Microwave Mesoscopics Speckle and Phase Singularity Evolution for Diffusive and Localized Waves
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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
ieA
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Re{E}
Im{E}
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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.