Lévy Statistics and the Glassy Behavior of Light in Random Fiber Lasers

The interest in random fiber lasers (RFLs), first demonstrated one decade ago, is still growing and their basic characteristics have been studied by several authors. RFLs are open systems that present instabilities in the intensity fluctuations due to the energy exchange among their non-orthogonal quasi-modes. In this work, we present a review of the recent investigations on the output characteristics of a continuous-wave erbium-doped RFL, with an emphasis on the statistical behavior of the emitted intensity fluctuations. A progression from the Gaussian to Levy and back to the Gaussian statistical regime was observed by increasing the excitation laser power from below to above the RFL threshold. By analyzing the RFL output intensity fluctuations, the probability density function of emission intensities was determined, and its correspondence with the experimental results was identified, enabling a clear demonstration of the analogy between the RFL phenomenon and the spin-glass phase transition in disordered magnetic systems. A replica-symmetry-breaking phase above the RFL threshold was characterized and the glassy behavior of the emitted light was established. We also discuss perspectives for future investigations on RFL systems.

[1]  Y. Rao,et al.  Tailoring the Properties of CW Random Fiber Lasers , 2016 .

[2]  Zhaona Wang,et al.  Two-threshold silver nanowire-based random laser with different dye concentrations , 2014 .

[3]  Raman Kashyap,et al.  Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser , 2016 .

[4]  E. I. Dontsova,et al.  Frequency doubling of Raman fiber lasers with random distributed feedback. , 2016, Optics letters.

[5]  V. S. Letokhov,et al.  Astrophysical lasers operating in optical Fe II lines in stellar ejecta of η carinae , 2004, astro-ph/0409069.

[6]  A. Crisanti,et al.  The sphericalp-spin interaction spin glass model: the statics , 1992 .

[7]  Yan-qing Lu,et al.  Study on the Polarization of Random Lasers from Dye-Doped Nematic Liquid Crystals , 2017, Nanoscale Research Letters.

[8]  V. Letokhov,et al.  The possibility of the laser effect in stellar atmospheres , 1975 .

[9]  Lulu Wang,et al.  Random Laser With Multiphase-Shifted Bragg Grating in Er/Yb-Codoped Fiber , 2015, Journal of Lightwave Technology.

[10]  C. Mendonça,et al.  Random laser emission from a Rhodamine B-doped GPTS/TEOS-derived organic/silica monolithic xerogel , 2017 .

[11]  N. P. Puente,et al.  Single-mode Er-doped fiber random laser with distributed Bragg grating feedback. , 2009, Optics express.

[12]  J. Goodman.  Speckle Phenomena in Optics: Theory and Applications , 2020 .

[13]  Fabrizio Martelli,et al.  A new class of optical sensors: a random laser based device , 2016, Scientific Reports.

[14]  Glassy behavior of light. , 2005, Physical review letters.

[15]  R. Sastre,et al.  Dye‐Doped POSS Solutions: Random Nanomaterials for Laser Emission , 2009 .

[16]  Ravitej Uppu,et al.  Identification of statistical regimes and crossovers in coherent random laser emission. , 2012, Optics letters.

[17]  Andrea Crisanti,et al.  The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra , 2014, Scientific Reports.

[18]  Z. N. Wang,et al.  All optical mode controllable Er-doped random fiber laser with distributed Bragg gratings. , 2015, Optics letters.

[19]  Raman Kashyap,et al.  Observation of Lévy statistics in one-dimensional erbium-based random fiber laser , 2017 .

[20]  Erdan Gu,et al.  Colloidal quantum dot random laser. , 2011, Optics express.

[21]  Zeev Valy Vardeny,et al.  Naturally occurring resonators in random lasing of π -conjugated polymer films , 2010 .

[22]  Giancarlo Ruocco,et al.  Glassy behavior of light in random lasers , 2006 .

[23]  P. G. Kryukov,et al.  A Laser with Nonresonant Feedback , 1966 .

[24]  Ekaterina A. Zlobina,et al.  High-order random Raman lasing in a PM fiber with ultimate efficiency and narrow bandwidth , 2016, Scientific Reports.

[25]  Luca Leuzzi,et al.  Complex spherical 2 + 4 spin glass: A model for nonlinear optics in random media , 2014, 1412.8706.

[26]  Diederik S. Wiersma,et al.  Statistical regimes of random laser fluctuations , 2007 .

[27]  N. Lawandy,et al.  Laser action in strongly scattering media , 1994, Nature.

[28]  Timothy J. N. Smith,et al.  Reverse mode switching of the random laser emission in dye doped liquid crystals under homogeneous and inhomogeneous electric fields , 2016 .

[29]  L Angelani,et al.  Phase diagram and complexity of mode-locked lasers: from order to disorder. , 2008, Physical review letters.

[30]  Jianlin Liu,et al.  An Sb-doped p-type ZnO nanowire based random laser diode , 2016, Nanotechnology.

[31]  S. Mujumdar,et al.  Dependence of the Gaussian-Lévy transition on the disorder strength in random lasers , 2013 .

[32]  E. Raposo,et al.  Observation of Lévy distribution and replica symmetry breaking in random lasers from a single set of measurements , 2016, Scientific Reports.

[33]  Koji Fujita,et al.  Coherent random lasers in weakly scattering polymer films containing silver nanoparticles , 2009 .

[34]  S. Mujumdar,et al.  Exponentially tempered Lévy sums in random lasers. , 2015, Physical review letters.

[35]  Yulong Tang,et al.  A random Q-switched fiber laser , 2015, Scientific Reports.

[36]  M. Sargent,et al.  Theory of Multimode Laser Operation , 1973 .

[37]  E. Raposo,et al.  Analytical solution for the Lévy-like steady-state distribution of intensities in random lasers , 2015 .

[38]  Ad Lagendijk,et al.  Spatial extent of random laser modes. , 2007, Physical review letters.

[39]  Sergei K. Turitsyn,et al.  Random distributed feedback fiber laser , 2011, 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference.

[40]  Brandon Redding,et al.  Speckle-free laser imaging using random laser illumination , 2011, Nature Photonics.

[41]  Benjamin R. Anderson,et al.  Self-healing organic-dye-based random lasers. , 2015, Optics letters.

[42]  Frequency Stability of a He-Xe Laser with Nonresonant Feedback , 1968 .

[43]  Zejin Liu,et al.  Short cavity-length random fiber laser with record power and ultrahigh efficiency. , 2016, Optics letters.

[44]  Pu Zhou,et al.  Investigation on random distributed feedback Raman fiber laser with linear polarized output , 2015 .

[45]  Ad Lagendijk,et al.  Intrinsic intensity fluctuations in random lasers , 2006 .

[46]  Mikhail A. Noginov,et al.  Solid-State Random Lasers , 2010 .

[47]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[48]  Arkadi Chipouline,et al.  Random lasing in π-conjugated films and infiltrated opals , 2001 .

[49]  K. Xie,et al.  Polarized random laser emission from an oriented disorder polymer optical fiber. , 2016, Optics letters.

[50]  A. Gomes,et al.  Tunable ultraviolet and blue light generation from Nd:YAB random laser bolstered by second-order nonlinear processes , 2016, Scientific Reports.

[51]  Yunjiang Rao,et al.  High Power Random Fiber Laser With Short Cavity Length: Theoretical and Experimental Investigations , 2015, IEEE Journal of Selected Topics in Quantum Electronics.

[52]  Wei Li Zhang,et al.  Fiber-Type Random Laser Based on a Cylindrical Waveguide with a Disordered Cladding Layer , 2016, Scientific Reports.

[53]  R. Kashyap,et al.  Demonstration of a 3 mW threshold Er-doped random fiber laser based on a unique fiber Bragg grating. , 2009, Optics express.

[54]  Z N Wang,et al.  Graphene based widely-tunable and singly-polarized pulse generation with random fiber lasers , 2015, Scientific reports.

[55]  Federico Tommasi,et al.  Robustness of replica symmetry breaking phenomenology in random laser , 2016, Scientific Reports.

[56]  P. Sebbah,et al.  Adaptive pumping for spectral control of random lasers , 2014 .

[57]  C. D. de Matos,et al.  Random fiber laser. , 2007, Physical review letters.

[58]  Shuangchun Wen,et al.  Lasing in nanocomposite random media , 2015 .

[59]  L. Leuzzi,et al.  Experimental evidence of replica symmetry breaking in random lasers , 2014, Nature Communications.

[60]  Wei Li Zhang,et al.  Random Distributed Feedback Fiber Laser Based on Combination of Er-Doped Fiber and Single-Mode Fiber , 2015, IEEE Journal of Selected Topics in Quantum Electronics.

[61]  S. Mujumdar,et al.  Lévy exponents as universal identifiers of threshold and criticality in random lasers , 2014 .

[62]  L. Leuzzi,et al.  Complexity of waves in nonlinear disordered media , 2010, 1009.3290.

[63]  S. Babin,et al.  Random distributed feedback fibre lasers , 2014 .

[64]  Gary D. Noojin,et al.  Evidence of Anderson localization effects in random Raman lasing , 2016, SPIE LASE.

[65]  Yunjiang Rao,et al.  Role of the mirror's reflectivity in forward-pumped random fiber laser. , 2015, Optics express.

[66]  Vladilen S. Letokhov,et al.  Generation of Light by a Scattering Medium with Negative Resonance Absorption , 1968 .

[67]  A. Gomes,et al.  Multi-wavelength emission through self-induced second-order wave-mixing processes from a Nd3+ doped crystalline powder random laser , 2015, Scientific Reports.

[68]  S. Ribeiro,et al.  Random laser action from flexible biocellulose-based device , 2014 .

[69]  William Guerin,et al.  A cold-atom random laser , 2013 .

[70]  Lei Zhang,et al.  Ultra-wide wavelength tuning of a cascaded Raman random fiber laser. , 2016, Optics letters.

[71]  Z. S. Macedo,et al.  Multi-photon excited coherent random laser emission in ZnO powders. , 2015, Nanoscale.

[72]  A. Crisanti,et al.  General phase diagram of multimodal ordered and disordered lasers in closed and open cavities. , 2014, Physical review letters.

[73]  Diederik S. Wiersma,et al.  The physics and applications of random lasers , 2008 .

[74]  Optofluidic random laser , 2012, 1203.0091.

[75]  E. Raposo,et al.  Observation of photonic paramagnetic to spin-glass transition in a specially designed TiO2 particle-based dye-colloidal random laser. , 2016, Optics letters.

[76]  Stanley,et al.  Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight. , 1994, Physical review letters.

[77]  Clement Yuen,et al.  Random laser action in ZnO nanorod arrays embedded in ZnO epilayers , 2004 .

[78]  M. Kues,et al.  Emission polarization of random lasers in organic dye solutions. , 2012, Optics letters.

[79]  Xiong Zeng,et al.  Temperature-controlled mode selection of Er-doped random fiber laser with disordered Bragg gratings , 2016 .

[80]  Frederic Bartumeus,et al.  Stochastic Optimal Foraging: Tuning Intensive and Extensive Dynamics in Random Searches , 2014, PloS one.

[81]  Youdou Zheng,et al.  Electrically pumped random lasing based on Au-ZnO nanowire Schottky junction , 2015, 2015 Conference on Lasers and Electro-Optics (CLEO).

[82]  N. Lawandy,et al.  Laser action in strongly scattering media , 1994, Nature.

[83]  Claudio Conti,et al.  The mode-locking transition of random lasers , 2011, 1304.3652.

[84]  Yunjiang Rao,et al.  Recent advances in fundamentals and applications of random fiber lasers , 2015 .

[85]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[86]  A. Crisanti,et al.  Statistical mechanics models for multimode lasers and random lasers , 2015, 1509.06955.

[87]  P. Prasad,et al.  Direct three-photon excitation of upconversion random laser emission in a weakly scattering organic colloidal system. , 2014, Optics express.

[88]  H. Brand,et al.  Multiplicative stochastic processes in statistical physics , 1979 .

[89]  G. L. Vasconcelos,et al.  Turbulence hierarchy in a random fibre laser , 2017, Nature Communications.

[90]  Xiaojun Xu,et al.  Hundred-watt-level high power random distributed feedback Raman fiber laser at 1150 nm and its application in mid-infrared laser generation. , 2015, Optics express.