- Source: Power-law index profile
For optical fibers, a power-law index profile is an index of refraction profile characterized by
n
(
r
)
=
{
n
1
1
−
2
Δ
(
r
α
)
g
r
≤
α
n
1
1
−
2
Δ
r
≥
α
{\displaystyle 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
Δ
=
n
1
2
−
n
2
2
2
n
1
2
,
{\displaystyle \Delta ={n_{1}^{2}-n_{2}^{2} \over 2n_{1}^{2}},}
and
n
(
r
)
{\displaystyle n(r)}
is the nominal refractive index as a function of distance from the fiber axis,
n
1
{\displaystyle n_{1}}
is the nominal refractive index on axis,
n
2
{\displaystyle n_{2}}
is the refractive index of the cladding, which is taken to be homogeneous (
n
(
r
)
=
n
2
f
o
r
r
≥
α
{\displaystyle n(r)=n_{2}\mathrm {\ for\ } r\geq \alpha }
),
α
{\displaystyle \alpha }
is the core radius, and
g
{\displaystyle g}
is a parameter that defines the shape of the profile.
α
{\displaystyle \alpha }
is often used in place of
g
{\displaystyle g}
. Hence, this is sometimes called an alpha profile.
For this class of profiles, multimode distortion is smallest when
g
{\displaystyle 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
{\displaystyle g}
, the profile becomes a step-index profile.
See also
Graded-index fiber
References
This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.
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