1. A.A. Chabanov, Abe Pena (UT-San Antonio) Jing Wang, A.Z. Genack (Queens College of CUNY) Speckle Fluctuations and Correlation

2. Speckles

3. Wave propagation in disordered media mean free path wavelength Field Intensity

4. Average intensity: Gaussian statistics: only the pairs of identical paths have the same phase and thus give a contribution to the average intensity Wave diffusion in a disordered medium wavelength mean free path

5. Diffusion equation for the average intensity: Wave diffusion in a disordered medium (This equation would yield the Ohm’s law for a disordered conductor)

6. Wave interference A A*A* Probability of return: waveparticle transport reduction nonlocal correlation weak localization non-Gaussian statistics

7. Transmission coefficients a′a′ b Transmitted intensity = speckle intensity Total transmission = brightness Transmittance = conductance a b′b′

8. Transmission coefficients i.e., Beenakker, RMP (1997)

9. Statistics of t ab and T ab Kogan & Kaveh, PRB (1995) AAC & Genack, PRA (2005)

10. Alumina sample d=0.9 cm n=3.14 f=0.068 alumina sphere: copper tube: D=7.3 cm

11. L=60 cm, 10,000 sample configurations A: ν =14.7-15.7 GHz, var( s ab )=1.18, diffusive wave B: ν =9.95-10.15 GHz, var( s ab )=6.18, localized wave C: t=740 ns, var[ s ab (t)]=20.1, strongly localized wave Transmission in alumina samples Frequency (GHz) time (ns) ABC σ = 5 MHz

12. Transmitted field distribution Gaussian statistics:

13. Characteristic and distribution functions of total transmission Nieuwenhuizen & vanRossen (1995) Stoytchev & Genack (1999)

14. Factorizing of statistics of the field and intensity Fluctuations: Correlations:

15. Correlation with polarization AAC, Hu & Genack (2004)

16. Statistics of total transmission In localized regime (only one open channel):

17. Statistics of transmission quantities in localized regime Pnini (2001)

18. Correlation with wave polarization

19. Intensity correlation of localized waves

21. In a given random configuration, the statistics of transmitted field is Gaussian for both diffusive and localized waves; non- Gaussian mesoscopic field statistics arise in ensemble of configurations due to mesoscopic fluctuations of transmission In localized regime, the transmitted intensity can be written as a product of three statistically independent variables; two of them have Rayleigh distribution Future work: Conclusions In diffusive regime (many channels): ?