Abstract
The field of multiple scattering of classical waves (electromagnetic, acoustic and elastic waves, etc.) in disordered media has revived in the eighties [1]– [6], when the far-reaching analogies between the diffuse transport of waves and electrons in mesoscopic systems have been realized (see Ref. [7] for a comprehensive review of the latter issue). Using classical waves to study such phenomena as weak and strong localization, mesoscopic correlations and universal conductance fluctuations (see Refs. [8]–[10] for reviews) appears to be advantageous in many aspects: no need for low temperatures and small samples, better control of the experimental apparatus, possibility of more sensitive measurements, etc. In addition, experiments with classical waves can be readily performed in the linear regime, excluding interaction between scattered waves and hence simplifying the interpretation of experimental data, whereas the electron-electron interaction is always present in the realm of mesoscopic electronics and cannot simply be ‘turned off’, introducing significant difficulties in the theoretical model [11].
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References
Van Albada, M.P. and Lagendijk, A. (1985) Observation of weak localization of light in a random medium, Phys. Rev. Lett. 55, 2692–2695; Wolf, P.-E. and Maret, G. (1985) Weak localization and coherent backscattering of photons in disordered media, Phys. Rev. Lett. 55, 2696–2699.
Shapiro, B. (1986) Large intensity fluctuations for wave propagation in random media, Phys. Rev. Lett. 57, 2168–2171.
Stephen, M.J. and Cwilich, G. (1987) Intensity correlation functions and fluctuations in light scattered from a random medium, Phys. Rev. Lett. 59, 285–287.
Zyuzin, A.Yu. and Spivak, B.Z. (1987) Langevin description of mesoscopic fluctuations in disordered media, Sov. Phys. JETP 66, 560–566; Pnini, R. and Shapiro B. (1989) Fluctuations in transmission of waves through disordered slabs, Phys. Rev. B 39, 6986–6994.
Maret, G. and Wolf, P.-E. (1987) Multiple light scattering from disordered media. The effect of Brownian motion of scatterers, Z. Phys. B 65, 409–413; Pine, D.J., Weitz, D.A., Chaikin, P.M., and Herbolzheimer, E. (1988) Diffusing wave spectroscopy, Phys. Rev. Lett. 60, 1134–1137.
Sheng, P. (ed.) (1990) Scattering and Localization of Classical Waves in Random Media, World Scientific, Singapore.
Lagendijk, A. and Van Tiggelen, B.A. (1996) Resonant multiple scattering of light, Phys. Rep. 270, 143–215.
Berkovits, R. and Feng S. (1994) Correlations in coherent multiple scattering, Phys. Rep. 238, 135–172.
Van Rossum, M.C.W. and Nieuwenhuizen, Th.M. (1999) Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion, Rev. Mod. Phys. 71, 313–371.
Sebbah, P. (ed.) (2001) Waves and Imaging through Complex Media, Kluwer Academic Publishers, Dordrecht.
Altshuler, B.L., Lee, P.A., and Webb, R.A. (eds.) (1991) Mesoscopic Phenomena in Solids, Elsevier, Amsterdam; S. Datta (1995) Electronic transport in mesoscopic systems, Cambridge University Press, Cambridge.
Boyd, R.W. (2002) Nonlinear Optics, Academic Press, New York; Bloembergen, N. (1996) Nonlinear Optics, World Scientific, Singapore.
Hamilton, M.F. and Blackstock, D.T. (1998) Nonlinear Acoustics, Academic Press, New York; Morse, P.M. and Ingard, K.U. (1986) Theoretical Acoustics, Ch. 14, Princeton University Press, Princeton.
Kandidov, V.P. (1996) Monte Carlo method in nonlinear statistical optics, Physics-Uspekhi 39, 1243–1272; Yahel, R.Z. (1990) Turbulence effects on high energy laser beam propagation in the atmosphere, Appl. Opt. 29, 3088–3095; Strohbehn, J.W. (ed.) (1978) Laser Beam Propagation in the Atmosphere, Springer-Verlag, Berlin.
De Boer, J.F., Lagendijk, A., Sprik, R., and Feng, S. (1993) Transmission and reflection correlations of second harmonic waves in nonlinear random media, Phys. Rev. Lett. 71, 3947–3950; Yoo, K.M., Lee, S., Takiguchi, Y., and Alfano, R.R. (1989) Search for the effect of weak photon localization in second-harmonic waves generated in a disordered anisotropic nonlinear medium, Opt. Lett. 14, 800–801.
Skipetrov, S.E. and Maynard, R. (2000) Instabilities of waves in nonlinear disordered media, Phys. Rev. Lett. 85, 736–739; Skipetrov, S.E. (2001) Temporal fluctuations of waves in weakly nonlinear disordered media, Phys. Rev. E 63, 056614.
Bressoux, R. and Maynard, R. (2000) On the speckle correlation in nonlinear random media, Europhys. Lett. 50, 460–465; Bressoux, R. and Maynard, R. (2001) Speckle correlations and coherent backscattering in nonlinear random media, in Ref. [10], 445–453.
Skipetrov, S.E. (2003) Langevin description of speckle dynamics in nonlinear disordered media, Phys. Rev. E 67, 016601.
Skipetrov, S.E. (2003) Instability of speckle patterns in random media with nonin-stantaneous Kerr nonlinearity, Opt. Lett., to appear.
Ishimaru, A. (1978) Wave Propagation and Scattering in Random Media, Academic Press, New York.
Shapiro, B. (1999) New type of intensity correlation in random media, Phys. Rev. Lett. 83, 4733–4735; Skipetrov, S.E. and Maynard, R. (2000) Nonuniversal correlations in multiple scattering, Phys. Rev. B 62, 886–891.
Ikeda, K., Daido, H., and Akimoto, O. (1980) Optical turbulence: Chaotic behavior of transmitted light from a ring cavity, Phys. Rev. Lett. 45, 709–712; Nakatsuka, H., Asaka, S., Itoh, H., Ikeda, K., and Matsuoka M. (1983) Observation of bifurcation to chaos in an all-optical bistable system, Phys. Rev. Lett. 50, 109–112.
Silberberg, Y. and Bar Joseph, I. (1982) Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction, Phys. Rev. Lett. 48, 1541–1543; Silberberg, Y. and Bar Joseph, I. (1984) Optical instabilities in a nonlinear Kerr medium, J. Opt. Soc. Am. B 1, 662–670.
Gibbs, H.M. (1985) Optical Bistability: Controlling Light With Light, Academic Press, New York.
Arecchi, F.T., Boccaletti, S., and Ramazza, P. (1999) Pattern formation and competition in nonlinear optics, Phys. Rep. 318, 1–83.
Vorontsov, M.A. and Miller, W.B. (eds.) (1999) Self-Organization in Optical Systems and Applications in Information Technology, Springer Verlag, Berlin.
Soljacic, M., Segev, M., Coskun, T., Christodoulides, D.N., and Vishwanath, A. (2000) Modulation instability of incoherent beams in noninstantaneous nonlinear media, Phys. Rev. Lett. 84, 467–470; Kip, D., Soljacic, M., Segev, M., Eugenieva, E., and Christodoulides, D.N. (2000) Modulation instability and pattern formation in spatially incoherent light beams, Science 290, 495–498; Klinger, J., Martin, H., and Chen, Z. (2001) Experiments on induced modulational instability of an incoherent optical beam, Opt. Lett. 26, 271–273; Chen, Z., Sears, S.M., Martin, H., Christodoulides, D.N., and Segev, M. (2002) Clustering of solitons in weakly correlated wavefronts, Proc. Nat. Acad. Sci. 99, 5223–5227.
Spivak, B. and Zyuzin, A. (2000) Mesoscopic sensitivity of speckles in disordered nonlinear media to changes of the scattering potential, Phys. Rev. Lett. 84, 1970–1973.
Muenster, R., Jarasch, M., Zhuang, X., and Shen, Y.R. (1997) Dye-induced enhancement of optical nonlinearity in liquids and liquid crystals, Phys. Rev. Lett. 78, 42–45.
Kao, M.H., Jester, K.A., Yodh, A.G., and Collings, P.J. (1996) Observation of light diffusion and correlation transport in nematic liquid crystals, Phys. Rev. Lett. 77, 2233–2236.
Wiersma, D.S., Van Albada, M.P., and Lagendijk, A. (1995) An accurate technique to record the angular distribution of backscattered light, Rev. Sci. Inst. 66, 5473–5476.
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Skipetrov, S., Maynard, R. (2003). Diffuse Waves in Nonlinear Disordered Media. In: van Tiggelen, B.A., Skipetrov, S.E. (eds) Wave Scattering in Complex Media: From Theory to Applications. NATO Science Series, vol 107. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0227-1_5
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DOI: https://doi.org/10.1007/978-94-010-0227-1_5
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