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
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
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
Seismic waves in the French Auvergne ric Larose,, Ludovic Margerin,, Michel Campillo et Bart van Tiggelen, RL, July Operator noise Mesoscopic signal Background noise
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
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
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/
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, 999 5 dφ dω dφ dω
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
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) 5 5 5 3 35 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) - - -6-8 t (s) 3 Time (seconds!),, -, (e) π π
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 ) -6 - - 6-6 - - 6, Φ (rad)
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) ]
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
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 = =
robability distribution of SECOND derivative φ " t DAWS Slope - DAWS signal or dynamic noise? Noise is interesting
L 6D atrick Sebbah Azriel Genack M. Berry, J. hys.a., 7 (978).
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
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)
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.?
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