1. Marco Leonetti1, Salman Karbasi2, Arash Mafi2, Claudio Conti3
 Observation of Anderson localization of light in nonlinear nonlocal media 
Marco Leonetti1, Salman Karbasi2, Arash Mafi2, Claudio Conti3
1: IPCF-CNR c/o Dep. of Physics, Univ. “Sapienza”, Rome, Italy
2: Dep. of Electr. Eng. and Comp. Sci., Univ. of Wisconsin-Milwaukee ,USA
3: ISC-CNR and Dep. of Physics, University “Sapienza”, Roma, Italy
03/06/2014; Waves and Disorder

2. www.complexlight.org The Complexlight Lab
Optical shocks in complex media
S. Gentilini et. al; Opt. Expr 22, 1667 (2014)
Random lasers in microstructured materials
N. Ghofraniha et. al.; J.Mater. Chem C., (2013)
Granular active matter
V. Folli et. al. Scientific Reports, 3, 2251 (2013)
03/06/2014; Waves and Disorder

3. Marco Leonetti1, Salman Karbasi2, Arash Mafi2, Claudio Conti3
 Observation of Anderson localization of light in nonlinear nonlocal media 
Marco Leonetti1, Salman Karbasi2, Arash Mafi2, Claudio Conti3
1: IPCF-CNR c/o Dep. of Physics, Univ. “Sapienza”, Rome, Italy
2: Dep. of Electr. Eng. and Comp. Sci., Univ. of Wisconsin-Milwaukee ,USA
3: ISC-CNR and Dep. of Physics, University “Sapienza”, Roma, Italy
03/06/2014; Waves and Disorder

4. Trapping light in a tiny space
Anderson Localization
Photonic Crystals
B.S. Song et. al; Nat. Mater 4, 207 (2005)
Self Focusing
M. Storzer et. al; Phys. Rev. Lett. 96, (2006)
E. Delre et. al; Nat. Phot. 5, 39(2011)
03/06/2014; Waves and Disorder

5. Outline Anderson localization and transversal localization regime
Nonlocality and nonlinearity in the localized regime
Adaptive optics In the localized regime
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6. The Anderson Localization
03/06/2014; Waves and Disorder

7. Transverse Anderson Localization
Ioffe- Regel criterion
Three dimensional localization
Transverse Localization
03/06/2014; Waves and Disorder

8. Transverse localization in optical fibers
2007: Transverse localization with photonic lattices
Refractive index mismatch: Δn= 10-4
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9. Transverse localization in optical fibers
40000 PMMA and PS fibers
In a preform to Draw a single fiber
Average over 100 experimental realizations
PMMA & PS Refractive index mismatch: Δn=10-1
03/06/2014; Waves and Disorder

10. Experimental setup Laser: Ti:Sapphire femtosecond:
80 nm
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
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11. Nonlinear Effects Broadband & micron sized 1 µm Input:
Shrinking of the output when intensity is increased
Output (broadband):
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

12. Focusing or de-focusing?
Thermal origin of nonlinearity
Shutter closes
Shutter opens
1 µm
Measured focusing behaviour
... by two de focusing materials PS
PMMA
Laser Welding of Plastics, First Edition. Rolf Klein (2011).
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

13. Thermal origin of de-focusing
Shutter closes
Shutter opens
1 µm
AbsPMMA: 2500 dB/km
AbsPS : 600 dB/km
Term. ConductancePMMA =0.25 W/mC°
Term. ConductancePS =0.033 W/mC°
From simulations temperature difference: ΔT≈2*10-2
Corresponding to a Δn ≈10-5
Light absorption in binary systems increases refractive index mismatch
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

14. Nonlinear effects in the Anderson Regime
Scannig the fiber output with a spectrograph
1 µm
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

15. Disorder induced Focusing
1 µm
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

16. Disorder induced Focusing
1 µm
Model: HNA for the paraxial wave equations
Average Refractive Index
Nonlinear nonlocal perturbation
Refractive index distribution (PMMA-PS)
Nonlinear part depends on intensity: T
Nonlocal kernel thermal response r
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

17. Disorder induced Focusing
1 µm T
Field is local r
r2=x2+y2
K expanded in a Taylor series
Δn1 is the nolinear index perturbation at a unitary input power P
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

18. Disorder induced Focusing
1 µm
Searching solutions like wave equation becomes:
The main effect of nonlinearity is modify the refractive index: that is to shift eigenvalues of the disorder induced localized states
Eigenvalues are:
Localization length:
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
03/06/2014; Waves and Disorder

19. Disorder induced Focusing
1 µm
From fit ΔnNL ≈10-5 In agreemnt with heat diffusion simulations
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
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20. Two modes interaction Probe mode output: Input: Probe beam Pump beam
Displacement:
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
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21. The modes migration Modes positions: 03/06/2014; Waves and Disorder
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
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22. The modes migration Modes Density Along X and Y:
M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
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23. Part I : Conclusions Transversal Localization in Optical fibers
Disorder induced self-focusing
Nolocality induced modes migration
Controlled beam steering in systems with transverse disorder
M. Leonetti et. al.; Submitted
03/06/2014; Waves and Disorder

24. Adaptive focusing in the Anderson regime
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25. Adaptive focusing in the Anderson regime
SLM controls the
focusing
procedure
Optimization
evolution
M. Leonetti et. al.; Accepted Nat. Commun.
03/06/2014; Waves and Disorder

26. Adaptive focusing in the Anderson regime
Light focusing in
the Anderson regime:
Localized mode:
Focus
Optimized focus in a disordered fiber:
Optimized focus in a homogeneous fiber:
Fraction of focused intensity Φ= 0.5 for disordered fibers
Fraction of focused intensity Φ= 0.01 for homogeneous fibers
M. Leonetti et. al.; Accepted Nat. Commun.
03/06/2014; Waves and Disorder

27. Localized modes and focusing
Simulations:
Numerical solution of the paraxial wave equation solution:
Experiments:
Image of the section of the fiber tip
A transverse localized mode in correspondance of the focusing target
Weak scattering
High Scattering
M. Leonetti et. al.; Accepted Nat. Commun.
03/06/2014; Waves and Disorder

28. Conclusions Part I: Part II:
Disorder induced focusing and migration in the transversal localization regime
Part II:
Adaptive focusing in the Transversal localization regime
Coexistence between localized modes and adaptive focusing
Increased fraction of light gathered to target
03/06/2014; Waves and Disorder

29. Thank you for the attention
Observation of Migrating Transverse Anderson Localizations of Light in Nonlocal Media M. Leonetti et. al.; Phys. Rev. Lett., 112, (2014)
Light Focusing in the Anderson Regime M. Leonetti et. Al; Accepted Nat. Commun.
03/06/2014; Waves and Disorder