Cavity Pattern Formation and Its Dynamics of Fiber Fuse in Single-Mode Optical Fibers
DOI:
https://doi.org/10.26713/jims.v12i4.1459Keywords:
Nonlinear oscillation model, Van der Pol equation, Fiber fuse phenomenon, Kuramoto modelAbstract
The nonlinear oscillation model using the Van der Pol equation was able to phenomenologically explain the formation of periodic cavities, the cavity shape, and the regularity of the cavity pattern in the core layer as a result of the relaxation oscillation and cavity compression and/or deformation. We assumed the relationships between the parameters of the population dynamics of interacting self-oscillators using the Kuramoto model and the fiber fuse propagation, and found an equation describing the power dependence of the periodic cavity interval. The experimentally determined cavity intervals at \(P_{th} \leq P_0 \leq 5\) W satisfied this equation. Furthermore, the experimental cavity intervals at \(P_0 >6\) W can be explained by considering the power dependence of the propagation velocity of the fiber fuse and the constant period of the Van der Pol oscillator.
Downloads
References
K. S. Abedin and M. Nakazawa, Real time monitoring of a fiber fuse using an optical time-domain reflectometer, Optics Express 18(20) (2010), 21315 – 21321, DOI: 10.1364/oe.18.021315.
J. A. Acebron, L. L. Bonilla, C. J. P. Vicente, F. Ritort and R. Spigler, The Kuramoto model: a simple paradigm for synchronization phenomena, Reviews of Modern Physics 77(1) (2005), 137 – 185, DOI: 10.1103/RevModPhys.77.137.
P. F. C. Antunes, M. F. F. Domingues, N. J. Alberto and P. S. André, Optical fiber microcavity strain sensors produced by the catastrophic fuse effect, IEEE Photonics Technology Letters 26(1) (2014), 78 – 81, DOI: 10.1109/LPT.2013.2288930.
R. M. Atkins, P. G. Simpkins and A. D. Yablon, Track of a fiber fuse: a Rayleigh instability in optical waveguides, Optics Letters 28(12) (2003), 974 – 976, DOI: 10.1364/OL.28.000974.
R. Brout, Phase Transitions, Chapter 2, W. A. Benjamin, Inc., New York (1965).
I. A. Bufetov, A. A. Frolov, E. M. Dianov, V. E. Fortov and V. P. Efremov, Dynamics of fiber fuse propagation, Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (OFC/NFOEC 2005), Optical Society of America, paper OThQ7 (2005), https://www.osapublishing.org/abstract.cfm?uri=OFC-2005-OThQ7.
I. A. Bufetov, A. A. Frolov, V. P. Efremov, M. Y. Schelev, V. I. Lozovoi, V. E. Fortov and E. M. Dianov, Fast optical discharge propagation through optical fibres under kW-range laser radiation, in Proceedings of 31st European Conference on Optical Communications (ECOC 2005), Vol. 6, pp. 39–40 (2005), DOI: 10.1049/cp:20050866.
E. D. Bumarin and S. I. Yakovlenko, Temperature distribution in the bright spot of the optical discharge in an optical fiber, Laser Physics 16(8) (2006), 1235 – 1241, DOI: 10.1134/S1054660X06080123.
H. Daido, Discrete-time population dynamics of interacting self-oscillators, Progress of Theoretical Physics 75(6) (1986), 1460 – 1463, DOI: 10.1143/PTP.75.1460.
H. Daido, Population dynamics of randomly interacting self-oscillators. I, Progress of Theoretical Physics 77(3) (1987), 622 – 634, DOI: 10.1143/PTP.77.622.
H. Daido, Order function and macroscopic mutual entrainment in uniformly coupled limit-cycle oscillators, Progress of Theoretical Physics 88(6) (1992), 1213 – 1218, DOI: 10.1143/ptp/88.6.1213.
D. D. Davis, S. C. Mettler and D. J. DiGiovanni, Experimental data on the fiber fuse, in Proceedings of 27th Annual Boulder Damage Symposium: Laser-Induced Damage in Optical Materials, Vol. 2714 (1995), 202 – 210, DOI: 10.1117/12.240382.
D. D. Davis, S. C. Mettler and D. J. DiGiovanni, A comparative evaluation of fiber fuse models, in Proceedings of Conference ‘Laser-Induced Damage in Optical Materials', Vol. 2966 (1996), 592 – 606, DOI: 10.1117/12.274220.
E. M. Dianov, V. M. Mashinsky, V. A. Myzina, Y. S. Sidorin, A. M. Streltsov and A. V. Chickolini, Change of refractive index profile in the process of laser-induced fibre damage, Soviet Lightwave Communications 2 (1992), 293 – 299.
E. M. Dianov, I. A. Bufetov and A. A. Frolov, Destruction of silica fiber cladding by the fuse effect, Optics Letters 29(16) (2004), 1852 – 1854, DOI: 10.1364/OL.29.001852.
E. M. Dianov, V. E. Fortov, I. A. Bufetov, V. P. Efremov, A. E. Rakitin, M. A. Melkumov, M. I. Kulish and A. A. Frolov, High-speed photograpy, spectra, and temperature of optical discharge in silica-based fibers, IEEE Photonics Technology Letters 18(6) (2006), 752 – 754, DOI: 10.1109/LPT.2006.871110.
E. M. Dianov, V. E. Fortov, I. A. Bufetov, V. P. Efremov, A. A. Frolov, M. Ya. Schelev and V. I. Lozovoi, Detonation-like mode of the destruction of optical fibers under intense laser radiation, JETP Letters 83(2) (2006), 75 – 78, DOI: 10.1134/S002136400602007X.
F. Domingues, A. R. Frias, P. Antunes, A. O. P. Sousa, R. A. S. Ferreira and P. S. André, Observation of fuse effect discharge zone nonlinear velocity regime in erbium-doped fibres, Electronics Letters 48(20) (2012), 1295 – 1296, DOI: 10.1049/el.2012.2917.
F. Domingues, P. Antunes, N. Alberto and P. André, Refractive index sensor based on optical fiber void cavities produced by the catastrophic fuse effect, Advanced Photonics 2013, SM4C.3 (2013), DOI: 10.1364/SENSORS.2013.SM4C.3.
M. F. F. Domingues, T. B. Paixí£o, E. F. T. Mesquita, N. Alberto, A. R. Frias, R. A. S. Ferreira, H. Varum, P. F. C. Antunes and P. S. André, Liquid hydrostatic pressure optical sensor based on micro-cavity produced by the catastrophic fuse effect, IEEE Sensors Journal 15(10) (2015), 5654 – 5658, DOI: 10.1109/JSEN.2015.2446534.
M. F. Domingues, C. A. Rodriguez, J. Martins, N. Alberto, C. Marques, M. Ferreira, P. André and P. Antunes, Cost effective in-line optical fiber fabry perot interferometric pressure sensor, Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS), JTu4A.15 (2017), DOI: 10.1364/IPRSN.2017.JTu4A.15.
G. B. Ermentrout, Synchronization in a pool of mutually coupled oscillators with random frequencies, Journal of Mathematical Biology 22(1) (1985), 1 – 9, DOI: 10.1007/BF00276542.
M. Fací£o, A. Rocha and P. André, Traveling solution of the fuse effect in optical fibers, IEEE Journal of Lightwave Technology 29(1) (2011), 109 – 114, DOI: 10.1109/JLT.2010.2094602.
D. P. Hand and P. St. J. Russell, Solitary thermal shock waves and optical damage in optical fibers: the fiber fuse, Optics Letters 13(9) (1988), 767 – 769, DOI: 10.1364/OL.13.000767.
D. P. Hand and P. St. J. Russell, Soliton-like thermal shock-waves in optical fibers: origin of periodic damage tracks, Fourteenth European Conference on Optical Communication, pp. 111 – 114 (1988), https://ieeexplore.ieee.org/document/93535.
C. Hayashi, Nonlinear Oscillations in Physical Systems, Chapter 2, McGraw-Hill, Inc., New York (1964), https://press.princeton.edu/books/hardcover/9780691639222/nonlinear-oscillations-in-physical-systems.
S. Jiang, L. Ma, X. Fan, B. Wang and Z. He, Real-time locating and speed measurement of fibre fuse using optical frequency-domain reflectometry, Scientific Reports 6 (2016), Article number 25585, DOI: 10.1038/srep25585.
R. Kashyap and K. J. Blow, Observation of catastrophic self-propelled self-focusing in optical fibres, Electronic Letters 24(1) (1988), 47 – 49, DOI: 10.1049/el:19880032.
R. Kashyap, Self-propelled self-focusing damage in optical fibres, in Lasers'87: Proceedings of 10th International Conference on Lasers and Applications, pp. 859 – 866, STS Press, McLean (1988).
R. Kashyap, High average power effects in optical fibres and devices, in Proceedings of ‘Reliability of Optical Fiber Components, Devices, Systems, and Networks', Vol. 4940, pp. 108–117 (2003), DOI: 10.1117/12.477395.
Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39, pp. 420 – 422, Springer-Verlag, New York (1975), DOI: 10.1007/BFb0013365.
Y. Kuramoto, Cooperative dynamics of oscillator community, Progress of Theoretical Physics Supplement 79 (1984), pp. 223 – 240, DOI: 10.1143/PTPS.79.223.
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, Tokyo (1984), DOI: 10.1007/978-3-642-69689-3.
K. Kurokawa and N. Hanzawa, Fiber fuse propagation and its suppression in hole assisted fibers, IEICE Transactions on Communications E94-B(2) (2011), 384 – 391, DOI: 10.1587/transcom.E94.B.384.
G.-R. Lin, M. D. Baiad, M. Gagne, W.-F. Liu and R. Kashyap, Harnessing the fiber fuse for sensing applications, Optics Express 22(8) (2014), 8962–8969, DOI: 10.1364/OE.22.008962.
A. Rocha, P. Antunes, M. F. Domingues, M. Fací£o and P. André, Detection of fiber fuse effect using FBG sensors, IEEE Sensors Journal 11(6) (2011), 1390 – 1394, DOI: 10.1109/JSEN.2010.2094183.
H. Sakaguchi and Y. Kuramoto, A soluble active rotator model showing phase transitions via mutual entrainment, Progress of Theoretical Physics 76(3) (1986), 576 – 581, DOI: 10.1143/PTP.76.576.
H. Sakaguchi, S. Shinomoto and Y. Kuramoto, Local and global self-entrainments in oscillator lattices, Progress of Theoretical Physics 77(5) (1987), 1005 – 1010, DOI: 10.1143/PTP.77.1005.
H. Sakaguchi, Cooperative phenomena in coupled oscillator systems under external fields, Progress of Theoretical Physics 79(1) (1988), 39 – 46, DOI: 10.1143/PTP.79.39.
S. Shinomoto and Y. Kuramoto, Phase transitions in active oscillator systems, Progress of Theoretical Physics 75(5) (1986), 1105 – 1110, DOI: 10.1143/PTP.75.1105.
Y. Shuto, Cavity formation modeling of fiber fuse in single-mode optical fibers, Advances OptoElectronics 2017 (2017), Article ID 5728186, 1 – 11, DOI: 10.1155/2017/5728186.
Y. Shuto, Cavity generation modeling of fiber fuse in single-mode optical fibers, in P. Steglich and F. De Matteis (eds.) Fiber Optics – From Fundamentals to Industrial Applications, Chapter 4, IntechOpen, London (2019), DOI: 10.5772/intechopen.74877.
Y. Shuto, S. Yanagi, S. Asakawa, M. Kobayashi and R. Nagase, Fiber fuse phenomenon in stepindex single-mode optical fibers, IEEE Journal of Quantum Electronics 40(8) (2004), 1113 – 1121, DOI: 10.1109/JQE.2004.831635.
S. H. Strogatz, From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena 143 (2000), 1 – 20, DOI: 10.1016/S0167-2789(00)00094-4.
J. Sun, Q. Xiao, D. Li, X. Wang, H. Zhang, M. Gong and P. Yan, Fiber fuse behavior in kWlevel continuous-wave double-clad field laser, Chinese Physics B 25(1) (2016), 014204-1–014204-4, DOI: 10.1088/1674-1056/25/1/014204.
S. Todoroki, Quantitative evaluation of fiber fuse initiation probability in typical single-mode fibers, Optical Fiber Communication Conference (OFC2015) (Optical Society of America) W2A.33 (2015), DOI: 10.1364/OFC.2015.W2A.33.
S. Todoroki, Quantitative evaluation of fiber fuse initiation with exposure to arc discharge provided by a fusion splicer, Scientific Reports 6 (2016), Article number 25366, DOI: 10.1038/srep25366.
S. Todoroki, Origin of periodic void formation during fiber fuse, Optics Express 13(17) (2005), 6381 – 6389, DOI: 10.1364/OPEX.13.006381.
S. Todoroki, Transient propagation mode of fiber fuse leaving no voids, Optics Express 13(23) (2005), 9248 – 9256, DOI: 10.1364/OPEX.13.009248.
S. Todoroki, In situ observation of modulated light emission of fiber fuse synchronized with void train over hetero-core splice point, PLoS ONE 3(9) (2008), e3276, DOI: 10.1371/journal.pone.0003276.
S. Todoroki, Fiber fuse propagation modes in typical single-mode fibers, Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013 (OFC2013) (Optical Society of America), JW2A.11 (2013), DOI: 10.1364/NFOEC.2013.JW2A.11.
S. Todoroki, Fiber Fuse: Light-Induced Continuous Breakdown of Silica Glass Optical Fiber, Chapter 3, NIMS Monographs, Springer, Tokyo (2014), DOI: 10.1007/978-4-431-54577-4.
S. Todoroki, Threshold power reduction of fiber fuse propagation through a white tightbuffered single-mode optical fiber, IEICE Electronics Express 8(23) (2011), 1978 – 1982, DOI: 10.1587/elex.8.1978.
K. Tsujikawa, K. Kurokawa, N. Hanzawa, S. Nozoe, T. Matsui and K. Nakajima, Hole-assisted fiber based fiber fuse terminator supporting 22W input, Optical Fiber Technology 42 (2018), 24 – 28, DOI: 10.1016/j.yofte.1018.02.009.
B. van der Pol, The nonlinear theory of electric oscillations, Proceedings of the Institute of Radio Engineers 22(9) (1934), 1051 – 1086, DOI: 10.1109/JRPROC.1934.226781.
B. van der Pol, On "relaxation oscillations” I, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2 (1926), 978 – 992, DOI: 10.1080/14786442608564127.
A. T. Winfree, Biological rhythms and behavior of populations of coupled oscillators, Journal of Theoretical Biology 16 (1967), 15 – 42, DOI: 10.1016/0022-5193(67)90051-3.
S. I. Yakovlenko, Plasma behind the front of a damage wave and the mechanism of laser-induced production of a chain of caverns in an optical fibre, Quantum Electronics 34(8) (2004), 765 – 770, DOI: 10.1070/QE2004v034n08ABEH002845.
S. I. Yakovlenko, Mechanism for the void formation in the bright spot of a fiber fuse, Laser Physics 16(3) (2006), 474 – 476, DOI: 10.1134/S1054660X0603008X.
S. I. Yakovlenko, Physical processes upon optical discharge propagation in optical fiber, Laser Physics 16(9) (2006), 1273 – 1290, DOI: 10.1134/S1054660X06090015.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
