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Article

Fractional-Order Modeling of a Multistable Erbium-Doped Fiber Laser

by
Jorge Eduardo Silva Gómez
1,
José de Jesús Barba Franco
2,
Luís Armando Gallegos Infante
3,
Juan Hugo García López
1,
Rider Jaimes Reátegui
1,* and
Alexander N. Pisarchik
4,*
1
Complex Systems and Innovation Laboratory, Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno 47463, Jalisco, Mexico
2
Departamento de Ciencias Básicas, Tecnológico Nacional de México, Instituto Tecnológico José Mario Molina Pasqual y Henríquez, Arandas 47180, Jalisco, Mexico
3
Departamento de Ciencias Exactas y Tecnología, Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno 47463, Jalisco, Mexico
4
Centro de Tecnología Biomédica, Universidad Politecnica de Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain
*
Authors to whom correspondence should be addressed.
Photonics 2025, 12(10), 1014; https://doi.org/10.3390/photonics12101014
Submission received: 15 September 2025 / Revised: 9 October 2025 / Accepted: 10 October 2025 / Published: 14 October 2025
(This article belongs to the Special Issue Optical Fiber Lasers and Laser Technology)

Abstract

We propose a novel mathematical model of a multistable erbium-doped fiber laser based on Caputo fractional derivative equations. The model is used to investigate how the laser dynamics evolve as the derivative order is varied. Our results demonstrate that the fractional-order formulation provides a more accurate description of the experimentally observed laser dynamics compared to conventional integer-order models. This study highlights the importance of fractional calculus in modeling complex nonlinear photonic systems and offers new insights into the dynamics of multistable lasers.
Keywords: erbium-doped fiber laser; fractional calculus; Caputo derivative; laser dynamics; multistability; fractional differential equations; Runge–Kutta method; memory effects; nonlinear systems; fractional-order systems erbium-doped fiber laser; fractional calculus; Caputo derivative; laser dynamics; multistability; fractional differential equations; Runge–Kutta method; memory effects; nonlinear systems; fractional-order systems

Share and Cite

MDPI and ACS Style

Silva Gómez, J.E.; Barba Franco, J.d.J.; Gallegos Infante, L.A.; García López, J.H.; Jaimes Reátegui, R.; Pisarchik, A.N. Fractional-Order Modeling of a Multistable Erbium-Doped Fiber Laser. Photonics 2025, 12, 1014. https://doi.org/10.3390/photonics12101014

AMA Style

Silva Gómez JE, Barba Franco JdJ, Gallegos Infante LA, García López JH, Jaimes Reátegui R, Pisarchik AN. Fractional-Order Modeling of a Multistable Erbium-Doped Fiber Laser. Photonics. 2025; 12(10):1014. https://doi.org/10.3390/photonics12101014

Chicago/Turabian Style

Silva Gómez, Jorge Eduardo, José de Jesús Barba Franco, Luís Armando Gallegos Infante, Juan Hugo García López, Rider Jaimes Reátegui, and Alexander N. Pisarchik. 2025. "Fractional-Order Modeling of a Multistable Erbium-Doped Fiber Laser" Photonics 12, no. 10: 1014. https://doi.org/10.3390/photonics12101014

APA Style

Silva Gómez, J. E., Barba Franco, J. d. J., Gallegos Infante, L. A., García López, J. H., Jaimes Reátegui, R., & Pisarchik, A. N. (2025). Fractional-Order Modeling of a Multistable Erbium-Doped Fiber Laser. Photonics, 12(10), 1014. https://doi.org/10.3390/photonics12101014

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