C 2 and C 3 in the optical speckle pattern represent one of the most interesting phenomena in multiple scattering of light. Despite the strong scattering these correlations survive the averaging process of light diffusion and are even enhanced with increased randomness. In this article we are going to discuss the microscopic origin of these particular correlations which are explained in the simple picture of one and twofold crossing of multiple scattering paths. We present a comprehensive experimental study of dynamic speckle correlations, C 2(t) and C 3(t), where the phase shift between the multiple scattering paths is caused by the Brownian motion of the scattering particles. The shape and amplitude of the correlation functions C 2(t) and C 3(t) are in good overall agreement with theory. Deviations are found in the case of C 2(t) when correlations are generated close to the incoming surface which can be explained by single scattering contributions.
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References
P. W. Anderson, Phil. Mag. 52 505 (1985); S. John, Phys. Rev. B 31, 304 (1985).
S. John, Physics Today, May 1991, p.32–40.
M. P. van Albada and A. Lagendjik, Phys. Rev. Lett. 55, 2692 (1985).
P. E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696, (1985).
P. Sheng (Ed.): Scattering and localization of classical waves in random media, World Scientific, Singapore 1990, Ping Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena, Academic Press, Boston, 1995.
C. M. Soukoulis (Ed.): Photonic band gaps and localization, Nato ASI Series B, Physics 308, (Plenum, N.Y., 1993).
G. Maret in: Mesoscopic Quantum Physics, E. Akkermans, G. Montambaux, J-L. Pichard and J. Zinn-Justin, eds (Elsevier Science B. V., North Holland, 1995), p. 147.
D. S. Wiersma, P. Bartolini, A. Lagendijk and R. Righini, Nature 390, 671 (1997).
F. Scheffold, R. Lenke, R. Tweer and G. Maret, Nature 398, 206 (1999).
F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh and A. Lagendijk, Phys. Rev. Lett 83, 2183 (1999).
S. Feng, C. Kane, P. A. Lee and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
R. Pnini and B. Shapiro, Phys. Rev. B 39, 6986 (1989).
S. Feng and P. A. Lee, Science 251, 633 (1991).
R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994).
M. C.W. van Rossum and T. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
A. Z. Genack, N. Garcia, W. Polkosnik, Phys. Rev. Lett. 65, 2129 (1990).
M. P. van Albada, J. F. de Boer and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
F. Scheffold, W. Härtl, G. Maret and E. Matijević, Phys. Rev. B 56, 10942 (1997).
F. Scheffold and G. Maret, Phys. Rev. Lett. 81, 5800 (1999).
C. P. Umbach et al., Phys. Rev. B. 30, 4048 (1984); R. A. Webb et al., Phys. Rev. Lett. 54, 2696 (1985).
This differs by a factor of 2 from the original results for scalar waves [12] due to the two polarization states of electromagnetic waves [22].
J. F. de Boer, M. P. van Albada and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
G. Maret and P. E. Wolf, Z. Phys. B 65, 409 (1987); D. J. Pine, D. A. Weitz, P. M. Chaikin and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988); D. A. Weitz and D. J. Pine in Dynamic Light Scattering, W. Brown Ed. (Oxford Univ. Press, New York, 1993), pp 652-720.
P. D. Kaplan, M. H. Kao, A. G. Yodh and D. J. Pine, Appl. Opt. 32, 21, 3828 (1993).
G. Maret, Curr. Opin. Coll. Int. Sci. 2, 251–257 (1997).
S. Romer, F. Scheffold and P. Schurtenberger, submitted to Phys. Rev. Lett.
F. Scheffold and G. Maret, in preparation.
F. Scheffold, PhD thesis, University of Konstanz (1998).
We note that a first diagrammatic calculation of C 3 (t) has been published by Berkovits and Feng [14] but we were not able to reproduce their plots which are based on a complex combination of different diverging functions. Recently van Rossum and Nieuwenhuizen have presented an new calculation of C 3 (t) which has not been compared yet to the results of our simple integral approximation, Eq. (16) [15]. Attempts are now underway to do so [27].
Y-S. Her, E. Matijević and M. C. Chon, J. Mater. Res. 10, 12,3106 (1995).
A. Garcia-Martin, F. Scheffold, M. Nieto-Vesperinas and J. J. Saenz, in preparation.
The prefactor to Eq. (12) and the value of β = 16/15 where determined by comparing the limiting cases [w ≪ L, w ≫ L] to the results of Eq. (6).
Mott, N. F. Metal Insulator Transitions (Taylor and Franzis, London, 1974).
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Scheffold, F., Maret, G. (2001). Dynamic Speckle Correlations. In: Sebbah, P. (eds) Waves and Imaging through Complex Media. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0975-1_24
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DOI: https://doi.org/10.1007/978-94-010-0975-1_24
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