Abstract
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.
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References
Snyder, A. W. and Young, W. R. (1978) Modes of optical waveguides. J. Opt. Soc. Am., 68, 297–309.
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.
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.
Pask, C. (1979) Exact expressions for scalar modal eigenvalues and group delays in power-law optical fibres. J. Opt. Soc. Am., 69, 1599–1603.
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.
Sammut, R. A. (1979) Analysis of approximations for the mode dispersion in monomode fibres. Electron. Lett., 15, 590–1.
Marcuse, D. (1972) Theory of Dielectric Optical Waveguides, Academic Press, New York.
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.
Love, J. D. (1984) Exact, analytical solutions for modes on a graded-profile fibre. Opt. Quant. Elect., (submitted).
Yamada, R. and Inabe, K. (1974) Guided waves in an optical square-law medium. J. Opt. Soc. Am., 64, 964–8.
Gambling, W. A., Payne, D. N. and Matsumura, H. (1977) Cut-off frequency in radially inhomogeneous single-mode fibre. Electron. Lett., 13, 139–40.
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.
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.
Snyder, A. W. and Sammut, R. A. (1978) Dispersion in graded, single-mode fibres. Electron. Lett., 15, 269–71.
Snyder, A. W. (1981) Understanding monomode optical fibres. Proc. I.E.E.E., 69, 6–13.
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© 1983 Allan W. Snyder and John D. Love
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Snyder, A.W., Love, J.D. (1983). Circular fibers. In: Optical Waveguide Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2813-1_16
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DOI: https://doi.org/10.1007/978-1-4613-2813-1_16
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