Core/cladding power distribution, propagation constant, and group delay: Simple relation for power-law graded-index fibers

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Abstract
Using Brown’s identity and the scalar wave equation, we found a simple relation between the normalized propagation constant, normalized group delay, and the portion of the power propagating in the core. It is valid for each particular LP mode in power-law graded-index fibers. In the case of quadratic index variation, it states that the latter two quantities are identical. Our relation yields correction terms for previously published equations and it may be helpful to check numerical calculations.

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