Skip to main content Accessibility help
×
Home

Electromagnetic Waves Through Disordered Systems: Comparison of Intensity, Transmission and Conductance

  • Fredy R Zypman (a1) and Gabriel Cwilich (a1)

Abstract

We obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU (x) = xne−xμ . This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.

Copyright

References

Hide All
1 Rayleigh, J. W. Strutt Lord, Phil. Mag. 47, 375 (1899)
2 Chandrasekhar, S., “Radiative Transfer”, Dover publishing, New York (1960)
3 Anderson, P. W., Phys. Rev. 109, 1492, (1958)
4 Abrahams, E., Anderson, P.W., Licciardello, D. C., Ramakrishnan, T.V., Phys. Rev. Lett. 42, 673 (1979)
5 Stephen, M., Phys. Rev. Lett. 56,18091810 (1986)
6 Albada, M. P. van, Lagendijk, A., Phys. Rev. Lett. 55, 26922695 (1985)
7 Lee, P.A., in STATPHYS 16, (Stanley, H. E., ed.), North Holland, Amsterdam, 169–174 (1986).
8 Cwilich, G. and Fu, Y., Phys. Rev. B46, 1201512018 (1992)
9 Albada, M. P. van, Tiggelen, B.A. van, Lagendijk, Ad, Tip, Adriaan, Phys. Rev. Lett. 66, 31323135 (1991)
10 Stone, A.D., Phys. Rev. Lett. 54, 26922695 (1985)
11 Webb, R.A., Washburn, S., Umbach, C.P., and Laibowitz, R.B., Phys. Rev. Lett. 54, 26962699 (1985).
12 Garcia, N., Genack, A. Z., Phys. Rev. Lett. 63,16781681 (1989)
13 Soukulis, C., in Diffuse Waves in Complex Media (Fouque, J. P. ed.), Kluwer, 93107 (1998).
14 Yablonovitch, E., Leung, K.M., Nature 401, 539 (1999)
15 Fink, Mathias, Physics Today 50, 34 (1997)
16 Campillo, M., Margerin, L. and Shapiro, N.M., in Diffuse Waves in Complex Media, (Fouque, J.P. ed.) Kluwer, 383404 (1999)
17 Beenakker, C.W.J., Phys. Rev. Lett. 81, 18291832 (1998)
18 Wiersma, D.S., Albada, M.P. van, Lagendijk, A., Nature 373, 203204 (1995).
19 Wang, L., Appl. Optics 32, 5043 (1993) L. Wang, P.P. Ho, C. Liu, Science 253, 769 (1991)
20 Kaiser, R., in Diffuse Waves in Complex Media, (Fouque, J.P. ed.), 249288, Kluwer (1999)
21 Wiersma, D.S., Bartolini, P., Lagendijk, Ad, Righini, R., Nature 390, 671673 (1997)
22 Kogan, E., Kaveh, M., Phys. Rev. B52, R3813–R3815 (1995); Kogan, E., Baumgartner, R. and Berkovits, R., Physica A200, 469 (1993); Kogan, M. Kaveh, R. Baumgartner, R. Berkovits, Phys. Rev. B48, 9404-9410 (1993)
23 Cwilich, G., in OSA Proc. on Adv. in Opt. Imaging and Photon Migration (Alfano, R., ed.), 21 (1994)
24 Stoytchev, M., Genack, A.Z., Phys. Rev. Lett. 79, 309 (1997)
25 Sebbah, P., Legrand, O., Tiggelen, B. A. van, and Genack, A. Z., Phys. Rev. E56, 36193623 (1997)
26 Chabanov, A.A., Stoychev, M. and Genack, A.Z., Nature 404, 850853 (2000); M. Stoytchev, A.Z. Genack, Opt. Lett. 24, 262 (1999)
27The properly normalized distribution is given by where Γ(x) stands for the Gamma function.
28 Cwilich, Gabriel, Zypman, Fredy R, “Transmittance quantities probability distributions of waves through disordered systems”, in Advances in Materials Theory and Modeling--Bridging Over Multiple-Length and Time Scales, Editors Vasily Bulatov, Fabrizio Cleri, Luciano Colombo, Laurent Lewis, Normand Mousseau, p 6671 (2001)
29Suggested by Genak, A.Z., private communication.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed