# Step-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 power-law index profile with the profile parameter approaching infinity. The step-index profile is used in most single-mode fibers[1] and some multimode fibers.[2]

A step-index fiber is characterized by the core and cladding refractive indices n1 and n2 and the core and cladding radii a and b. Examples of standard core and cladding diameters 2a/2b are 8/125, 50/125, 62.5/125, 85/125, or 100/140 (units of µm). The fractional refractive-index change ${\displaystyle \triangle \,={\frac {n_{1}-n_{2}}{n_{1}}}\ll \ 1}$. The value of n1 is typically between 1.44 and 1.46, and ${\displaystyle \triangle }$ is typically between 0.001 and 0.02.

Step-index optical fiber is generally made by doping high-purity fused silica glass (SiO2) with different concentrations of materials like titanium, germanium, or boron.

Pulse dispersion in a step index optical fiber is given by

${\displaystyle {\text{pulse dispersion}}={\frac {\triangle \ n_{1}\ \ell }{c}}\,\!}$

where

${\displaystyle \triangle \,\!}$ is the difference in refractive indices of core and cladding.
${\displaystyle n_{1}\,\!}$ is the refractive index of core
${\displaystyle \ell \,\!}$ is the length of the optical fiber under observation
${\displaystyle c}$ is the speed of light