2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Journal of Lightwave Technology
Volume 18 Number 2, February 2000

Table of Contents for this issue

Complete paper in PDF format

Comprehensive Theory of Dispersion in Graded-Index Optical Fibers

G. Yabre Member, IEEE

Page 166.

Abstract:

This paper presents a theoretical investigation on the dispersion in graded-index silica glass fibers under overfilled launching with equal excitation of modes. This theory incorporates both chromatic effect and modal contribution which takes not only the modal delay into account but also the distributed loss and mode-coupling. Random microbends are considered to be the most dominant source of coupling. All index perturbations and intrinsic core diameter variations are assumed to be negligible, but they could readily be included without changing the basic structure of the model. The 3-dB bandwidth is analyzed through the study of the fiber transfer function which introduces the wavelength and modal effects as two separate filter functions. The formal derivation of the chromatic transfer function is analytical. On the other hand, the modal transfer function is obtained by numerically solving the power flow equation in the frequency domain using Crank-Nicholson method. As an application, the results are illustrated showing, in particular, the influence of the fiber core/outside diameters, for the first time.

References

  1. R. E. Epworth, "The phenomenon of modal noise in analog and digital optical fiber systems", in Proc. 4th ECOC, Genova, Italy, 1978, pp.  492-501. 
  2. R. J. S. Bates, D. M. Kuchta and K. P. Jackson, "Improved multimode fiber link BER calculations due to modal noise and non self-pulsating laser diodes", Optic. Quantum Electron., vol. 27, pp.  203- 224, 1995.
  3. D. G. Cunningham, D. C. Hanson, M. C. Nowell and C. S. Joiner, "Developing leading-edge fiber-optic network link standards", The Hewlett-Packard J., pp.  62- 73, Dec.  1997.
  4. " Information technology-Generic cabling for consumer premises", ISO/IEC 11801: 1995 (E),
  5. " Mode scrambler requirements for overfilled launching conditions to multimode fibers", EIA/TIA 455-54A,
  6. R. Olshansky and D. B. Keck, "Pulse broadening in graded-index optical fibers", Appl. Opt., vol. 15, pp.  483- 491, 1976.
  7. M. J. Adams, D. N. Payne, F. M. E. Sladen and A. H. Hartog, "Optimum operating wavelength for chromatic equalization in multimode optical fibers", Electron. Lett., vol.  14, pp.  64- 66, 1978.
  8. Z. Haas and M. A. Santoro, "A mode-filtering scheme for improvement of the bandwidth-distance product in multimode fiber systems", J. Lightwave Technol., vol. 11, pp.  1125- 1131, 1993.
  9. L. Raddatz, I. H. White, D. G. Cunningham and M. C. Nowell, "An experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links", J. Lightwave Technol., vol. 16, pp.  324- 331, 1998.
  10. M. J. Yadlowsky and A. R. Mickelson, "Distributed loss and their effects on time-dependent propagation in multimode fibers", Appl. Opt., vol. 32, pp.  6664- 6678, 1993.
  11. D. Gloge, "Impulse response of clad optical multimode fibers", Bell Syst. Tech. J., vol. 52, pp.  801- 817, 1973.
  12. R. Olshansky, "Mode coupling effects in graded-index optical fibers", Appl. Opt., vol. 14, pp.  935- 945, 1975.
  13. R. Olshansky, "Multiple- index profiles", Appl. Opt., vol. 18, pp.  683- 689,  1979.
  14. A. R. Mickelson and M. Eriksrud, "Mode-continuum approximation in optical fibers", Opt. Lett., vol. 7, pp.  573- 574, 1982.
  15. G. J. Meslener, "Chromatic induced distortion of modulated monochromatic light employing direct modulation", IEEE J. Quantum Electron. , vol. QE-20, pp.  1208- 1216, 1984.
  16. S. E. Miller, and A. G. Chenoweth, Eds., Optcal Fiber Telecommunications, New York : Academic, 1979.
  17. S. D. Personick, "Baseband linearity and equalization in fiber optic digital communication systems", Bell Syst. Tech. J., vol. 52 , pp.  1175- 1195, 1973.
  18. D. G. Duff, "Computer-aided design of digital lightwave systems ", IEEE J. Select. Areas Commun., vol. SAC-2, pp.  171- 185, 1984.
  19. J. Gimlett and N. Cheung, "Dispersion penalty analysis for LED/single-mode fiber transmission systems", J. Lightwave Technol., vol. LT-4, pp.  1381- 1392, 1986.
  20. T. P. Lee, C. A. Burrus, D. Marcuse, A. G. Dentai and R. J. Nelson, "Measurement of beam parameters of index-guided and gain-guided single-frequency InGaAsP injection lasers", Electron. Lett., vol. 18, pp.  902- 904, 1982.
  21. E.-G. Neumann, Single-Mode Fibers, Berlin : Germany : Springer-Verlag, 1988, pp.  246- 247. 
  22. D. Gloge, "Optical power flow in multimode fibers", Bell Syst. Tech. J., vol. 51, pp.  1767- 1783, 1972.
  23. R. Olshansky and D. A. Nolan, "Mode-dependent attenuation of optical fibers: Excess loss", Appl. Opt., vol. 15, pp.  1045 - 1047, 1976.
  24. D. Gloge, "Weakly guiding fibers", Appl. Opt., vol. 10, pp.  2252- 2258, 1971.
  25. D. Marcuse, "Coupled mode theory of round optical fibers ", Bell Syst. Tech. J., vol. 52, pp.  817- 843, 1973.
  26. J. N. Kutz, J. A. Cox and D. Smith, "Mode mixing and power diffusion in multimode optical fibers", J. Lightwave Technol., vol. 16, pp.  1195- 1202, 1998.
  27. R. Olshansky, "Distortion losses in cabled optical fibers ", Appl. Opt., vol. 14, pp.  20- 21, 1975.
  28. K. Nagano and S. Kawakami, "Measurement of mode conversion coefficients in graded-index fibers", Appl. Opt., vol. 19, pp.  2426 - 2434, 1980.
  29. W. B. Gardner, "Microbending loss in optical fibers", Bell Syst. Tech. J., vol. 54, pp.  457- 465, 1975.
  30. M. Rousseau and L. Jeunhomme, "Numerical solution of the coupled-power equation in step-index optical fibers", IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp.  577- 585, 1977.
  31. M. Rousseau and L. Jeunhomme, "Optimum index profile in multimode optical fiber with respect to mode coupling", Opt. Commun., vol. 23, pp.  275- 278,  1977.
  32. T. P. Tanaka and S. Yamada, "Numerical solution of power flow in multimode W-type optical fibers", Appl. Opt., vol. 19, pp.  1647 - 1652, 1980.
  33. W. Hermann and D. U. Wiechert, "Refractive index measurement on PCVD-bulk material", Philips Research Laboratories, Aachen, Germany, Internal Rep., 1988 .
  34. S. D. Personick, "Time dispersion in dielectric waveguides ", Bell Syst. Tech. J., vol. 50, pp.  843- 859, 1971.
  35. R. van Laere, S. Alers and G. Kuyt, "Metingen aan vezels uit een voorvorm met een bewuste dip", Plasma Optical Fiber BV, Eindhoven, The Netherlands , Intern. Rep. TM97/171, 1997 .
  36. M. K. Soudagar and A. A. Wali, "Pulse broadening in graded-index optical fibers: Errata", Appl. Opt., vol. 32, p.  6678 , 1993.