Nonlinear Optical Waves in Disordered Ferroelectrics

Transcription

1 PhD candidate: Nonlinear Optical Waves in Disordered Ferroelectrics Davide Pierangeli Supervisor: Prof. Eugenio DelRe Physics Department, Unversity of Rome La Sapienza, Rome, Italy PhD in Physics, XXIX Cycle 27 October 2016, Rome

2 Nonlinear optics meets disorder Group & Research Initiatives Eugenio DelRe, in collaboration with Claudio Conti 2 Spatial solitons Anti-diffraction Disordered ferroelectrics Rogue waves Electro-Optics Optical turbulence Super-resolution Shock-waves

3 Contents 3 i. Super-crystals in composite ferroelectrics D.Pierangeli et al., Nat. Commun. 7, (2016) condensed matter physics ii. Ferroelectric phase-transition of disordered perovskites Observation of macroscopically ordered ferroelectric states Spontaneous formation of coherent polar-domain structures i. Group & Research Initiatives Rogue waves in photorefractive ferroelectrics D.Pierangeli et al., Phys. Rev. Lett. 115, (2015) D.Pierangeli et al., Phys. Rev. Lett. 117, (2016) nonlinear waves dynamics Extreme events in random optical fields Observation of spatial rogue waves in nonlinear media Optical instabilities and turbulent transitions Control of extreme events through spatial incoherence Spatiotemporal soliton dynamics in a saturable nonlinearity

4 Disordered ferroelectrics 4 compositional disorder in ABO 3 perovskites single-crystals from A.J.Agranat, Habrew University of Jerusalem dielectric spectroscopy from G-B.Parravicini, University of Pavia KNTN: KLTN: dielectric susceptibility FE/DG phase PE phase existence of polar-nano regions (PNR) complex relaxation properties (freezing etc.) out-of equilibrium responses (giant responses, memory, aging etc. ) giant photorefractive effect E.DelRe et al., Nat. Photon. 5 (2011) anomalous electro-optic effect linear EO effect broken symmetry quadratic EO effect inversion symmetry T.T.A.Lummen et al., Nat. Commun. 5 (2014) ordered states? D.Pierangeli et al., Opt. Mater. Express. 4 (2014) D.Pierangeli et al., Opt. Lett. 39 (2014)

5 Ferroelectric super-crystals 5 microstructured samples: KLTN transmission microscopy local critical properties spatially-varying transition temperature Visible-light diffractometry Spontaneous mesoscopic/photonic crystals Γ x T C (x) Λ 5.5 μm A.J.Agranat et al., Appl. Phys. Lett. 90, (2007) diffraction experiments: coherence T = T C - 2K λ=532nm direct space Λ 5.5 μm

6 Ferroelectric super-crystals 6 Polarization-resolved Bragg scattering standard periodic material (coupled wave theory) H.Kogelnik, Bell Syst. Tech. J super-lattice Nonlinear behavior P s is directed along the x-axis P 2 s is periodic with wavevector Γ one-dimensional model

7 static electric field E along Γ Electro-optic Bragg diffraction standard EO effect 7 field-induced phase transition super-lattice diffraction enhancement fully-hysteretic loop

8 Ordered polar-domain configuration 8 domain dynamics in presence of a fixed spatial scale basic domain configurations charge density minimization 45 domain walls ferroelectricity can be arranged into new phases on macroscopic scales It is a general property of polar-domains in quasi-periodic potentials atomic-scale imaging in layered oxide thin films: Second Harmonic Generation (inelastic scattering)? in collaboration with L. Tartara, University of Pavia Domains structure from the polarization transfer matrix? in collaboration with M. Ferraro, INLN? G.Stone et al., Nat. Commun. 7 (2016)

9 Nonlinear optical waves in the spatial domain 9 y Generalized Nonlinear Schrodinger Equation (NLSE) x z Spatial Solitons: diffraction nonlinearity photorefractive localized and stationary perturbations particle-like interactions experiments in photorefractive ferroelectric crystals top view Input Diffraction Soliton D. Pierangeli et al., Phys. Rev. Lett. 114 (2015)

10 Nonlinear optical waves in the spatial domain 10 y Generalized Nonlinear Schrodinger Equation (NLSE) x z Anti-diffraction: diffraction nonlinearity photorefractive paraxial and subwavelength experiments collapse length E. DelRe et al., Nat. Photon. 9 (2015) F. Di Mei et al., Phys. Rev. Lett. 116 (2016)

11 Optical rogue waves 11 Generalized Nonlinear Schrodinger Equation (NLSE) Disordered Field: interference of random waves diffraction? nonlinearity Gaussian amplitude distribution J.W.Goodman (1975) nonlinear behavior abnormal waves extreme events in complex systems hydrodynamics, acoustic etc Special solutions NLSE? Solitons? Instabilities? Wave-turbulence? D.R.Solli et al., Nature 450 (2007) M.Onorato et al. Phys. Rep. 528 (2013) J.M.Dudley et al. Nat. Photon. 8 (2014) C.Liu et al. Nat. Phys. 11 (2015) A.Montina et al., Phys. Rev. Lett. 103 (2009). beam propagation in nonlinear crystals?

12 Nonlinear optical waves in critical ferroelectrics 12 experimental setup: High-voltage control (0 2kV) Local temperature control (0.1K, T amb ) Time-resolved detection ( s) High spatial resolution (0.5 µm) tuning light self-interaction 1D bright localized peaks highly nonlinear regime input output

13 Rogue waves observation 13 Output intensity distributions: Statistics: highly nonlinear x-independent weakly nonlinear normal statistics long-tail statistics Nonlinear origin

14 Model and numerical analysis 14 Generalized NLSE (2+1)D: Kerr-saturated nonlocal highly nonlinear regime Nonlinear origin Soliton mergers? A.Armaroli et al., Optica 2(2015) S.Birkholz et al., Phys. Rev. Lett. 111 (2013) soliton phase-space

15 Controlling the nonlinearity 15 the photorefractive nonlinearity is nonistantaneous and accumulates in time time-resolved detection complete tunability KTN T > T C E-field input intensity Modulational instability (MI) spontaneous amplification of noise in a gain spectral region fixing a typical time scale: beam symmetry-breaking threshold Q.Lu et al., IEEE Phot.J. 7 (2015) T T C + 2K

16 Transitions to optical turbulence 16 quasi-homogeneous input wave spatially-modulated input wave MI stage Maximally-amplified wavevector How an optical field lose coherence E.G. Turitsyna et al., Nat. Photon. 7 (2014) turbulent transitions in a fiber lasers first observation for propagating waves Shot-to-shot fluctuations and correlations? ongoing experiments in a ferroelectric slab waveguide? no MI stage Probability Distribution Function I / <I> rogue waves are triggered by the onset of a turbulent regime

17 Role of the spatial coherence scale 17 partially-incoherent excitations NA=0.5 speckled beams intensity autocorrelation: Scale-dependent statistics source size: Y. Bromberg et al., Nat. Photon. 6 (2010) linear nonlinear rogue waves enhancement scale σ 2 Control of optical extreme events through spatial incoherence

18 Unveiling rogue waveforms 18 high-resolution measurements of optical rogue waveforms challenging in time-domain: P.Suret et al., Nat. Commun. 7 (2016) nonlinear-wave parameters wave size (FWHM) wave peak intensity self-similarity rogue waves enhancement σ 2 intensity independent Existence of a typical scale for rogue waves a general property? In saturable nonlinearities?

19 Understanding rogue waves 19 Non-stationary solitons in a saturable nonlinearity transient self-trapping on a localization scale E.DelRe et al., JOSA B 23 (2006) intensity independent weakly-dependent on the field E spatiotemporal phase-space of non-stationary solitons time dynamics Intensity (a.u.) x ( m) optical rogue waves Coherent structures in turbulent nonlinear wave fields Spatiotemporal dynamics of non-stationary solitons

20 References Thanks for your attention! [1] D.Pierangeli, M.Ferraro, F.Di Mei, G.Di Domenico, C.E.M.de Oliveira, A.J.Agranat and E.DelRe, Super-crystals in composite ferroelectrics, Nat. Commun. 7, (2016). [2] D.Pierangeli, F.Di Mei, C.Conti, A.J.Agranat, and E.DelRe, Spatial Rogue Waves in Photorefractive Ferroelectrics, Phys. Rev. Lett. 115, (2015). [3] D.Pierangeli, F.Di Mei, G.Di Domenico, A.J.Agranat, C.Conti, and E.DelRe, Evidence of turbulent transitions in optical wave propagation, Phys. Rev. Lett. 117, (2016). [4] D.Pierangeli, G.Musarra, F.Di Mei, G.Di Domenico, A.J.Agranat, C.Conti, and E.DelRe, Control of optical extreme events through spatial incoherence, submitted, (2016). [5] D.Pierangeli, M.Flammini, F.Di Mei, J.Parravicini, C.E.M.de Oliveira, A.J.Agranat, and E.DelRe, Continuous Solitons in a Lattice Nonlinearity, Phys. Rev. Lett. 114, (2015). [6] F.Di Mei, P.Caramazza, D.Pierangeli, G.Di Domenico, H.Ilan, A.J.Agranat, P.Di Porto, and E.DelRe, Intrinsic negative mass from nonlinearity, Phys. Rev. Lett. 114, (2015). [7] D.Pierangeli, F.Di Mei, J.Parravicini, GB.Parravicini, A.J.Agranat, C.Conti and E.DelRe, Observation of an intrinsic nonlinearity in the electro-optic response of relaxors ferroelectrics, Opt. Mat. Express 4, 1487 (2014) [8] D.Pierangeli, J.Parravicini, F.Di Mei, GB.Parravicini, A.J.Agranat, and E.DelRe, Photorefractive light needles in glassy nanodisordered KNTN, Opt. Lett. 39, 1657 (2014). [9] F.Di Mei, D.Pierangeli, J.Parravicini, C.Conti, A.J.Agranat, and E.DelRe, Observation of diffraction cancellation for nonparaxial beams in the scale-free-optics regime, Phys. Rev. A 92, (2015). [10] F.Di Mei, J.Parravicini, D.Pierangeli, C.Conti, A.J.Agranat and E.DelRe, Anti-diffracting beams through the diffusive optical nonlinearity, Opt. Express 22, (2014). [11] J.Parravicini, D.Pierangeli, F.Di Mei, GB.Parravicini, C.Conti, and E.DelRe, Aging solitons in photorefractive dipolar glasses, Opt. Express 21, (2013). [12] J.Parravicini, R.Martinez Lorente, F.Di Mei, D.Pierangeli, A.J.Agranat, and E.DelRe, Volume integrated phase modulator based on funnel waveguides for miniaturized optical circuits, Opt. Lett. 40, 1386 (2013). 20