A note on stability of traveling waves in a Q-switched fiber laser

Authors

  • M. Reza-Rahmati CIO
  • Z. Malacara-Hernandez CIO

DOI:

https://doi.org/10.31349/RevMexFis.72.011303

Keywords:

Floquet laser stability; Tm/Er fiber dynamics; periodic solutions; singular perturbation theory; Q-switching

Abstract

This study presents a unified theoretical and experimental framework for ensuring stable, high-repetition–rate operation in passively Qswitched hybrid thulium/erbium fiber lasers. A key challenge in such systems-the limited lifetime of the Tm3+ 3H4 energy level (300 − 500 µs)–has traditionally restricted pulse frequency and stability. By applying nonlinear dynamical systems theory, we provide a rigorous Floquet-based analysis that certifies the stability of periodic pulse solutions under perturbations. The theoretical model is complemented by experimental results demonstrating that spectral complementarity between Tm and Er ions eliminates gain competition, thereby enhancing pulse consistency. This combined approach offers new design principles for rare-earth-doped fiber systems, with direct implications for high-performance applications in biomedical laser processing and free-space optical communication.

References

R. Paschotta, Passively Q-switched lasers, in Encyclopedia of Laser Physics and Technology, (Wiley-VCH, 2008)

G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn, Lyapunov Characteristic Exponents for Smooth Dynamical Systems, Meccanica, 15 (1980) 9

W. Blanc, T. L. Sebastian, B. Dussardier, C. Michel, B. Faure, M. Ude, and G. Monnom, Thulium environment in a silica doped optical fibre, arXiv:0808.3949, Aug. 2008. Demonstrates that the 3H4 → 3F4 transition in silica has very low quantum efficiency (≈ 2%) and a short upper-level lifetime ( 300-500 µs), limiting performance

G. Floquet, Sur les équations différentielles linéaires á coefficients périodiques, Annales Scientifiques de l’école Normale Supérieure, 12 (1883) 47

M. Krupa, B. Sandstede, and P. Szmolyan, Fast and Slow Waves in the FitzHugh-Nagumo Equation, Journal of Differential Equations 133 (1997) 49

T. Jiang, K. Yin, X. Zheng, H. Yu, X.-A. Cheng, Black phosphorus as a new broadband saturable absorber for infrared passively Q-switched fiber lasers, arXiv preprint arXiv:1504.07341, Apr. 2015. Demonstrates broadband PQS operation at 1.55 µm and 2 µm with BP saturable absorbers, highlighting the self-modulating dynamics via fiber-integrated SAs

M. Tao, et al., Theoretical modeling and analysis of a passively Q-switched Er-doped fiber laser with Tm-doped fiber saturable absorber. Optics Communications, 319 (2014) 128-132

G. P. Agrawal, Applications of Nonlinear Fiber Optics, (Academic Press, 2001)

A. E. Siegman, Lasers, (University Science Books, 1986)

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology, (Academic Press, 1999)

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications, (Wiley-Interscience, 1994)

S. D. Jackson, Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 µm Tm3+-doped silica fibre lasers, Optics Communications 230 (2004) 197

J. Yao, A tutorial on microwave photonic, IEEE Photonics Society Newsletter, 32 (2012) 4

N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of Differential Equations, 31 (1979) 53

P. Szmolyan and M. Wechselberger, Canards in R 3 , Journal of Differential Equations, 177, (2001) 419

C. Kuehn, Multiple Time Scale Dynamics, 191 of Applied Mathematical Sciences, (Springer, 2015)

C. K. R. T. Jones, Geometric singular perturbation theory, in Dynamical Systems (Montecatini Terme, 1994), 1609 of Lecture Notes in Mathematics, 44-118, (Springer, 1995)

F. Kreichbaum, Large-mode-area fibers, RP Photonics Encyclopedia, 2025. Available at: https://www.rp-photonics.com/large_mode_area_fibers.html Large-mode-area (LMA) fibers reach effective mode areas of hundreds to thousands of µm 2 ; typical step-index fibers have overlap factors Γ ≈ 0.70–0.75, while photonic crystal and advanced designs exceed Γ > 0.85

Thorlabs Inc., Endlessly Single Mode, Large Mode Area Photonic Crystal Fiber, 2023. Available at: https://www.thorlabs.com Demonstrates optical mode-core overlap Γ > 90% in LMA photonic crystal fibers, enhancing extraction efficiency and slope performance

F. Todorov et al., Active Optical Fibers and Components for Fiber Lasers Emitting in the 2-µm Spectral Range, Materials (Basel), 13 (2020). Reviews applications of thulium-doped fibers around 1.9-2.0 µm, including biomedical/eye-safe uses, and discusses stability issues in passively Q-switched systems

Q. Zhu, L. Yu, B. Wen, J. Cheng, Y. Deng, J. Li, Passive Qswitched fiber laser based on NiSe2 saturable absorber, Opt. Quant. Electron., 56 (2024). Reports a stable PQS EDFL with NiSe2 SA exhibiting high repetition rate, narrow pulses, and robust all-fiber architecture-an exemplar of fiber-integrated SA performance

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Published

2026-01-01

How to Cite

[1]
M. R. Rahmati and Z. Malacara-Hernandez, “A note on stability of traveling waves in a Q-switched fiber laser”, Rev. Mex. Fís., vol. 72, no. 1 Jan-Feb, pp. 011303 1–, Jan. 2026.