Power-law index profile

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

$n(r)=\{\begin{array}{cc}{n}_1\sqrt{1-2\mathrm{\Delta }{\left(\frac{r}{\alpha }\right)}^g}& r\le \alpha \\ n_1\sqrt{1-2\mathrm{\Delta }}& r\ge \alpha \end{array}$

where $\mathrm{\Delta }=\frac{n_1^2-n_2^2}{2n_1^2},$

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 ($n(r)=n_2\mathrm{f}\mathrm{o}\mathrm{r}r\ge \alpha$), $\alpha$ 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

• Template:FS1037C

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