Polarization (waves)

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

$n(r)={\begin{cases}n_{1}{\sqrt {1-2\Delta \left({r \over \alpha }\right)^{g}}}&r\leq \alpha \\n_{1}{\sqrt {1-2\Delta }}&r\geq \alpha \end{cases}}$

where $\Delta ={n_{1}^{2}-n_{2}^{2} \over 2n_{1}^{2}},$

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 ($n(r)=n_{2}\mathrm {\ for\ } r\geq \alpha$), $\alpha$ 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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