power-law index profile

For optical fibers, a class of graded-index profiles characterized by
where n(r) is the nominal refractive index as a function of distance from the fiber axis, n₁ is the nominal refractive index on axis, n₂ is the refractive index of the homogeneous cladding (n(r) = n₂ when r ), is the core radius, and g is a parameter that defines the shape of the profile. Note 1: is often used in place of g. Hence, this is sometimes called an alpha profile. Note 2: 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. When g increases without limit, the profile tends to a step-index profile.