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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 69, Iss. 12 — Dec. 1, 1979
  • pp: 1663–1671

Fundamental (HE11) modes of graded optical fibers

Allan W. Snyder and Rowland A. Sammut  »View Author Affiliations

JOSA, Vol. 69, Issue 12, pp. 1663-1671 (1979)

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The HE11 fields of weakly guiding fibers with graded refractive-index profiles are nearly identical to the fields of a step-index fiber with dimensionless frequency V¯ and radius ρ¯, where V¯ and ρ¯ are found by an elementary variational method. The results are remarkably accurate, with errors of a fraction of a percent at most, so that a simple, closed-form expression for the HE11 fields of graded fibers is now available. The step-fiber approximation is more widely applicable than the Gaussian field approximation which is inadequate for small V and for describing the evanescent field. However, the variational procedure also complements the Gaussian field approximation by providing analytical expressions for the spot size and propagation constant in several profiles of interest.

© 1980 Optical Society of America

Allan W. Snyder and Rowland A. Sammut, "Fundamental (HE11) modes of graded optical fibers," J. Opt. Soc. Am. 69, 1663-1671 (1979)

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  1. J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976).
  2. A. Ankiewicz and C. pask, "Geometric optics approach to light acceptance and propagation in graded-index fibres," Opt. Quantum Electron. 9, 87–109 (1977).
  3. W. Streiffer and C.N. Kurtz, "Scalar analysis of radially inhomogeneous guiding media," J. Opt. Soc. Am. 57, 779–786 (1967)
  4. D. Gloge and E. A. J. Marcatili, "Multimode theory of graded core fibres," Bell Syst. Tech. J. 52, 1563–1578 (1973).
  5. A. W. Snyder and J. D. Love, "Attenuation coefficient for rays in graded fibres with absorbing cladding," Electron. Lett. 12, 255–257 (1976).
  6. A. W. Snyder and J. D. Love, "Attenuation coefficient for tunnelling leaky rays in graded fibers," Electron. Lett. 12, 324–326 (1976).
  7. A. W. Snyder and W. R. Young, "Modes of optical waveguides," J. Opt. Soc. Am. 68, 297–309 (1978).
  8. R. Yamada, T. Meiri, and N. Okamoto, "Guided waves along an optical fiber with parabolic index profile," J. Opt. Soc. Am. 67, 96–103 (1977).
  9. W. A. Gambling and H. Matsumura, "Propagation in radially-inhomogeneous single-mode fibre," Opt. Quantum Electron. 10, 31–40 (1978).
  10. J. D. Love, "Power series solutions of the scalar wave equation for cladded, power-law profiles of arbitrary exponent," Opt. Quantum Electron. 11, September, 1979.
  11. W. A. Gambling and H. Matsumura, "Simple characterization factor for practical single-mode fibres," Electron. Lett. 13, 691–693 (1977).
  12. D. Marcuse, "Loss analysis of single-mode fiber splices," Bell Syst. Tech. J. 56, 703–718 (1977).
  13. D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers," J. Opt. Soc. Am. 68, 103–109 (1978).
  14. M. O. Vassell, "Calculation of propagating modes in a graded-index optical fibre," Opto-electronics 6, 271–286 (1974); see also references cited therein.
  15. M. Matsuhara, "Analysis of TEM modes in dielectric waveguides, by a variational method," J. Opt. Soc. Am. 63, 1514–1517 (1973).
  16. T. Okoshi and K. Okamoto, "Analysis of wave propagation in inhomogeneous optical fibers using a variational method," IEEE Trans. Microwave Theory Tech. MTT-22, 938–945 (1974).
  17. K. Okamoto and T. Okoshi, "Vectorial wave analysis of inhomogeneous optical fibers using finite element method," IEEE Trans. Microwave Theory Tech. MTT-26, 109–114 (1978).
  18. S. E. Miller, "Light propagation in generalized lens-like media," Bell Syst. Tech. J. 44, 2017–2064 (1965).
  19. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1112.
  20. The HE11 mode is the mode with the largest value of β, or equivalently, the smallest value of U.
  21. A. W. Snyder, "Asymptotic expressions for eigenfunctions and eigenvalues of dielectric or optical waveguides," IEEE Trans. Microwave Theory Tech. MTT-17, 1130–1138 (1969).
  22. C. Pask and R. A. Sammut, "Developments in the theory of fibre optics," Proc. IREE (Aust.) 40, 89–101 (1979).
  23. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  24. A. W. Snyder, "Mode propagation in an optical waveguide," Electron. Lett. 6, 561–562 (1970).

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