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A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles

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Abstract

A numerical technique, based on transforming the scalar wave equation to a finite interval before discretization is applied, is proposed for the solution of the scalar wave equation defining the modal fields and propagation constants of optical fibres. It is used to compute the propagation constants and modal fields of weakly guiding fibres of circular cross-section when the refractive index profile has a Gaussian or smoothed-out form. The smoothed-out profiles are studied because they vary continuously from the Gaussian to the step profile. Results are compared with and shown to be accurately approximated by simply explicit functions, dependent only on the fibre parameter.

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Authors and Affiliations

  1. Division of Mathematics and Statistics, CSIRO, PO Box 1965, 2601, Canberra City, ACT, Australia

    R. S. Anderssen & F. R. De Hoog

  2. Department of Applied Mathematics, Institute of Advanced Studies, Australian National University, 2600, Canberra, ACT, Australia

    J. D. Love

Authors
  1. R. S. Anderssen
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  2. F. R. De Hoog
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  3. J. D. Love
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Anderssen, R.S., De Hoog, F.R. & Love, J.D. A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles. Opt Quant Electron 13, 217–224 (1981). https://doi.org/10.1007/BF00620324

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  • DOI: https://doi.org/10.1007/BF00620324

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