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Applied Optics

Applied Optics


  • Vol. 17, Iss. 24 — Dec. 15, 1978
  • pp: 3990–3998

Light propagation in graded-index optical fibers

M. D. Feit and J. A. Fleck, Jr.  »View Author Affiliations

Applied Optics, Vol. 17, Issue 24, pp. 3990-3998 (1978)

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An accurate numerical method is described for solving the Helmholtz equation for a general class of optical fibers. The method yields detailed information about the spatial and angular properties of the propagating beam as well as the modal propagation constants for the fiber. The method is applied to a practical graded-index fiber under the assumptions of both coherent and incoherent illumination. A spectral analysis of the calculated field shows that leaky modes are lost and steady-state propagating conditions are established over a propagation distance of a fraction of a meter.

© 1978 Optical Society of America

Original Manuscript: April 21, 1978
Published: December 15, 1978

M. D. Feit and J. A. Fleck, "Light propagation in graded-index optical fibers," Appl. Opt. 17, 3990-3998 (1978)

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  1. For a comprehensive survey of research in this field see, for example, Optical Fiber Technology, D. Gloge, Ed. (IEEE Press, New York, 1976).
  2. See also J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976).
  3. Examples of modal theory can be found in D. Gloge, E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563 (1973); D. Gloge, IEEE Trans. Microwave Theory Tech. MIT-23, 106 (1975); D. Marcuse, Theory of Dielectrical Optical Waveguides (Academic, New York, 1964); and R. Olshansky, D. B. Keck, Appl. Opt. 15, 483 (1976). [CrossRef] [PubMed]
  4. EVA Buffered Corguide Fibers Product Bulletin No. 2 (Telecommunication Products Dept., Corning Glass Works, Corning, N.Y. 14830, 1May1976).
  5. See, for example, J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976). [CrossRef]
  6. Operator splitting results in a separation of the propagation and phase updating parts of the calculation. Since the operators inside the bracket in Eq. (7) do not commute, splitting must involve an approximation that holds for limited propagation distances Δz. By symmetrizing the splitting, the commutation error is further reduced. For a more complete discussion of this question see the Appendix of Ref. 5.
  7. For a comprehensive review of the application of the Fresnel approximation to problems in nonlinear optics see, for example, J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975). [CrossRef]
  8. This follows from the sampling theorem; see, for example, E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Engle-wood Cliffs, N.J., 1974), pp. 99–102.
  9. It is more usual to write n as n = n0[1 − Δ(r/a)2] rather than in the form of Eq. (19). However, in the present development, the peak refractive index plays no role whereas the cladding index does.
  10. See, for example, P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965). [CrossRef]
  11. It has been shown that beam aberration and an erratic focusing pattern are general consequences of propagation in a nonquadratic lenslike medium. M. D. Feit, J. A. Fleck, J. R. Morris, J. Appl. Phys. 48, 3301 (1977). [CrossRef]
  12. S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973). [CrossRef]
  13. E. O. Brigham, Proc. IEEE 61, 141 (1973).
  14. We have expressed the modal z dependences in the form exp(−ikz + iβnz) in order to emphasize the similarity between the waveguide problem and the quantum mechanical problem of a particle in a potential well.
  15. J. M. Blatt, V. F. Weisskoff, Theoretical Nuclear Physics (Wiley, New York, 1952), p. 64.
  16. The short decay length for the leaky mode radiation may seem surprising in the light of previous discussion of the subject. See, for example, A. W. Snyder, Appl. Phys. 4, 273 (1974); and A. W. Snyder, D. J. Mitchell, J. Opt. Soc. Am. 64, 599 (1974). [CrossRef]

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