Circular fibers

  • Allan W. Snyder
  • John D. Love


We showed in the previous chapter how the modes of weakly guiding waveguides are constructed from solutions of the scalar wave equation. Here we consider fibers of circular cross-section and solve the scalar wave equation analytically for specific refractive-index profiles with axial symmetry. We pay particular attention to single-mode fibers and to the properties of the fundamental HE11 modes. One important observation for a general class of single-mode fibers with a power-law variation in core profile and a uniform cladding is that both the distribution of fundamental-mode power over the cross-section, and the maximum value of the fiber parameter V for single-mode operation depend primarily on the profile ‘volume’ and are relatively insensitive to profile shape. This volume is proportional to the integral over the core cross-section of the excess of the profile above its cladding value. Conversely, pulse dispersion on single-mode fibers depends principally on profile shape and is comparatively insensitive to the profile volume.


Fundamental Mode Eigenvalue Equation Core Radius Modify Bessel Function Distortion Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Snyder, A. W. and Young, W. R. (1978) Modes of optical waveguides. J. Opt. Soc. Am., 68, 297–309.CrossRefGoogle Scholar
  2. 2.
    Snyder, A. W. (1969) Asymptotic expressions for eigenfunctions and eigenvalues of a dielectric or optical waveguide. I.E.E.E. Trans. Microwave Theory Tech. 17, 1130–8.CrossRefGoogle Scholar
  3. 3.
    Kurtz, C. N. and Streiffer, W. (1969) Guided waves in inhomogeneous focussing media, Part I: Formulation, solution for quadratic inhomogeneity. I.E.E.E. Trans. Microwave Theory Tech., 17, 11–15.CrossRefGoogle Scholar
  4. 4.
    Pask, C. (1979) Exact expressions for scalar modal eigenvalues and group delays in power-law optical fibres. J. Opt. Soc. Am., 69, 1599–1603.CrossRefGoogle Scholar
  5. 5.
    Rudolph, H. D. and Neumann, E. G. (1976) Approximations for the eigenvalues of the fundamental mode of a step index glass fiber waveguide. Nachrichtentech. Z., 29, 328–9.Google Scholar
  6. 6.
    Sammut, R. A. (1979) Analysis of approximations for the mode dispersion in monomode fibres. Electron. Lett., 15, 590–1.CrossRefGoogle Scholar
  7. 7.
    Marcuse, D. (1972) Theory of Dielectric Optical Waveguides, Academic Press, New York.Google Scholar
  8. 8.
    Snyder, A. W. and de la Rue, R. (1970) Asymptotic solution of eigenvalue equations for surface waveguide structures. I.E.E.E. Trans. Microwave Theory Tech., 9, 650–1.CrossRefGoogle Scholar
  9. 9.
    Love, J. D. (1984) Exact, analytical solutions for modes on a graded-profile fibre. Opt. Quant. Elect., (submitted).Google Scholar
  10. 10.
    Yamada, R. and Inabe, K. (1974) Guided waves in an optical square-law medium. J. Opt. Soc. Am., 64, 964–8.CrossRefGoogle Scholar
  11. 11.
    Gambling, W. A., Payne, D. N. and Matsumura, H. (1977) Cut-off frequency in radially inhomogeneous single-mode fibre. Electron. Lett., 13, 139–40.CrossRefGoogle Scholar
  12. 12.
    Love, J. D. (1979) Power series solutions of the scalar wave equation for cladded, power-law profiles of arbitrary exponent. Opt. Quant. Elect., 11, 464–6.CrossRefGoogle Scholar
  13. 13.
    Love, J. D., Hussey, C. D., Snyder, A. W. and Sammut, R. A. (1982) Polarization corrections to mode propagation on weakly guiding fibres. J. Opt. Soc. Am., 72, 1583–91.CrossRefGoogle Scholar
  14. 14.
    Snyder, A. W. and Sammut, R. A. (1978) Dispersion in graded, single-mode fibres. Electron. Lett., 15, 269–71.CrossRefGoogle Scholar
  15. 15.
    Snyder, A. W. (1981) Understanding monomode optical fibres. Proc. I.E.E.E., 69, 6–13.Google Scholar

Copyright information

© Allan W. Snyder and John D. Love 1983

Authors and Affiliations

  • Allan W. Snyder
    • 1
  • John D. Love
    • 1
  1. 1.Institute of Advanced StudiesAustralian National UniversityCanberraAustralia

Personalised recommendations