A.A. Chabanov, Abe Pena (UT-San Antonio) Jing Wang, A.Z. Genack (Queens College of CUNY) Speckle Fluctuations and Correlation
Speckles
Wave propagation in disordered media mean free path wavelength Field Intensity
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
Diffusion equation for the average intensity: Wave diffusion in a disordered medium (This equation would yield the Ohm’s law for a disordered conductor)
Wave interference A A*A* Probability of return: waveparticle transport reduction nonlocal correlation weak localization non-Gaussian statistics
Transmission coefficients a′a′ b Transmitted intensity = speckle intensity Total transmission = brightness Transmittance = conductance a b′b′
Transmission coefficients i.e., Beenakker, RMP (1997)
Statistics of t ab and T ab Kogan & Kaveh, PRB (1995) AAC & Genack, PRA (2005)
Alumina sample d=0.9 cm n=3.14 f=0.068 alumina sphere: copper tube: D=7.3 cm
L=60 cm, 10,000 sample configurations A: ν = GHz, var( s ab )=1.18, diffusive wave B: ν = 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
Transmitted field distribution Gaussian statistics:
Characteristic and distribution functions of total transmission Nieuwenhuizen & vanRossen (1995) Stoytchev & Genack (1999)
Factorizing of statistics of the field and intensity Fluctuations: Correlations:
Correlation with polarization AAC, Hu & Genack (2004)
Statistics of total transmission In localized regime (only one open channel):
Statistics of transmission quantities in localized regime Pnini (2001)
Correlation with wave polarization
Intensity correlation of localized waves
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): ?