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 http://www.complexlight.org/ http://www.mlphotonics.it marcoleonetti1@gmail.com 03/06/2014; Waves and Disorder

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., 1 8128 (2013) Granular active matter V. Folli et. al. Scientific Reports, 3, 2251 (2013) 03/06/2014; Waves and Disorder

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 http://www.complexlight.org/ http://www.mlphotonics.it marcoleonetti1@gmail.com 03/06/2014; Waves and Disorder

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, 063904 (2006) E. Delre et. al; Nat. Phot. 5, 39(2011) 03/06/2014; Waves and Disorder

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

The Anderson Localization 03/06/2014; Waves and Disorder

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

Transverse localization in optical fibers 2007: Transverse localization with photonic lattices Refractive index mismatch: Δn= 10-4 03/06/2014; Waves and Disorder

Transverse localization in optical fibers 40000 PMMA and 40000 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

Experimental setup Laser: Ti:Sapphire femtosecond: 80 nm Bandwidth @800nm M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

Nonlinear effects in the Anderson Regime Scannig the fiber output with a spectrograph 1 µm M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

Disorder induced Focusing 1 µm M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

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, 193902 (2014) 03/06/2014; Waves and Disorder

Disorder induced Focusing 1 µm From fit ΔnNL ≈10-5 In agreemnt with heat diffusion simulations M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

Two modes interaction Probe mode output: Input: Probe beam Pump beam Displacement: M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

The modes migration Modes positions: 03/06/2014; Waves and Disorder M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

The modes migration Modes Density Along X and Y: M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) 03/06/2014; Waves and Disorder

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

Adaptive focusing in the Anderson regime 03/06/2014; Waves and Disorder

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

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

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

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

Thank you for the attention Observation of Migrating Transverse Anderson Localizations of Light in Nonlocal Media M. Leonetti et. al.; Phys. Rev. Lett., 112, 193902 (2014) Light Focusing in the Anderson Regime M. Leonetti et. Al; Accepted Nat. Commun. http://www.complexlight.org/ http://www.mlphotonics.it marcoleonetti1@gmail.com 03/06/2014; Waves and Disorder