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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