Considerable use is made of power-law refractive-index profiles in fiber optics. These profiles have simple scaling properties that are exploited in this paper to obtain formulas for the exact modal propagation constants and group delays. When an infinite profile is assumed, the results of the exact, WKB, and geometric optics theories are all shown to agree. This conclusion remains valid when linear material dispersion is included. The effect of the cladding is discussed. The results are correct for noncircular fibers of power-law type.
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C. Pask (1979) studied this question.
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