(49-1) 04 * << * >> * Russian * English * Content * All Issues

Calculation of parameters (propagation constant, phase and group velocities) of a graded-index optical fiber
V.A. Gladkikh 1, V.D. Vlasenko 1

1 Computer Center of the Far Eastern Branch of the Russian Academy of Sciences,
680000, Russia, Khabarovsk, Kim Yu Chen str., 65

 PDF, 772 kB

DOI: 10.18287/2412-6179-CO-1521

Pages: 30-35.

Full text of article: Russian language.

Abstract:
For a weakly guiding, single-mode, graded-index circular optical fiber, the general form of the dependence of the propagation constant on the waveguide parameter is obtained. From Maxwell's equations, an equation for the field in a light guide with a gradient refractive index profile is derived. Using a power-law refractive index profile for the first three powers and a Gaussian index profile as examples, dependences of the propagation constant, phase and group velocities on the waveguide parameter are obtained. For the ratio of the power transferred by the mode to the total stored energy per unit length of the waveguide, a dependence on the waveguide parameter is plotted. It is shown that as the waveguide parameter increases and the degree of the power-law profile increases, the fraction of transferred power decreases and approaches the fraction of transmitted power for the Gaussian profile. The results obtained can be used to create waveguides for specific applications.

Keywords:
fiber optic light guide, Gaussian profile, propagation constant, phase velocity, group velocity.

Citation:
Gladkikh VA, Vlasenko VD. Calculation of parameters (propagation constant, phase and group velocities) of a graded-index optical fiber. Computer Optics 2025; 49(1): 30-35. DOI: 10.18287/2412-6179-CO-1521.

References:
  1. Adams M. An introduction to optical waveguides. New York: Wiley; 1981. ISBN: 0471279692.
  2. Jacobsen G, Hansen JJR. Propagation constants and group delays of guided modes in graded-index fibers: a comparison of three theories. Appl Opt 1979; 18(16): 2837-2842. DOI: 10.1364/AO.18.002837.
  3. Mosley PJ, Gris-Sánchez I, Stone JM, Francis-Jones RJA, Ashton DJ, Birks TA. Characterizing the variation of propagation constants in multicore fiber. Opt Express 2014; 22(21): 25689-25699. DOI: 10.1364/OE.22.025689.
  4. Shuyupova YaO, Kotlyar VV. Finding propagation constants using the Krylov method when calculating modes of photonic waveguides [In Russian]. Computer Optics 2007; 31(1): 27-31.
  5. Strilets TS, Kotlyar VV, Nalimov AG. Simulation of waveguide modes in multilayer structures [In Russian]. Computer Optics 2010; 34(4): 487-493.
  6. Karchevskii EM, Beilina L, Spiridonov AO, Repina AI.  Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements. arXiv Preprint. 2015. Source: <https://arxiv.org/abs/1512.06764>. DOI: 10.48550/arXiv.1512.06764.
  7. Okamoto K. Fundamentals of optical waveguides. 3rd ed. Elsevier Inc; 2022. ISBN: 9780128156025.
  8. Pereira JMB, Grüner-Nielsen L, Rottwitt K, Town G, Laurell F, Margulis W. Electrooptic control of the modal distribution in a silicate fiber. Opt Express 2022; 30(8): 12474-12483. DOI: 10.1364/OE.453006.
  9. Boyd RW. Nonlinear optics. Academic Press; 2020. DOI: 10.1016/C2015-0-05510-1.
  10. Jeppesen P, Tromborg B. Optical Communications from a Fourier perspective. Fourier theory and optical fiber devices and systems. Elsevier; 2023. ISBN: 9780443238000.
  11. Listvin AV, Listvin VN, Shvyrkov DV. Optical fibers for communication lines [In Russian]. Moscow: "LESARart" Publisher; 2003. ISBN: 5-902367-01-8.
  12. Portnov EL. Optical communication cables and passive components of fiber-optic communication lines [In Russian]. Moscow: "Hotline – Telecom" Publisher; 2007. ISBN: 978-5-9912-0219-0.
  13. Polyakova EA, Badeeva EA, Murashkina TI, Badeev AV, Slavkin IE. Influence of optical fiber bends on metrological and operational characteristics of fiber-optic measuring transducers [In Russian]. Models, Systems, Networks in Economics, Technology, Nature and Society 2020; 1: 126-135. DOI: 10.21685/2227-8486-2020-1-10.
  14. Niu HW, Zhang S, Chen WH, Liu Y, Li X, Yan YX, Wang SJ, Geng T, Sun WM, Yuan LB. Optical fiber sensors based on core-offset structure: A review. IEEE Sensors J 2021; 21(20): 22388-22401. DOI: 10.1109/JSEN.2021.3110852.
  15. Barshak EV, Yavorsky MA, Vikulin DV, Lapin BP, Volyar AV, Alexeyev CN. Polarization and topological mode dispersion of optical vortices in circular optical fibers. Computer Optics 2019; 43(1): 25-34. DOI: 10.18287/2412-6179-2019-43-1-25-34.
  16. Lapin BP, Barshak EV, Vikulin DV, Alexeyev CN, Yavorsky MA. Dispersion of optical vortices in twisted elliptical-core optical fibers with torsional stresses. Computer Optics 2024; 48(1): 53-60. DOI: 10.18287/2412-6179-CO-1340.
  17. Alexeyev CN, Barshak EV, Lapin BP, Yavorsky MA. Dispersions of robust optical vortices in multihelicoidal fibers with torsional mechanic stress. J Opt Soc Am B 2024; 41(3): 610-616. DOI: 10.1364/JOSAB.513654.
  18. Osovitsky AN. Peculiarities of light scattering on the rough surface of a gradient waveguide. Bulletin of RUDN University. Series Mathematics. Computer Science. Physics 2009; 1: 96-101.
  19. Zhang S, Guo H, Liu X, Wang P, Wang Z, Liu Y. A simple refractive index measurement method for step-index fiber based on radial displacement optical power scan. Opt Commun 2023; 544: 129628. DOI: 10.1016/j.optcom.2023.129628.
  20. Unger HG. Planar optical waveguides and fibres. Oxford: Clarendon Press; 1977. ISBN: ‎978-0198561330.
  21. Listvin VN, Treshchikov VN. DWDM-systems [In Russian]. Photon Express 2012; 7: 34-37.
  22. Gladkikh VA. Calculation of the power of the electric field penetrating into the outer cladding of a weakly guiding single-mode fiber. Computer Optics 2019; 43(4): 557-561. DOI: 10.18287/2412-6179-2019-43-4-557-561.
  23. Snyder AW, Love JD. Optical waveguide theory. London, New York: Chapman and Hall; 1983. ISBN: 978-0-412-24250-2.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20