Power-law index profile
Encyclopedia
For optical fiber
s, a power-law index profile is an index of refraction profile characterized by
where
and
is the nominal refractive index as a function of distance from the fiber axis, 
is the nominal refractive index on axis, 
is the refractive index of the cladding
, which is taken to be homogeneous (
), 
is the core radius, and 
is a parameter that defines the shape of the profile. 
is often used in place of 
. Hence, this is sometimes called an alpha profile.
For this class of profiles, multimode distortion is smallest when
takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limit
of infinite
, the profile becomes a step-index profile
.
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
s, a power-law index profile is an index of refraction profile characterized by
where
and
is the nominal refractive index as a function of distance from the fiber axis, is the nominal refractive index on axis, is the refractive index of the claddingCladding (fiber optics)
Cladding is one or more layers of material of lower refractive index, in intimate contact with a core material of higher refractive index. The cladding causes light to be confined to the core of the fiber by total internal reflection at the boundary between the two. Light propagation in the...
, which is taken to be homogeneous (
), is the core radius, and is a parameter that defines the shape of the profile. is often used in place of . Hence, this is sometimes called an alpha profile.For this class of profiles, multimode distortion is smallest when
takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the limitLimit of a function
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input....
of infinite
, the profile becomes a step-index profileStep-index profile
For an optical fiber, a step-index profile is a refractive index profile characterized by a uniform refractive index within the core and a sharp decrease in refractive index at the core-cladding interface so that the cladding is of a lower refractive index. The step-index profile corresponds to a...
.