Bart van Tiggelen Laboratoire de Physique et Modélisation des Milieux Condensés CNRS/University

Transcription

1 Dynamic correlations, interference and time-dependent speckles Bart van Tiggelen Laboratoire de hysique et Modélisation des Milieux Condensés CNRS/University of Grenoble, France Collaborators: Michel Campillo (LGIT-Grenoble) Grenoble) Ludovic Margerin (LGIT-Grenoble) Geert Rikken (LCM-Toulouse) atrick Sebbah (LMC-Nice) Sergey Skipetrov (LMMC Grenoble) hd: Eric Larose (LGIT) John age (Winnipeg, Canada) Michael Cowan (Toronto, Canada) Azriel Genack (Queens College,, NY) Support: GDR RIMA & IMCODE (CNRS), Ministère de la Recherche (ACI jeune chercheur), NSF (USA),( ESA

2 abstract Coherent Backscattering with Seismic Waves Eric Larose,, Ludovic Margerin,, Michel Campillo, BavT hase Statistics John age, Micheal Cowan, BAvT, Azriel Genack,, atrick Sebbah The Feigel process Geert Rikken, BavT

3 receiver source Free surface. Distance source receiver < wavelength. Symmetry source = symmetry receiver & magnitude measure y CBS( r) u Earth quake x x u y J π r λ x measure div u Explosion e t/τ magnitude measure u z Sledge hammer

4 Seismic waves in the French Auvergne ric Larose,, Ludovic Margerin,, Michel Campillo et Bart van Tiggelen, RL, July Operator noise Mesoscopic signal Background noise

5 oherent Backscattering in the French Auvergne 5 Hz λ Mean free time=.7 seconds Wavelength= = meter c Rayleigh = 3 m/s Mean free path = m

6 ImΨ Ψ Ψ = Ψ Ψ Ψ3... ReΨ probability distribution exp π detc ( ) ( * Ψ Ψ Ψ = ) *,... Ψ C Ψ C <Ψ Ψ >, N N ij i j diffusion equation

7 Ψ = Gaussian Speckles I e iφ intensity phase. Stationary: : Distribution of speckle intensity ( I ) =, φ exp( I/ < > ) < I> I. Dynamics :Distribution of «Wigner delay» time Ω Ω ( * Ψ C Ω Ψ) Ψ Ψ = ω, ω exp ( ) π det C dφ = φ ' dω = Q Q dφ dω ( ˆ' φ ) 3/

8 Speckles of Micro-waves in Quasi D media Distribution of delay time in transmission L 6D dφ = φ ' dω = Q Q ( ˆ' φ ) diffusion equation : Q = 3/ Genack, Sebbah, Stoytchev & Van Tiggelen RL, dφ dω dφ dω

9 Diffuse Acoustic Wave Spectroscopy ψ t, τ) ( τ ψ t, τ) ( ψ ( t, τ ), ψ( t, τ ) ψ( t) = g( τ) = exp ( ( ) ) k n r τ 6 ct n= l* g( τ ) exp τ 6 t D AWS

10 Diffuse Acoustic wave Spectroscopy John age, Dave Weitz, Michael Cowan amplitude Wrapped phase unwrapped phase l* =.5mm; τ* = µs NORMALIZED FIELD AM -, HASE (rad),, - INUT (a) TRANSIT TIME (µs) FIELD 7,5 8, 8,5 (c) t s AMLITUDE 7,5 8, 8,5 (d) TRANSIT TIME (µs) TRANSMITTED (b) HASE 7,5 8, 8,5, (f), - (g) (h) t (s) 3 Time (seconds!),, -, (e) π π

11 robability distribution ( Φ) ( ) for phase shift Φ τ after time τ, (a) τ = ms (c) τ = 3 ms, dφ dτ = Q Q = 6t DAWS Q dφ dτ 3/ ( Φ), E-3, (b) τ = ms (d) τ = s,,5, t DAWS =ms,,5 π ( φ ) = ( π φ ) , Φ (rad)

12 robability distribution of SECOND derivative [ ψ t ), ψ( t ), ψ( t ), ψ( )] ( 3 t [ ] φ ) φ( ), φ '( ), φ '( ) ( t t t t t t da da t 3 da t 3 da dφ φ( t ) = φ φ' t φ" φ ''' t 6 ( t) ( ) 3? [ φ '( t), φ "( t), φ '''( t) ]

13 robability distribution of SECOND derivative φ( t ) = φ ± t [ ψ t ), ψ( t ), ψ( t ), ψ( )] ( 3 t [ ] φ ) φ( ), φ '( ), φ '( ) ( t t t t φ' t φ "( ) t t da da t 3 da t 3 da dφ [ ] φ '( t), φ "( t), φ " ( t) hase is not an analytic function

14 robability robability distribution of distribution of SECOND SECOND derivative derivative [ ] ( ) ( ) 3/ " ) ( " = R x x R x dx φ π φ [ ] ( ) 3/ " " " " = T T φ φ φ φ ( ) ( ) () () "() () 3 "() () g g T g g R = =

15 robability distribution of SECOND derivative φ " t DAWS Slope - DAWS signal or dynamic noise? Noise is interesting

16 L 6D atrick Sebbah Azriel Genack M. Berry, J. hys.a., 7 (978).

17 theorem dl φ( r) = πq Q= q i zero i - - θ Q = - R Q = dφ θ dφ π dθ dθ ( ) π circle d θ θ

18 dimensions 3 dimensions Q Count the mean free path? = dφ θ dφ π dθ dθ ( ) π circle d θ θ [ ( r ), ψ( r ), ψ( r3 ), ψ( r )] ψ ψ ( rψ ) *( r') = J( k r)exp( r/l)

19 The Feigel process: Momentum from nothing?. Feigel,, hys. Rev.. Lett. 9,, () avt & G. Rikken,, RL Comment bi-anisotropic media: D H = ε = B E χ χ E B ħω E = ρvv hω 3 π c B c kl ρ vn = ( ε ) ε E 3 nklχ hωc B Lorentz invariance? divergence.?

20 The Feigel process: Momentum from nothing? L ħω E d = ρvv B BAvT & G. Rikken En préparation ρ v 3 π = L hc χ E B 3 L πd πd sin L 3 πd cos L