Spatio-temporal control of light in complex media

Spatio-temporal control of

light in complex media

SébastienPOPOFF

Directors : M. Fink et C. BoccaraSupervisors : S. Gigan et G. Lerosey

114/12/2011

Introduction

214/12/2011

Imaging in optics

Look smaller

Look furtherWhat are optical systems useful for?

Introduction

3

Imaging in optics

Aberrations

Atmospheric

aberrations

14/12/2011

Introduction

414/12/2011

Real-time correction of aberrations with adaptive opticsCourtesy: F. Lacombe/observatoire de Paris

Wavefront Sensor(ex: Hartmann-Schack)

Wavefront Sensor(ex: Hartmann-Schack)

Wavefront correction(ex: deformable mirror)Wavefront correction

(ex: deformable mirror)

Real-time control loop

Imaging device (CCD)

Imaging device (CCD)

Adaptive optics

Introduction

514/12/2011

AO convenient for wavefront perturbation :

Large spatial scale / small amplitude

Relevant for astronomy, free space optics, some biological applications…

Strong perturbations

What about stronger pertubations?

Multiple scattering, multiple reflections…

Techniques in Acoustics / Electromagnetism

Time reversal

Can we apply them in optics?

Introduction

614/12/2011

Hypothesis : linearity, reversibility of wave equation

Time reversal

Time reversal mirror

Spatial and temporal focusing

One-channel time reversal

Temporal focusing Spatial focusingC. Draeger and M. Fink, Phys. Rev. Lett., 79, 407 (1997)

(Ultrasound experiment)

A. Derode, P. Roux et M. Fink, Phys. Rev. Lett., 75, 4206 (1995)

importance of reflections

Introduction

714/12/2011

Time reversal

Monochromatic counterpart of TR: Phase conjugation

If no access to temporal details

Spatial focusing

Reverse time conjugate the phase

Introduction

814/12/2011

New techniques of light control

Spatial light modulators (SLM)

Deformable mirrors: up to 4000 elements – kHz – expensiveLiquid cristals technology: ~1 million pixels – ~100Hz – cheap

Temporal control:

- Pulse shaping

- Modulators

Acousto-optic modulators (up to GHz)

Electro-optic modulators ( > 10 GHz)

Allow a high degree of control on light propagation!

What about optics?

Outline

914/12/2011

I. Transmission matrix in scattering media

II. Reflection matrix and optical “DORT”

III. Complex envelope time reversal

Transmission matrix in scattering media

Introduction

1014/12/2011

In every day life…

…clouds… …white paint…

…biological tissues !


Scattering: complex but coherent process

11

Simple caseYoung slits:Fringes : Two waves interference

Thick disordered media:Speckle- Multiple events of diffusion- Position of diffuser unknown

14/12/2011


Multiple scattering: too complex

12

>108 particlesImpossible to simulate

100μm

1mm²

White paint(particle size ≤ 1 μm)

Only predictions accessible: Mesoscopic physicsStatistical properties on transport, correlations, fluctuationsNo knowledge of the field for a given realization

14/12/2011


A pioneering experiment

1314/12/2011

A speckle grain:• Interference of a great number of optical paths Sum of terms of random phases (phasors)• Contributions in phase constructive interferences of multiple paths


A pioneering experiment

1414/12/2011


Improve the resolution

λf1/D1

Acoustics: A. Derode, P. Roux and M. Fink , Phys. Rev. Lett., 75, 4206 (1995)Optics: I. M. Vellekoop, A. Lagendijk and A. P. Mosk, Nature Photonics 4, 320 - 322 (2010)

1514/12/2011

λf2/D2


First experiment

1614/12/2011

Remarks:

- 1 optimization = 1 focal spot Need to optimize for each target- Optimization: only indirect information on the medium

Can we go further?


Basic principle

14/12/2011 17

SLM : array of pixels Linear system CCD camera : array of pixels

= ==


Linear media and matrices

inn

nmn

outm EhE

N..1

outE Output field

inE Input field.out inE H E

Ou

tpu

t k

Free space

Identity Matrix

Direct access to information

Input k

Scattering sample

Seemingly Random Matrix

Information shuffled but not lost!O

utp

ut

k

Input k

1814/12/2011


Setup

Objective : Measuring the Transmission MatrixHypothesis : Coherence of the illumination, Stability of the Medium, Linearity

Input ControlSpatial Light Modulator (SLM) in Phase Only Modulationmacropixel ↔ k vector

Output Detection

(Interferometry)1 macropixel ↔ k vector

Sample

ZnO L = 80 ± 25

μm l* = 6 ± 2 μm

14/12/2011 19


Measurement of the Transmission Matrix

1..Nout inm mn n

n

E h E

Step by step reconstruction

Pixel off Pixel on

, , , etc…

In practice, we use Hadamard vectors

φ=+π/2

φ=-π/2

(Phase-only SLM,SNR)

14/12/2011 20

E. Herbert, M. Pernot, G. Montaldo, M. Fink and M. Tanter, IEEE UFFC, 56, 2388, (2009)


Construction of the Transmission Matrix

14/12/2011 21

Transmission matrix (filtered to remove effect of the reference)


Applications: Focusing

What can we do with the TM?Calculate the mask to display!

14/12/2011 22

Plane wave illumination

SL

MS

LM

SL

M

CC

DC

CD

CC

D

sample

sample

sample

Only one measurement of the TM

14/12/2011


Applications: Focusing

* target.out tE H H E* targetin tE H E

N=256 modes (16x16 pixels on the CCD)

N=2

56 *tH H

Strong values in the diagonal We can focus everywhere

Non-diagonal elements not zero Imperfection inherent to PC

23

Which mask to focus?

?Phase conjugated mask

Put contributions in phase on one spot ↔ A. Mosk experiment


14/12/2011 24

Can we go beyond phase conjugation?

Transfer of information (image) Statistical properties of the TM


Statistical properties of the transmission matrix

Tool: Singular Value Decomposition (generalization of diagonalization for any Matrix)

We study the distribution of (normalized) singular values ρ(λ)

1

2

0 0 0

0 0 0

0 0 ... ...

0 0 ... N

--i >0 represents the amplitude transmission through the ith channel.

-Σλi2 corresponds to the total transmittance for a

plane wave

*H U V Output basis

Input basis

14/12/2011 25



Transmission matrix (filtered to remove effect of the

reference)

A general Random Matrix Theory prediction : quarter circle law distribution

14/12/2011 26

Signature of randomnessIn acoustics:A. Aubry et al., Phys. Rev. Lett., 102, 84301, (2009)


Applications: Image transmission

14/12/2011 27

sample

SL

MC

CD

?

Finding Eobj knowing Eout Shaping

TM

. .img out objE O E OH E We want OH close to Identity



What operator to reconstruct a complex image? (knowing the TM)

Inversion : 1O H Perfect reconstructionNot stable in presence of noise

OH I

1

2

0 0 0

0 0 0

0 0 ... ...

0 0 ... N

1

2

1/ 0 0 0

0 1/ 0 0

0 0 ... ...

0 0 ... 1/ N

low λi high 1/λi If noise, H-1 dominated by noise !

14/12/2011 28



Very stableReconstruction perturbated when the image is complex

Phase Conjugation : *tO H*tOH H H

2914/12/2011

What operator to reconstruct a complex image ?N

=100

N=100

*tH H

λi λiH *tH



(Noiseless)0 1O H

Optimal Operator for σ = Noise variance

1* *.t tH H I HO

A tradeoff : Tikhonov Regularization(A.N.Tikhonov, Soviet. Math. Dokl., 1963)

(Noisy) *tO H

14/12/2011 30

Rec

on

stru

ctio

n



Experimental Results :

Input Mask (Eobj)

Inversion

C = 11%

Phase Conjugation

C = 76%

Regularization

C = 95%

Output Speckle (Eout)

14/12/2011 31



3214/12/2011


Conclusion and Perspective

- Focusing and information transfer through complex medium

We did:

- Develop a faster setup (micromirror arrays, ferromagnetic SLMs) for biological purposes

More:

References :- S.M. Popoff, G. Lerosey, R. Carminati, M. Fink, A.C. Boccara and S. Gigan, Phys. Rev. Lett 104, 100601, (2010)- S.M. Popoff, G. Lerosey, M. Fink, A.C. Boccara and S. Gigan, Nat. Commun., 1,1 ncomms1078 (2010)

Related papers :- I.M. Vellekoop and A.P. Mosk, Opt. Lett. 32, 2309 (2007).-Z. Yaqoob, D. Psaltis, M.S. and Feld and C. Yang, Nat. Phot., 2, 110 (2008).

And many many more !

- Study more complex media (Anderson localization, photonic cristals…)

- Studied statistical properties of a scattering medium

14/12/2011 33

From transmission matrix to reflection matrix

3414/12/2011

SLM

Linear sample CCD camera

= ==

CCD camera : array of pixels

3514/12/2011

SLM : array of pixels

Linear sample

From transmission matrix to reflection matrix

Reflection matrix and optical “DORT”

3614/12/2011





Introduction

3714/12/2011

Applications of the RM for multiply scattering media?

Measure of the CBS cone as in acoustics

Optics: M.P.V. Albada and A. Lagendijk, Phys. Rev. Lett., 55,2692 (1985)Acoustics: A; Tourin et al, Phys. Rev. Lett., 79, 3637, (1997)

A. Aubry et al., Phys. Rev. Lett., 102, 84301, (2009) Problem:Measurement in optics: noise, specular reflections…

Application in freespace / aberrating medium (simple scattering):The DORT method in optics (suggested by A. Aubry)


Introduction

3814/12/2011

0KE

* *0KK E

*0KK KE

* *0K E

0E

*0K KE

Itera

tive

time

reve

rsal


Introduction

3914/12/2011

1

2

0 0 0

0 0 0

0 0 ... ...

0 0 ... N

21 0 0 0

2 0 0 0 0

0 0 ... ...

0 0 ... 0

n

n

2 *0

nn tE K K E

2 2 21 2 ...n n n

N

*K U V Output basis

Input basis

22 *0

nnE U V E

At step n:

SVD of K:


Introduction

4014/12/2011

1 strong singular value ↔ 1 scatterer ? DORT: - Mesure of the RM- SVD of the RM- Display the first singular vectors


Introduction

4114/12/2011

Works with an aberrating medium(single scattering only)

Hypothesis: linearity, single scattering regime


Setup

Control

Aberrating medium

Scatterers:100 nm isotropic gold particles on a glass slide

Cross Polarization

14/12/2011 42


Problems

4314/12/2011

The energy measured should only come from the scatterers

Problem:- Important contributions of specular reflections !

Solutions:- Cross polarization - (Dark field)

x

y

k

inP

x

y

k

outP

Focal planeAberating

medium

100 nm gold beads


Selective Focusing

14/12/2011 44

Reflection

Control


Setup

Aberrating medium

Scatterers:100 nm isotropic gold particles on a glass slide

Cross Polarization

14/12/2011 45


Adaptive optics

4614/12/2011

Aspect of the first input singular vector (phase mask)

Free space ~ lens With aberrating mediums

y component of the output field


Modes of a single particles

Particle ~ 3 orthogonal dipoles

14/12/2011 47

Need for sufficient NA to excite the dipoles with one input polarization


Modes of a single particleN

um

be

r o

f S

V

-

(vector diffraction theory)

Pz Dipole Px Dipole

Py Dipole

Theoretical singular value distribution

14/12/2011 48


Modes of a single particle

14/12/2011 49


Modes of a single particleN

um

be

r o

f S

V

-

Pz Dipole

Px Dipole

Py Dipole

Experimental singular value distribution

? Pz dipole Px dipole

14/12/2011 50


Conclusions and Perspectives

- Selective focusing through aberrating medium

We did:

- Reduce specular reflections (dark field)

More:

References :- S.M. Popoff, A. Aubry ,G. Lerosey, M. Fink, A.C. Boccara and S. Gigan, Phys. Rev. Lett. (in press)

- Develop a setup more stable (laser) Pattern analysis for characterization, plasmonic, …

- Radiation pattern analysis of a single nanobead

14/12/2011 51

Complex envelope time reversal

5214/12/2011





5314/12/2011

Spatio-temporal focusing in complex media

J. Aulbach et al., Phys. Rev. Lett., 106,103901 (2011)

O. Katz et al., Nat. Photonics, 5, 372, (2011)

With spatial degrees of freedom

D. McCabe et al., Nat Commun., 2, 447, (2011)

With temporal degrees of freedom (pulse shaping)


5414/12/2011

Modulation for telecommunications

When only low frequencies accessible Modulation (Telecomunications)

=Detector

Use high frequency waves with ‘low’ frequency generator / oscilloscope

Independent modulation in phase and quadrature (IQ)

Modulators and demodulators widely available for telecommunications ($$$)

x

Propagation

Carrier wave Signal

Lower bandwidth but very high spectral resolution


5514/12/2011

Time reversal

TR = reverse modulation + conjugate carrier wave

G. Lerosey et al., Phys. Rel. Lett., 92, 193904 (2004)


( ) ( ). j tABh t E t e

-t( ) ( ). j tABh t E t e

Pulse in modulation at A (on one quadrature)

Time (μs)

Signal received at A after time reversal

Time (μs)


5614/12/2011

Setup

Setup

Modulation Part:- 10 GHz arbitrary waveform generator- Triple Mach-Zehnder modulator

Demodulation Part:- Interferometric detection of 2 quadratures- 50 GHz oscilloscope


5714/12/2011

Modulation / Demodulation

Demodulation Part:- Interferometric detection of 2 quadratures- 20 GHz oscilloscope

Modulation Part:- 10 GHz arbitrary waveform generator- Triple Mach-Zehnder modulator (Photline)

A

B


5814/12/2011

Bandwidth vs medium’s correlation frequency

Lifetime in system need to be >> 1/Δf modulation

G. Lerosey et al., Phys. Rev. Lett., 92, 193904 (2004)

Electromagnetism experiment:Huge cavity needed ( > 13m3) Huge number of modes (λ2.45GHz = 12cm )

Same problem in opticsNeed for strong dispersion / strong enough signal

Impulse response B

Time (μs)


5914/12/2011

Temporal focusing

input output

Evanescent coupling

Looped single mode cavity

Impulseresponse

Channel I Channel Q

Numerical time reversal(correlations)


6014/12/2011

Temporal focusing

Numericaltime reversal(correlations)

Experimental time reversal

Channel I Channel Q

Demonstration of the compression of the impulse response by time reversal

Application : fiber optics telecommunication


6114/12/2011

Towards spatio-temporal focusing

Problems : Weak signals / Need for very strong dispersion

Multimode fiber cavity

Still in progress!

Chaotic3D cavity

input output

Scattering medium

Conclusion

6214/12/2011

I. Transmission matrix in scattering media- Spatial focusing

- Image transmission

- Singular value analysis

II. Reflection matrix and optical “DORT”- Selective focusing through an aberrating medium

- Scattering pattern analysis

III. Complex envelope time reversal- Temporal focusing

- Towards spatial and temporal focusing...

6314/12/2011

Remerciements :

Collaborateurs :Sylvain GiganGeoffroy LeroseyAlexandre AubryRemi CarminatiMathias FinkClaude Boccara

Préparation échantillons :Laurent BoitardGilles TessierBenoit MalherOlivier Loison

Aide au montage :Aurélien PeillouxSébastien BidaultThéorie :

Samuel Grésillon Caractérisation des échantillons :Matthieu LeclercSupport divers :

Marie Lattelais

Collaborateurs

6414/12/2011

Sylvain GIGAN

Geoffroy LEROSEY

Mathias FINK

ClaudeBOCCARA

Rémi CARMINATI

AlexandreAUBRY



Artefact :« raster » effect

due to the amplitude of Sref

Observed Matrix

.obs refH H

Effect of ref

14/12/2011 65


Setup

Objective : Measuring the Transmission MatrixHypothesis : Coherence of the illumination, Stability of the Medium, Linearity

Input ControlSpatial Light Modulator (SLM) in Phase Only ModulationA macropixel ↔ A k vector

Output Detection

CCD CameraA macropixel ↔ A k vector

Sample

ZnO L =

80 ± 25 μm l* = 6 ± 2

μm

14/12/2011 66

Matrice de Transmission Optique d’un Milieu Diffusant

Applications : Transmission d’Image

6714/12/2011

Efficacité de la reconstruction en fonction de σ

σ

Filtrage inverse Filtrage adapté

14/12/2011

Matrice de Transmission et Milieu Diffusant

Propriétés Statistiques de la Matrice de Transmission

Filtrage de Hobs pour éliminer les effets de la référence

obsfil mnmn obs

mnm

hh

h

Matrice FiltréeMatrice Observée

Une prédiction générale des matrices aléatoires : “Loi du quart de cercle”

68


Applications : Focusing

Expected focusing from measured matrix

Experimental focusing

Target

Theoretical focusing VS Experimental focusing

6914/12/2011


Stability and Measurement Time

TM Measurement Time (1024x1024 )

~ 15 min

Decorrelation Time of ZnO deposit

~ 1 hour

Decorrelation Time of Biological Tissues << 1s

14/12/2011 70


Introduction

7114/12/2011

The reflection matrix

nE

outE Output field

inE Input field

.out inE K E

1..Nout inm mn n

n

E k E

n

mmn nk E

Signal received at A

Optical time reversal in modulation

7214/12/2011

Time reversal

Time reversal in modulation



A

B

Signal received at B




The matrix model : A conveniant model

Free space Multiply scattering sample

Matrix Description to link input / output k vectors

Detrimental to Conventional Optical Techniques

7314/12/2011


Measuring the Complex Output Field

uniform

2

outout EI

2

refi

out EeEI

refE

3 1

2 20 ioutE I I i I e I

3 1

2 20

*.

i

out ref

I I i I e I

E E

No phase information !

Interferometric stability for several minutes !

not uniformrefE

OK as long as ….. …. is constantrefE

14/12/2011 74

Transmission Matrix of an Optical Scattering Medium

Theoretical Focus Spot

λf1/D1

I. M. Vellekoop, A. Lagendijk & A. P. Mosk, Nature Photonics 4, 320 - 322 (2010)

7514/12/2011

λf2/D2

Transmission Matrix of an Optical Scattering Medium

Theoretical Focus Spot

λF/D

F

D λl/LSLM

l

L

7614/12/2011

A

B

Signal received at A


7714/12/2011

Time reversal

Time reversal in modulation in a reverberant cavity



Signal received at B




Linear media and matrices

Ou

tpu

t k

Free space

Identity Matrix

Direct access to information

Input k

Scattering sample

Seemingly Random Matrix

Information shuffled but not lost !O

utp

ut

kInput k

inn

nmn

outm EhE

N..1

outE Output field

inE Input field.out inE H E

7814/12/2011

Technology

Spatio-temporal control of light in complex media