Definitions

# Power-law index profile

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

$n\left(r\right) =$
begin{cases} n_1 sqrt{1-2Deltaleft({r over alpha}right)^g} & r le alpha n_1 sqrt{1-2Delta} & r ge alpha end{cases} where $Delta = \left\{n_1^2 - n_2^2 over 2 n_1^2\right\},$

and $n\left(r\right)$ 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 ($n\left(r\right)=n_2 mathrm\left\{ for \right\} r ge alpha$), $alpha$ 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.
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