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Transmittance Quantities Probability Distributions of Waves through Disordered Systems

Published online by Cambridge University Press:  21 March 2011

Gabriel Cwilich  and
Fredy R Zypman
Gabriel Cwilich
Affiliation:
Yeshiva University, Department of Physics, New York, NY 10033-3201
Fredy R Zypman
Affiliation:
Yeshiva University, Department of Physics, New York, NY 10033-3201
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Abstract

Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a dependence on the length L of the sample that is characteristic of the regime. For example, I decays as L−1 in the diffusive regime. It is of current interest to characterize the transport regime of a wave, from statistical studies of the transmittance quantities through it. Studies suggest that the probability distribution of the intensity could be used to characterize the localized regime. There is an ongoing debate on what deviations from the classical Rayleigh distribution are to be expected. In this numerical work, we use scalar waves to obtain the intensity, transmission, and conductance of waves through a disordered system. We calculate the intensity, by setting an incoming plane wave towards the sample from a fixed direction. The outgoing intensity is then calculated at one point in space. This process is repeated for a collection of samples belonging to the same ensemble that characterizes the disorder, and we construct the probability distribution of the intensity. In the case of transmission, we evaluate the field arriving to a series of points distributed in the far field, and repeat the same statistical analysis. For the conductance, we calculate the field at the same series of points for incoming waves in different directions. We analyze the distribution of the transmittance quantities and their change with the degree of disorder.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 677: Symposium AA – Advances in Materials Theory and Modeling–Bridging Over Multiple-Length and Time Scales , 2001 , AA4.5
Copyright
Copyright © Materials Research Society 2001

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References

REFERENCES

1 Genack, A.Z., Phys. Rev. Lett. 58, 2043–2046 (1987)Google Scholar
2 Strutt, J. W. (Lord Rayleigh), Phil. Mag. 47, 375 (1899)Google Scholar
3 Chandrasekhar, S., “Radiative Transfer”, Dover publishing, New York (1960)Google Scholar
4. Anderson, P. W., Phys. Rev. 109, 1492, (1958)Google Scholar
5 Abrahams, E., Anderson, P.W., Licciardello, D. C., Ramakrishnan, T.V., Phys. Rev. Lett. 42, 673 (1979)Google Scholar
6 Stephen, M., Phys. Rev. Lett. 56, 1809–1810 (1986)Google Scholar
7 Albada, M. P. van, Lagendijk, A., Phys. Rev. Lett. 55, 2692–2695 (1985)Google Scholar
8 Lee, P.A., in STATPHYS 16, (Stanley, H.E., ed.), North Holland, Amsterdam, 169–174 (1986).Google Scholar
9 Cwilich, G. and Fu, Y., Phys. Rev. B46, 12015–12018 (1992)Google Scholar
10 Albada, M. P. van, Tiggelen, B.A. van, Lagendijk, Ad, Tip, Adriaan, Phys. Rev. Lett. 66, 3132–3135 (1991)Google Scholar
11 Stone, A.D., Phys. Rev. Lett. 54, 2692–2695 (1985)Google Scholar
12 Webb, R.A., Washburn, S., Umbach, C.P., and Laibowitz, R.B., Phys. Rev. Lett. 54, 2696–2699 (1985).Google Scholar
13 Garcia, N., Genack, A. Z., Phys. Rev. Lett. 63, 1678–1681 (1989)Google Scholar
14 Soukulis, C., in Diffuse Waves in Complex Media (Fouque, J. P. ed.), Kluwer, 93–107 (1998).Google Scholar
15 Yablonovitch, E., Leung, K.M., Nature 401, 539 (1999)Google Scholar
16 Mathias Fink, Physics Today 50, 34 (1997)Google Scholar
17 Campillo, M., Margerin, L. and Shapiro, N.M., in Diffuse Waves in Complex Media, (Fouque, J.P. ed.) Kluwer, 383–404 (1999)Google Scholar
18. Beenakker, C.W.J., Phys. Rev. Lett. 81, 1829–1832 (1998)Google Scholar
19 Wiersma, D.S., Albada, M.P. van, Lagendijk, A., Nature 373, 203–204 (1995).Google Scholar
20 Wang, L., Appl. Optics 32, 5043 (1993) L. Wang, P.P. Ho, C. Liu, Science 253, 769 (1991)Google Scholar
21 Kaiser, R., in Diffuse Waves in Complex Media, (Fouque, J.P. ed.), 249–288, Kluwer (1999)Google Scholar
22 Wiersma, D.S., Bartolini, P., Lagendijk, Ad, Righini, R., Nature 390, 671–673 (1997)Google Scholar
23 Kogan, E., Kaveh, M., Phys. Rev. B52, R3813–R3815 (1995); E. Kogan, R. Baumgartner and R. Berkovits, Physica A200, 469 (1993); Kogan, M. Kaveh, R. Baumgartner, R. Berkovits, Phys. Rev. B48, 9404-9410 (1993)Google Scholar
24 Cwilich, G., in OSA Proc. on Adv. in Opt. Imaging and Photon Migration (Alfano, R., ed.), 21 (1994)Google Scholar
25 Stoytchev, M., Genack, A.Z., Phys. Rev. Lett. 79, 309 (1997)Google Scholar
26 Sebbah, P., Legrand, O., Tiggelen, B. A. van, and Genack, A. Z., Phys. Rev. E56, 3619–3623 (1997)Google Scholar
27 Chabanov, A.A., Stoychev, M. and Genack, A.Z., Nature 404, 850–853 (2000); M. Stoytchev, A.Z. Genack, Opt. Lett. 24, 262 (1999)Google Scholar
28 Kogan, E., Kaveh, M., Phys. Rev. B22, 16400 (1995)Google Scholar