Power-law Index Profile

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

:$n(r) = \begin n_1 \sqrt & r \le \alpha\\ n_1 \sqrt & r \ge \alpha \end$
where
$\Delta = ,$

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 ($n(r)=n_2 \mathrm r \ge \alpha$), $\alpha$ 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

References

*

Fiber optics

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