Power-law index profile explained

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\Delta = {n ^{2} _{1} - n ^{2} _{2} \over 2 n ^{2 },} _{1}

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} 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.

See also

• Graded-index fiber