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{1-2\Delta\left({r \over \alpha}\right)^g} & r \le \alpha\\ n_1 \sqrt{1-2\Delta} & r \ge \alpha \end{cases}

where

and 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 the core radius, and is a parameter that defines the shape of the profile. is often used in place of . 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. In the limit of infinite, the profile becomes a step-index profile.

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