Microwave MesoscopicsMicrowave MesoscopicsSpeckle and Phase Singularity Evolution Speckle and Phase Singularity Evolution

for Diffusive and Localized Wavesfor Diffusive and Localized Waves

Patrick SebbahPatrick SebbahLaboratoire de Physique de la Matière Laboratoire de Physique de la Matière

CondenséeCondenséeCNRS, Université de Nice, FranceCNRS, Université de Nice, France

Collaborators: Collaborators: A.Z. Genack , B. Hu, J. A.Z. Genack , B. Hu, J. Klosner, S. Zhang, Klosner, S. Zhang, Queens College, CUNY, NYQueens College, CUNY, NY

O. Legrand, F. Mortessagne, C. Vanneste, O. Legrand, F. Mortessagne, C. Vanneste, LPMC, LPMC, NiceNice

V. Freilikher, V. Freilikher, Bar Ilan, Israel, Bar Ilan, Israel, K.Yu.K.Yu. Bliokh, Bliokh, IRA, IRA, UkraineUkraine,, Yu.P.Yu.P. Bliokh,Bliokh, Technion, IsraelTechnion, Israel..

Speckle constructionSpeckle construction

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Speckle PatternSpeckle Pattern

Diffusive RegimeDiffusive Regime

<T(L)><T(L)>ℓℓ/L/L

Localized RegimeLocalized Regime

<T(L)><T(L)>exp(-exp(-/L)/L)

Transmission SpectrumTransmission Spectrum

Degree of Spectral Overlap : Degree of Spectral Overlap : = < = <>/<>/<>>

0.000

0.001

0.002

10.20 10.25 10.30 10.35

Localized RegimeLocalized Regime

<1<1

GHz17.2

17.0 17.1Diffusive RegimeDiffusive Regime

Δν

>1>1

GHz

MotivationMotivation

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 ?

Experimental SetupExperimental Setup

~ 1 cm ~ 1 cm ~10GHz~10GHz

Medium:Medium:Polystyrene Spheres Polystyrene Spheres Diam~1cmDiam~1cmn~1.4n~1.4Vol. Fraction 52%Vol. Fraction 52%

Copper Tube Copper Tube L=1 mL=1 mDiam =7.5 cmDiam =7.5 cm

Experimental SetupExperimental Setup

~ 1 cm ~ 1 cm ~10GHz~10GHz

Medium:Medium:Polystyrene Spheres Polystyrene Spheres Diam~1cmDiam~1cmn~1.4n~1.4Vol. Fraction 52%Vol. Fraction 52%

Copper Tube Copper Tube L=1 mL=1 mDiam =7.5 cmDiam =7.5 cm

Experimental SetupExperimental Setup

Experimental SetupExperimental Setup

Speckle FieldSpeckle Field

Intensity

Frequency = 9.508 GHz ( )

X (mm)

Y (m

m)

10 20 30 40 50 60 70

10

20

30

40

50

60

70 +

-

0

Frequency = 9.508 GHz ( )

X (mm)

Y (m

m)

10 20 30 40 50 60 70

10

20

30

40

50

60

70 Max

Min

Phase

Phase SingularitiesPhase Singularities

Speckle in the diffusive regimeSpeckle in the diffusive regime

Frequency = 9.508 GHz ( )

X (mm)

Y (m

m)

10 20 30 40 50 60 70

10

20

30

40

50

60

70 Max

Min

• CI = |CE|2

- Short range correlation- Speckle spots independent- Self averaging pattern

• The field is Gaussian• P(I)= exp (-I)• …

Diffusive vs. LocalizedDiffusive vs. Localized

?Localized Regime

Diffusive Regime

Frequency = 9.508 GHz ( )

X (mm)

Y (m

m)

10 20 30 40 50 60 70

10

20

30

40

50

60

70

Localized Regime

Frequency = 10.454 GHz ( )

X (mm)

Y (m

m)

10 20 30 40 50 60 70

10

20

30

40

50

60

70

Diffusive vs. LocalizedDiffusive vs. Localized

Probability distributions of the magnitude of phase gradient normalized by its ensemble average

Speckle EvolutionSpeckle Evolution

Probability distributions of normalized average displacement of singularities within one

speckle pattern

In ConclusionIn Conclusion

• Fundamental aspects of multiple scattering and Fundamental aspects of multiple scattering and transport through random media reveal transport through random media reveal themselves in some aspects of the speckle field.themselves in some aspects of the speckle field.

• While the statistics of static speckle patterns are While the statistics of static speckle patterns are generic, fluctuations in the change within generic, fluctuations in the change within speckle patterns are greatly enhanced in the speckle patterns are greatly enhanced in the localization regime.localization regime.

• Speckle evolution reflects the interaction with Speckle evolution reflects the interaction with the underlying electromagnetic modes of the the underlying electromagnetic modes of the medium.medium.