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
where
Δ
=
n
1
2
−
n
2
2
2
n
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
f
o
r
r
≥
α
),
α
is the core radius, and
g
is a parameter that defines the shape of the profile.
α
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.
