101° CONGRESSO NAZIONALE DELLA SOCIETA ITALIANA DI FISICA Roma, settembre 2015 Spatial Rogue Waves in Photorefractive Ferroelectrics Fabrizio Di Mei, Claudio Conti, Aharon J. Agranat, Eugenio DelRe Physics Department, Unversity of Rome “La Sapienza”, Italy Center for Life Nano Istituto Italiano di Tecnologia ISC-CNR, Università di Roma “La Sapienza”, Italy Applied Physics Department, Hebrew University of Jerusalem, Israel Davide Pierangeli Physics Department, Unversity of Rome “La Sapienza”, Rome, Italy YIL15 Nonlinear Photonics in Disordered Media Group

Extreme Events earthquakes breakdowns in networks financial crashes ocean and optical dynamics Rogue Waves long-tail statistics M.Onorato et al., Phys. Reports 528, (2013) intensity-amplitude PDF

Optical Rogue Waves temporal domain: Rogue Waves PDF spatially-extended (2D-3D) optical systems Spatio-temporal events with extremely elevated amplitude light pulse propagation in optical fiber chaotic laser resonators D.R.Solli et al, Nature 450, (2007) J.M.Dudley et al., Nat. Photon. 8, (2014) C.Lecaplain et al., Phys. Rev. Lett. 108, (2012) C.Bonatto et al., Phys. Rev. Lett. 107, (2011) spatial domain: theoretical framework: Generalized Nonlinear Schrödinger Equation (GNLSE) Chaos and Complexity A.Montina et al., Phys. Rev. Lett. 103, (2009) x y P.Walczak et al., Phys. Rev. Lett. 114, (2015)

Spatial Rogue Waves instabilities role of nonlinearity key components: nonlinear cavities A.Montina et al., PRL 103, (2009) E.Louvergneaux et al., PRA 87, (2011) N.Marsal et al., OL 39, (2014) C.Liu et al., Nat. Phys. (2015) linear multimodal systems F.T.Arecchi et al., PRL 106, (2011) M.Leonetti et al., APL 106, (2015) optical filamentation S.Birkholz et al., PRL 111, (2013) beam propagation in optical crystals ? GNLSE random waves disorder turbulence out-of equilibrium a key study

I.Optical Rogue Waves II.Nanodisordered ferroelectrics III.Observation of spatial rogue waves IV.Nonlinear Shrodinger model V.Rogue Solitons Spatial Rogue Waves in Photorefractive Ferroelectrics

Nanodisordered ferroelectrics KLTN compositional disorder in perovskite structures potassium-lithium-tantalate-niobate K 1-α Li α Ta 1-β Nb β O 3 room-temperature ferroelectric phase transition TCTC dielectric susceptibility paraelectric ferroelectric (dipolar glass) complex relaxation properties out-of equilibrium responses giant electro-optic effect KNTN  10 5 D.Pierangeli et al., Opt. Mater. Express. 4, (2014) giant photorefractive nonlinearity photoinduced space-charge field E.DelRe et al., Nat. Photon. 5, (2011) D.Pierangeli et al., Opt. Lett. 39, (2014)

Nonlinear waves in critical ferroelectrics 2.4 mm z KLTN CL A experimental setup micrometric beams local-temperature control high-voltage control time-resolved detection tuning light self-interaction mW

Nonlinear waves in critical ferroelectrics using temperature gradients to explore different nonlinear propagation regimes local-temperature control high-voltage control time-resolved detection z z y E-field 20μm x y TCTC Modulation Instability Speckle-like Critical Opalescence x Applying E ≈ 2kV/cm x y bright localized peaks highly nonlinear regime T ≈ T C + 1K large-scale fluctuations

Rogue waves observation Output intensity distributions 20μm x y weakly nonlinear highly nonlinear rogue event small fluctuations I RW ≈ 20 extreme fluctuations STATISTICS highly nonlinear weakly nonlinear

Generalized nonlinear Schrödinger model photorefractive (Kerr-like) nonlinearity: Soliton mergers Nonlinear origin diffraction + nonlinearity: numerical results weakly nonlinear highly nonlinear input disorder key points: good agreement with experimental findings A.Armaroli et al., Optica 2, (2015)

Solitonic interpretation self-similarity existence curve analyzing each rogue waves in terms of soliton existence coditions normalized amplitude and waist higly-saturated region: highly-saturated region experimental dynamics soliton train time rogue event scale-invariance localized waves with arbitrary intensity can form soliton mergers

I.Observation of rogue waves for beam propagation in crystals II.Rogue waves from a generalized nonlinear Shrodinger model Outline Higly-nonlinear photorefractive response Media instabilities and turbulence at the ferroelectric phase transition Rogue waves control through nonlinearity strength Nonlinear origin Spatial soliton mergers and waveform scale-invariance Thanks for your attention! References D. Pierangeli, F. Di Mei, C. Conti, A.J. Agranat and E. DelRe, Phys. Rev. Lett. 115, (2015).