1. Microwave Mesoscopics Speckle and Phase Singularity Evolution for Diffusive and Localized Waves Patrick Sebbah Laboratoire de Physique de la Matière Condensée CNRS, Université de Nice, France Collaborators: A.Z. Genack, B. Hu, J. Klosner, S. Zhang, Queens College, CUNY, NY O. Legrand, F. Mortessagne, C. Vanneste, LPMC, Nice V. Freilikher, Bar Ilan, Israel, K.Yu. Bliokh, IRA, Ukraine, Yu.P. Bliokh, Technion, Israel.

2. Speckle construction   Re{E} Im{E} 

3. Speckle Pattern

4. Diffusive Regime  ℓ/ L  ℓ/ L

5. Localized Regime  exp(-  /L)  exp(-  /L)

6. Transmission Spectrum Degree of Spectral Overlap :  = / Degree of Spectral Overlap :  = /   Localized Regime  <1 GHz 17.2 17.017.1 Diffusive Regime ΔνΔν   >1 GHz

7. Motivation The statistics of the speckle pattern and its evolution are universal ? or rather They may reflect the changing character of radiation at the Anderson transition ?

8. Experimental Setup ~ 1 cm ~10GHz ~ 1 cm ~10GHzMedium: Polystyrene Spheres Diam~1cmn~1.4 Vol. Fraction 52% Copper Tube L=1 m Diam =7.5 cm

9. Experimental Setup ~ 1 cm ~10GHz ~ 1 cm ~10GHzMedium: Polystyrene Spheres Diam~1cmn~1.4 Vol. Fraction 52% Copper Tube L=1 m Diam =7.5 cm

10. Experimental Setup

12. Speckle Field Intensity Phase

14. Phase Singularities

15. Speckle in the diffusive regime C I = |C E | 2 - Short range correlation - Speckle spots independent - Self averaging pattern The field is Gaussian P(I)= exp (-I) …

16. Diffusive vs. Localized ? Localized Regime Diffusive Regime Localized Regime

17. Diffusive vs. Localized Probability distributions of the magnitude of phase gradient normalized by its ensemble average

18. Speckle Evolution

19. Probability distributions of normalized average displacement of singularities within one speckle pattern

20. In Conclusion Fundamental aspects of multiple scattering and transport through random media reveal themselves in some aspects of the speckle field. Fundamental aspects of multiple scattering and transport through random media reveal themselves in some aspects of the speckle field. While the statistics of static speckle patterns are generic, fluctuations in the change within speckle patterns are greatly enhanced in the localization regime.While the statistics of static speckle patterns are generic, fluctuations in the change within speckle patterns are greatly enhanced in the localization regime. Speckle evolution reflects the interaction with the underlying electromagnetic modes of the medium.Speckle evolution reflects the interaction with the underlying electromagnetic modes of the medium.