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Power-law index profile

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

n(r) =
begin{cases} n_1 sqrt{1-2Deltaleft({r over alpha}right)^g} & r le alpha n_1 sqrt{1-2Delta} & r ge alpha end{cases} where Delta = {n_1^2 - n_2^2 over 2 n_1^2},

and n(r) is the nominal refractive index as a function of distance from the fiber axis, n_1 is the nominal refractive index on axis, n_2 is the refractive index of the cladding, which is taken to be homogeneous (n(r)=n_2 mathrm{ for } r ge alpha), alpha is the core radius, and g is a parameter that defines the shape of the profile. alpha is often used in place of g. Hence, this is sometimes called an alpha profile.

For this class of profiles, multimode distortion is smallest when 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, the profile becomes a step-index profile.

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