S L I D E 1

Coherent control of the total transmission of light through disordered media

Effect of the open geometry and the mesoscopic correlations

S. M. Popoff, A. Goetschy, S. F. Liew, A. D. Stone, H. Cao

S L I D E 2

People

Experimetal part Theoretical part

Seng-Fatt Liew

Pr. Hui Cao

Arthur Goetschy

Pr. Douglas Stone

S L I D E 3

Transmission in random scattering media

Why is white paint opaque?

R

T

𝐿

S L I D E 4

Transmission in random scattering media

Why is white paint opaque?

𝑇 ∝𝑙

𝐿

R

T

Can we modify the transmission?

𝐿

S L I D E 5

Transmission in random scattering media

Theoretical predictions

Bimodal distribution

p(T)

T

O.N. Dorokhov Solid State Commun. 1984 P.A. Mello et al. Ann. Phys. 1988

Y. Nazarov PRL 1994

N N

∞ ∞

𝜌(𝑇) ∝𝑇

𝑇 1 − 𝑇

𝑇𝑚𝑎𝑥

𝑇=

1

𝑇

𝑇𝑚𝑖𝑛 ≪ 1 𝑇𝑚𝑎𝑥 = 1

Mesoscopic correlations!

S L I D E 6

Motivations

Experimental measure of the TM

Acoustics: A. Aubry et al. PRL 2009 Optics: S.M. Popoff et al. PRL 2010

Quarter circle law

?

Remaining effects of mesoscopic correlations?

𝑇𝑚𝑎𝑥

𝑇= (1 + 𝛾)2< 4 𝛾 =

𝑁𝑖𝑛𝑁𝑜𝑢𝑡

𝑇𝑚𝑎𝑥

𝑇> (1 + 𝛾)2

S L I D E 7

Control of the total transmission

Goals:

• Control the input optical field on a scattering sample with a high degree of control (two polarizations phase modulation, high NA, large illumination area) to take advantage of mesoscopic correlations to maximize/minimize the total transmission.

• Understand the effect of mesoscopic correlations on the total transmission in an open geometry with a localized illumination.

Previous studies: • I.M. Vellekoop and A.P. Mosk, PRL, 2008 • M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.H. Park and W. Choi, Nat. Photon., 2012

S L I D E 8

Experimental setup

Ir

It

Ii

Ii: input intensity Ir: backscattered intensity It: total transmitted intensity

• High input NA, output NA~1 • 2 polarizations phase modulation

• Large number of segments (up to ~2000) • Control of input and backscattered intensity

S L I D E 9

Typical results

𝐿~20 𝜇𝑚 𝑙~0.8 𝜇𝑚 𝐷~8.3 𝜇𝑚 𝑇𝑚𝑎𝑥 = 3.56 𝑇 ~18% 𝑇𝑚𝑖𝑛 = 0.32 𝑇 ~1.6% 𝑇𝑚𝑎𝑥

𝑇𝑚𝑖𝑛 ~𝟏𝟏. 𝟏

~10 fold variation of the total transmission

Uncorrelated model gives 𝑇𝑚𝑎𝑥~ 1.6 𝑇 , 𝑇𝑚𝑖𝑛~0.5 𝑇 , 𝑇𝑚𝑎𝑥

𝑇𝑚𝑖𝑛~𝟑. 𝟐

Effect of correlations but no open channels because of imperfect control

S L I D E 10

Effect of the correlations

5 samples with thickness L between ~ 7 μm and 30 μm 7 illumination sizes D between ~ 2.7 μm and 8.3 μm Comparison with uncorrelated model (Marcenko Pastur)

1

2

3

10 15 20 25 30 35

4

1

2

3

3 4 5 6 7 8

S L I D E 11

Predictions of Tmax and effect of the geometry

𝑇𝑚𝑎𝑥 = 1 𝑇𝑚𝑎𝑥 =?

Effect of imperfect channel control known A. Goetschy and A. D. Stone, PRL, 2013

S L I D E 12

Theory of imperfect control of channels (1)

A. Goetschy and A. D. Stone, PRL, 2013

𝑚1 =𝑀1

𝑁≤ 1

𝑚2 =𝑀2

𝑁≤ 1

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Theory of imperfect control of channels (2)

We showed and verified in simulation that this theory is true also for open geometries for m2=1 with the general definition of m1:

Implies a long range correlation term (C2) and depends on shape of the illumination beam

𝑡

𝑡

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Theory vs experiments and simulations (1)

2D

• Good agreement with simulations (recursive Green’s function) • Effect of the algorithm + phase only; 𝑚1 → 𝛼 𝑚1with 𝛼~0.26 (fitting)

S L I D E 15

Theory vs experiments and simulations (2)

3D

our model

our model with m1𝛼 and 𝛼~0.26

S L I D E 16

Conclusion

• Observation of a tenfold variation of the total transmission through a random scattering medium

• This results cannot be explained by an uncorrelated model; effect of the mesoscopic correlations

• Developed a model that explained the behavior of the transmission properties in open geometries with a localized illumination

S L I D E 17

Thank you!

More information about wavefront shaping:

www.wavefrontshaping.net

www.wavefrontshaping.com

(COPS at University of Twente)

S L I D E 18

Effect of the correlations (2)

= 0.9 0.66 0.46 0.39 0.17 0.07

1

1.4

1.8

2.2

0 0.2 0.4 0.6 0.8 1

S L I D E 19

Theory of imperfect control of channels (2)