Noise-Induced Dynamics in a Multistable Erbium-Doped Fiber Laser: A Short Review From Extreme Events to Photonic Information Processing
DOI:
https://doi.org/10.66131/JDSC13202660-79Keywords:
erbium-doped fiber laser, nonlinear dynamics, multistability, noise-induced intermittency, bifurcation, rogue waves, reservoir computing, optical logic gatesAbstract
Noise is often regarded as a source of instability and degraded performance in optical systems. In nonlinear dynamical systems, this view is incomplete: fluctuations can reveal critical susceptibility, activate transitions among coexisting attractors, generate rare extreme excursions, and enable probabilistic information processing. This review develops a unified narrative around diode-pumped erbium-doped fiber lasers (EDFLs), a compact photonic platform in which multistability, bifurcations, attractor hopping, prebifurcation noise amplification, rogue-wave generation, optical logic, and data-driven stochastic cloning have all been investigated. We first establish the EDFL as a class-B nonlinear oscillator and review its reduced rate-equation description, emphasizing the roles of pump modulation, amplified spontaneous emission, and basin geometry. We then examine noise-induced hopping among periodic attractors and the amplification of fluctuations near saddle-node, period-doubling, and crisis bifurcations. These mechanisms lead naturally to extreme-event physics, where filtered noise promotes rare visits to high-amplitude subharmonic states and produces non-Gaussian rogue-wave statistics. Finally, we review how noise-controlled state occupation can be used for optical logic and how reservoir computing differentiates strong trajectory cloning from weak statistical cloning in partially observed stochastic systems. The main conclusion is that noise in a multistable EDFL is simultaneously a perturbation, a probe of hidden dynamical structure, and a controllable resource for photonic information processing.
References
Stefan Kraut, Ulrike Feudel, and Celso Grebogi. “Experimental Observation of Noise-Induced Attractor Hopping in a Multistable System”. In: Physical Review E 59 (1999), pp. 5253–5256. doi: 10.1103/PhysRevE.59.5253.
Ulrike Feudel. “Complex Dynamics in Multistable Systems”. In: International Journal of Bifurcation and Chaos 18.6 (2008), pp. 1607–1626. doi: 10.1142/S0218127408021057.
Kurt Wiesenfeld. “Noisy Period-Doubling Bifurcation”. In: Journal of Statistical Physics 38 (1985), pp. 1071–1097. doi: 10.1007/BF01017865.
Kurt Wiesenfeld and Bruce McNamara. “Small-Signal Amplification in Bifurcating Dynamical Systems”. In: Physical Review A 33 (1986), pp. 629–642. doi: 10.1103/PhysRevA.33.629.
Benjamin Lindner et al. “Effects of Noise in Excitable Systems”. In: Physics Reports 392.6 (2004), pp. 321–424. doi: 10.1016/j.physrep.2003.10.015.
Oleg I. Moskalenko et al. “Characteristics of Noise-Induced Intermittency”. In: Chaos, Solitons & Fractals 117 (2018), pp. 269–275. doi: 10.1016/j.chaos.2018.10.026.
Fortunato T. Arecchi et al. “Experimental Evidence of Subharmonic Bifurcations, Multistability, and Turbulence in a Q-Switched Gas Laser”. In: Physical Review Letters 49 (1982), pp. 1217–1220. doi: 10.1103/PhysRevLett.49.1217.
Michel J. F. Digonnet, ed. Rare-Earth-Doped Fiber Lasers and Amplifiers. New York, NY: Marcel Dekker, 1993.
Oleg G. Okhotnikov, ed. Fiber Lasers. Weinheim, Germany: Wiley-VCH, 2012.
Guillermo Huerta-Cuellar, Alexander N. Pisarchik, and Yury O. Barmenkov. “Experimental Characterization of Hopping Dynamics in a Multistable Fiber Laser”. In: Physical Review E 78 (2008), p. 035202. doi: 10.1103/PhysRevE.78.035202.
Guillermo Huerta-Cuellar et al. “Prebifurcation Noise Amplification in a Fiber Laser”. In: Physical Review E 79 (2009), p. 036204. doi: 10.1103/PhysRevE.79.036204.
Alexander N. Pisarchik et al. “Rogue Waves in a Multistable System”. In: Physical Review Letters 107 (2011), p. 274101. doi: 10.1103/PhysRevLett.107.274101.
Alexander N. Pisarchik et al. “Multistate Intermittency and Extreme Pulses in a Fiber Laser”. In: Physical Review E 86 (2012), p. 056219. doi: 10.1103/PhysRevE.86.056219.
Alexander N. Pisarchik and Rider Jaimes-Reategui. “Control of basins of attraction in a multistable fiber laser”. In: Physics Letters A 374.2 (2009), pp. 228–234. doi: 10.1016/j.physleta.2009.10.061.
Alexander N. Pisarchik and B. K. Goswami. “Annihilation of one of the coexisting attractors in a bistable system”. In: Physical Review Letters 84.7 (2000), pp. 1423–1426. doi: 10.1103/PhysRevLett.84.1423.
Alexander N. Pisarchik, Yu. O. Barmenkov, and A. V. Kir’yanov. “Experimental demonstration of attractor annihilation in a multistable fiber laser”. In: Physical Review E 68.6, 066211 (2003). doi: 10.1103/PhysRevE.68.066211.
Safara Bibi et al. “Harnessing Multistability: A Novel Approach to Optical Logic Gate Construction Using Erbium-Doped Fiber Lasers”. In: Photonics 11.2 (2024), p. 176. doi: 10.3390/photonics11020176.
Andrey V. Andreev et al. “Stochastic Cloning of Dynamical Systems with Hidden Variables”. In: Physical Review E 112 (2025), p. 015303. doi: 10.1103/dynj-xqrm.
Alexander N. Pisarchik and Alexander E. Hramov. Multistability in Physical and Living Systems: Characterization and Applications. Cham, Switzerland: Springer, 2022.
Alexander N. Pisarchik et al. “Dynamics of an erbium-doped fiber laser with pump modulation: Theory and experiment”. In: Journal of the Optical Society of America B 22.10 (2005), pp. 2107–2114. doi: 10.1364/JOSAB.22.002107.
Daniel R. Solli et al. “Optical Rogue Waves”. In: Nature 450 (2007), pp. 1054–1057. doi: 10.1038/nature06402.
Miguel Onorato et al. “Freak Waves in Random Oceanic Sea States”. In: Physical Review Letters 86 (2001), pp. 5831–5834. doi: 10.1103/PhysRevLett.86.5831.
Miguel Onorato, Alfred R. Osborne, and Marina Serio. “Modulational Instability in Crossing Sea States: A Possible Mechanism for the Formation of Freak Waves”. In: Physical Review Letters 96 (2006), p. 014503. doi:10.1103/PhysRevLett.96.014503.
Sudeshna Sinha and William L. Ditto. “Dynamics-Based Computation”. In: Physical Review Letters 81 (1998), pp. 2156–2159. doi: 10.1103/PhysRevLett.81.2156.
Toshinori Munakata, Sudeshna Sinha, and William L. Ditto. “Chaos Computing: Implementation of Fundamental Logical Gates by Chaotic Elements”. In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49.11 (2002), pp. 1629–1633. doi: 10.1109/TCSI.2002.804540.
K. Murali et al. “Reliable Logic Circuit Elements That Exploit Nonlinearity in the Presence of a Noise Floor”. In: Physical Review Letters 102 (2009), p. 104101. doi: 10.1103/PhysRevLett.102.104101.
P. Ashokkumar et al. “Realization of All Logic Gates and Memory Latch in the SC-CNN Cell of the Simple Nonlinear MLC Circuit”. In: Chaos 22 (2012), p. 063119. doi: 10.1063/1.4754871.
Rui-Cheng Shen et al. “Long-Time Memory and Ternary Logic Gate Using a Multistable Cavity Magnonics System”. In: Physical Review Letters 127 (2021), p. 183202. doi: 10.1103/PhysRevLett.127.183202.
Rider Jaimes-Reategui et al. “Optoelectronic Flexible Logic Gate Based on a Fiber Laser”. In: The European Physical Journal Special Topics 223 (2014), pp. 2837–2846. doi: 10.1140/epjst/e2014-02270-5.
Chung-Kang Peng et al. “Mosaic Organization of DNA Nucleotides”. In: Physical Review E 49 (1994), pp. 1685–1689. doi: 10.1103/PhysRevE.49.1685.
Herbert Jaeger and Harald Haas. “Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication”. In: Science 304.5667 (2004), pp. 78–80. doi: 10.1126/science.1091277.
Mantas Lukosevicius and Herbert Jaeger. “Reservoir Computing Approaches to Recurrent Neural Network Training”. In: Computer Science Review 3.3 (2009), pp. 127–149. doi: 10.1016/j.cosrev.2009.03.005.
Zhixin Lu et al. “Reservoir Observers: Model-Free Inference of Unmeasured Variables in Chaotic Systems”. In: Chaos 27 (2017), p. 041102. doi: 10.1063/1.4979664.
Jaideep Pathak et al. “Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach”. In: Physical Review Letters 120 (2018), p. 024102. doi: 10.1103/PhysRevLett.120.024102.
Lu-Wang Kong et al. “Reservoir Computing as Digital Twins for Nonlinear Dynamical Systems”. In: Chaos 33 (2023), p. 033111. doi: 10.1063/5.0137822.
Soroush Panahi and Ying-Cheng Lai. “Adaptable Reservoir Computing: A Paradigm for Model-Free Data-Driven Prediction of Critical Transitions in Nonlinear Dynamical Systems”. In: Chaos 34 (2024), p. 051501. doi:10.1063/5.0202054.
Additional Files
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Guillermo Huerta Cuellar, Rider Jaimes Reátegui, Juan Hugo García López
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
