Power-law index profile

For optical fibers, a power-law index profile is an index of refraction profile characterized by where

is the nominal refractive index as a function of distance from the fiber axis,

is the nominal refractive index on axis,

is the refractive index of the cladding, which is taken to be homogeneous (

is a parameter that defines the shape of the profile.

Hence, this is sometimes called an alpha profile.

For this class of profiles, multimode distortion is smallest when

takes a particular value depending on the material used.

For most materials, this optimum value is approximately 2.

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