Computations are made of the mode parameter in a cylindrical dielectric waveguide whose permittivity is a function of the radius. The mode parameter, whose sign determines whether a mode is HE or EH, is computed as a function of the propagation constant and the values of the permittivities on each side of a cylindrical boundary in the waveguide. Fields in the waveguide are then computed as a function of the mode parameter. The expressions for the fields are valid when variations in the permittivity are large or when the permittivity is not continuous. The approach is demonstrated by computations of the mode parameter in two waveguides: one whose permittivity has a discontinuity at the interface between core and cladding and one whose permittivity is continuous everywhere. The characteristics of the propagation modes that arise from each case are described and compared with those of a cylindrical dielectric waveguide whose permittivity is constant in the core region and in the cladding region.
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