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For optical fibers, a power-law index profile is an index of refraction profile characterized by
where Δ = n 1 2 − n 2 2 2 n 1 2 , {\displaystyle \Delta ={n_{1}^{2}-n_{2}^{2} \over 2n_{1}^{2}},}
and n {\displaystyle n} is the nominal refractive index as a function of distance from the fiber axis, n 1 {\displaystyle n_{1}} is the nominal refractive index on axis, n 2 {\displaystyle n_{2}} is the refractive index of the cladding, which is taken to be homogeneous = n 2 f o r r ≥ α {\displaystyle n=n_{2}\mathrm {\ for\ } r\geq \alpha } ], α {\displaystyle \alpha } is the core radius, and g {\displaystyle g} is a parameter that defines the shape of the profile. α {\displaystyle \alpha } is often used in place of g {\displaystyle g}. Hence, this is sometimes called an alpha profile.
For this class of profiles, multimode distortion is smallest when g {\displaystyle g} takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limit of infinite g {\displaystyle g} , the profile becomes a step-index profile.