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
SLIDE 1

2. People
Experimetal part
Theoretical part
Seng-Fatt Liew
Arthur Goetschy
Pr. Hui Cao
Pr. Douglas Stone
SLIDE 2

3. Transmission in random scattering media
Why is white paint opaque?
T
R
𝐿
SLIDE 3

4. Transmission in random scattering media
Why is white paint opaque?
T
R
𝑙
𝑇 ∝
𝐿
𝐿
Can we modify the transmission?
SLIDE 4

5. Transmission in random scattering media
Theoretical predictions
N
N
Bimodal distribution
p(T)
O.N. Dorokhov Solid State Commun. 1984
P.A. Mello et al. Ann. Phys. 1988
𝜌(𝑇) ∝
𝑇
𝑇 1− 𝑇
T
∞
∞
𝑇 𝑚𝑖𝑛 ≪ 1
𝑇 𝑚𝑎𝑥 = 1
Y. Nazarov PRL 1994
𝑇 𝑚𝑎𝑥
1
=
𝑇
𝑇
Mesoscopic correlations!
SLIDE 5

6. Motivations
Experimental measure of the TM
?
Quarter circle law
Acoustics: A. Aubry et al. PRL 2009
Optics: S.M. Popoff et al. PRL 2010
𝑇 𝑚𝑎𝑥
= (1 +
𝑇
Remaining effects of
mesoscopic correlations?
𝛾)2 <
4
𝑁 𝑖𝑛
𝛾=
𝑁 𝑜𝑢𝑡
𝑇 𝑚𝑎𝑥
> (1 +
𝑇
𝛾)2
SLIDE 6

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
SLIDE 7

8. Experimental setup
Ir
It
Ii
Ii: input intensity
Ir: backscattered intensity
• High input NA, output NA~1
• 2 polarizations phase modulation
It: total transmitted intensity
• Large number of segments (up to ~2000)
• Control of input and backscattered intensity
SLIDE 8

9. Typical results
𝐿~20 𝜇𝑚
𝑙~0.8 𝜇𝑚
𝐷~8.3 𝜇𝑚
𝑇 𝑚𝑎𝑥 = 3.56 𝑇
~18%
𝑇 𝑚𝑖𝑛 = 0.32 𝑇
~1.6%
𝑇 𝑚𝑎𝑥
~𝟏𝟏. 𝟏
𝑇 𝑚𝑖𝑛
~10 fold variation of the total transmission
Uncorrelated model gives 𝑇 𝑚𝑎𝑥 ~ 1.6 𝑇 , 𝑇 𝑚𝑖𝑛 ~0.5 𝑇 ,
𝑇 𝑚𝑎𝑥
~𝟑.
𝑇 𝑚𝑖𝑛
𝟐
 Effect of correlations but no open channels because of
imperfect control
SLIDE 9

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)
4
3
3
2
2
1
10
15
20
25
30
35
1
3
4
5
6
7
8
S L I D E 10

11. Predictions of Tmax and effect of the geometry
𝑇 𝑚𝑎𝑥 = 1
𝑇 𝑚𝑎𝑥 =?
Effect of imperfect channel control known
A. Goetschy and A. D. Stone, PRL, 2013
S L I D E 11

12. Theory of imperfect control of channels (1)
𝑀1
𝑚1 =
≤1
𝑁
𝑀2
𝑚2 =
≤1
𝑁
A. Goetschy and A. D. Stone, PRL, 2013
S L I D E 12

13. 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
S L I D E 13

14. Theory vs experiments and simulations (1)
2D
• Good agreement with simulations (recursive Green’s function)
• Effect of the algorithm + phase only; 𝑚1 → 𝛼 𝑚1 with 𝛼~0.26 (fitting)
S L I D E 14

15. Theory vs experiments and simulations (2)
3D
our model
our model with m1 𝛼 and
𝛼~0.26
S L I D E 15

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 16

17. Thank you!
More information about wavefront shaping:
www.wavefrontshaping.net
www.wavefrontshaping.com
(COPS at University of Twente)
S L I D E 17

18. Effect of the correlations (2)
2.2
1.8
1.4
1
= 0.9
0.66
0
0.46
0.2
0.39
0.4
0.6
0.17
0.8
1
0.07
S L I D E 18

19. Theory of imperfect control of channels (2)
S L I D E 19