For optical fibers, a power-law index profile is 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 , n ₁ is the nominal refractive index on axis, n ₂ is the refractive index of the homogeneous cladding (n (r ) = n ₂ when r ≥ α), α is the core radius, and g is a parameter that defines the shape of the profile.

Note 1: α 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.

Source: from Federal Standard 1037C