Abstract
This work presents an alternative fast and simple method for the design of a graded refractive index profile of silica few-mode optical fibers (FMFs) with enlarged core diameter that extremely improves mode effective area, and low differential mode delay (DMD). We demonstrate some results of refractive index profile optimization for 16-LP-mode FMF with enlarged core diameter up to 42 μm and mode effective area more 130 μm2 under DMD reduction less 120 ps/km all over “C”-band and less 40 ps/km at λ = 1550 nm region. We also propose approach for simulation of the deviation of “real” optical fiber geometry from the optimized form and rigorous method for analysis of large core complicated optical fiber. Here, FMF core asymmetrical ellipticity together with the refractive index profile distortions were considered. They were set and simulated by data from reports of the real commercially available laser-optimized multimode optical fibers of TIA/ISO Cat. OM2+/OM3 refractive index profile measurements, performed by lab optical fiber analyzer kit. We present results of researches of considered FMF DMD spectral curve degradation due to described core geometry deviation from the optimized form. It was noticed, that unlike to only refractive index local fluctuations, FMF core non-circularity strongly distorts higher-order mode field distribution that affects to spectral mode delay curves and may lead to critical total DMD increasing.
Similar content being viewed by others
References
Adams, M.J.: An Introduction to Optical Waveguides. Wiley, New York (1981)
An, H., Tang, Y., McNamara, P., Fleming, S.: Characterization of surface crystallization in Ge doped graded-index silica glass. Opt. Express 12(6), 1055–1060 (2004)
Andreev, V.A., Burdin, V.A., Bourdine, A.V., Dashkov, M.V., Volkov, K.A.: Research of potentiality of nonlinear effects mitigation by considerable increasing of optical fiber core diameter. In: Proceedings of SPIE, vol. 9533, pp. 953306-1–953306-8 (2015)
Ankiewicz, A., Peng, G.-D.: Generalized Gaussian approximation for single-mode fibers. IEEE J. Lightwave Technol. 10(1), 22–27 (1992)
Bogolyubov, A.N., Krasilnikov, A.V., Sveshnikov, A.G.: Finite difference method for solution of the problem of waveguide system synthesis. Math. Model. 12(1), 13–24 (2000)
Bogolyubov, A.N., Butkarev, I.A., Sveshnikov, A.G.: Synthesis of optical fibers. Radiotechnika 12, 4–12 (2004)
Bottacchi, S.: Multi-Gigabit Transmission Over Multimode Optical Fibre. Theory and Design Methods for 10GbE Systems. Wiley, New York (2006)
Bourdine, A.V.: Design of refractive index profile for multimode optical fibers with low differential mode delay. J. Optoelectron. Eng. 1(1), 5–13 (2013a)
Bourdine, A.V.: Modeling and simulation of piecewise regular multimode fiber links operating in a few-mode regime. Adv. Opt. Technol. 2013, 469389-1–469389-18 (2013b)
Bourdine, A.V.: Fast and simple method for evaluation of polarization correction to propagation constant of arbitrary order guided modes in optical fibers with arbitrary refractive index profile. Math. Probl. Eng. 2015, 801243-1–801243-11 (2015)
Bourdine, A.V., Praporshchikov, D.E., Yablochkin, K.A.: Investigation of defects of refractive index profile of silica graded-index multimode fibers. In: Proceedings of SPIE, vol. 7992, pp. 799206-1–799206-8 (2011)
Bourdine, A.V., Delmukhametov, O.R.: Method for computing of higher order mode transmission parameters based on combination modified Gaussian approximation and finite element method. Telecommunications (Telecommunicacii) 9, 33–40 (2010)
Bourdine, A.V., Delmukhametov, O.R.: Calculation of transmission parameters of the launched higher-order modes based on the combination of a modified Gaussian approximation and a finite element method. Telecommun. Radio Eng. 72(2), 111–123 (2013)
Bourdine, A.V., Yablochkin, K.A.: Research of refractive index profile defects multimode optical fibers of communication cables. Infokommunikacionnye Tehnologii 2, 22–27 (2010)
Bourdine, A.V., Burdin, V.A., Delmukhametov, O.R., Sultanov, A.H.: Algorithm for singlemode optical fiber chromatic dispersion computing based on mixed finite element method. Infocommunicacionnye Technologii 7(2), 13–16 (2009)
Burdin, V.A.: Methods for computation of Sellmeier coefficients for dispersion analysis of silica optical fibers. Infokommunikacionnye Tehnologii 4(2), 30–34 (2006)
Chebaane, S., Fathallah, H., Seleem, H., Machhout, M.: Proposed raised cosine FMF for dispersion management in next-generation optical networks. IEEE Photonics J. 8(1), 7901812-1–7901812-11 (2016)
Chebaane, S., Fathallah, H., Seleem, H., Machhout, M.: Trenched raised cosine FMF for differential mode delay management in next generation optical networks. Opt. Commun. 408, 15–20 (2018)
Chiang, K.S.: Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Opt. Quantum Electron. 26, S113–S134 (1994)
Ellis, D.: The nonlinear Shannon limit and the need for new fibres. In: Proceedings of SPIE, vol. 8434, pp. 84340H-1–84340H-11 (2012)
Essiambre, R.-J., Tkach, R.W.: Capacity trends and limits of optical communication networks. Proc. IEEE 100(5), 1035–1055 (2012)
EXFO NR-9200 Optical Fiber Analyzer. Datasheet. EXFO (1999)
Ferreira, F., Sánchez, Ch., Sygletos St., Ellis, A.D.: On the feasibility of mode-division multiplexed transmission over few-mode fibres. In: Proceedings of International Microwave and Optoelectronics Conference (IMOC), pp. 1–5 (2017)
Ferreira, F.M., Fonseca, D., da Silva, H.J.A.: Design of few-mode fibers with M-modes and low differential mode delay. IEEE J. Lightwave Technol. 32(3), 353–360 (2014)
Gradstein, I., Ryjik, I.: Tables of Integrals. GIFML, Moscow (1963)
Holmes, M.J., Spirit, D.M., Payne, F.P.: New Gaussian-based approximation for modeling non-linear effects in optical fibers. IEEE J. Lightwave Technol. 12(2), 193–201 (1994)
Kaminow, I.P., Li, T., Willner, A.E.: Optical Fiber Telecommunications V. B: Systems and Networks. Elsevier, San-Diego (2008)
Kawano, K., Kitoh, T.: Introduction to Optical Waveguide Analysis. Solving Maxwell’s Equations and the Shrodinger Equation. Wiley, New York (2001)
Kholodny, S.D.: Methods for tests and diagnostics of cables and wires. Energoatomizdat, Moscow (1991)
Kleev, A.I., Manenkov, A.B., Rozhnev, A.G.: Numerical methods for calculations of the dielectric waveguides. Fiber optics waveguides. Special methods. J. Commun. Technol. Electron. (Radotehnika i Elecktronika) 38(5), 769–788 (1993)
Koshiba, M., Maruyama, S., Hirayama, K.: A vector finite element method with the high-order mixed interpolation-type triangular elements for optical waveguiding problems. J. Lightwave Technol. 12(3), 495–502 (1994)
Kubota, H., Morioka, T.: Few-mode optical fiber for mode-division multiplexing. Opt. Fiber Technol. 17(5), 490–494 (2011)
Maeda, Y., Montalti, F.: Optical fibres, cables and systems. ITU-T Manual. International Telecommunication Union, Geneva (2009)
Meher, H., Hosain, S.I.: Variational approximations for single-mode graded-index fibers: some interesting applications. J. Opt. Commun. 24(1), 25–30 (2003)
Mizuno, T., Takara, H., Sano, A., Miyamoto, H.: Dense space-division multiplexed transmission systems using multi-core and multi-mode fiber. IEEE J. Lightwave Technol. 34(2), 582–592 (2016)
Morioka, T.: Recent progress in space-division multiplexed transmission technologies. In: Proceedings of OFC/NFOEC, pp. OW4F.2-1–OW4F.2-2 (2013)
OFS: Few mode optical fiber series. OFS Fitel LLC. Product catalog. http://fiber-optic-catalog.ofsoptics.com/viewitems/few-mode-optical-fiber-series/few-mode-optical-fiber-series1? (2016). Accessed 31 July 2018
Okamoto, K.: Fundamentals of Optical Waveguides. Academic Press, San Diego (2000)
Oksanen, M.I., Lindell, I.V.: Variational analysis of anisotropic graded-index optical fibers. IEEE J. Lightwave Technol. 7(1), 87–91 (1989)
Richardson, D.J., Fini, J.M., Nelson, L.E.: Space-division multiplexing in optical fibers. Nat. Photonics 7(5), 354–362 (2013)
Shariati, B., Klonidis, D., Comellas, J., Velasco, L., Tomkos, I.: Spectrally and spatially flexible optical networks: recent developments and findings. In: Proceedings of International Conference on Transparent Optical Networks (ICTON), pp. We.C1.1-1–We.C1.1-4 (2018)
Sharma, A., Hosain, S.I., Ghatak, A.K.: The fundamental mode of graded-index fibres: simple and accurate variational methods. Opt. Quantum Electron. 14(1), 7–15 (1982)
Sillard, P.: Next-generation fibers for space-division-multiplexed transmission. IEEE J. Lightwave Technol. 35(5), 1092–1099 (2015)
Sillard, P., Molin, D., Bigot-Astruc, M., Amezcua-Correa, A., de Jongh, K., Achten, F.: 50 μm Multimode fibers for mode division multiplexing. IEEE J. Lightwave Technol. 34(8), 1672–1677 (2016)
Snyder, A., Love, J.: Optical Waveguide Theory. Springer, New York (1983)
Tewari, R., Hosain, S.I., Thyagarajan, K.: Scalar variational analysis of single mode fibers with Gaussian and smoothed-out profiles. Opt. Commun. 48(3), 176–180 (1983)
TIA/EIA-455-44B (FOTP-44B): Refractive Index Profile, Refracted Ray Method. IEC 60793 and ITU Recommendation G.651
Wintzer, P.J., Neilson, D.T., Chraplyvy, A.R.: Fiber optic transmission and networking: the previous 20 and the next 20 years. Opt. Express 26(18), 24190–24239 (2018)
Wu, M-Sh, Lee, M.-H., Tsai, W.-H.: Variational analysis of single-mode graded-core W-fibers. IEEE J. Lightwave Technol. 14(1), 121–125 (1996)
Acknowledgements
The reported study was funded by RFBR according to the research Project No. 16-37-60015 mol_a_dk.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This article is part of the Topical Collection on Optical Wave and Waveguide Theory and Numerical Modelling, OQTNM 2018.
Guest Edited by Stefan Helfert, Manfred Hammer, Dirk Schulz.
Rights and permissions
About this article
Cite this article
Bourdine, A.V., Burdin, V.A. & Delmukhametov, O.R. Simulation and research of few-mode optical fiber DMD degradation due to geometry deviation from optimized form. Opt Quant Electron 51, 153 (2019). https://doi.org/10.1007/s11082-019-1872-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-1872-2