Editing Power-law index profile

{{short description|Index of refraction profile in fiber optics}}

For [[optical fiber]]s, a '''power-law index profile''' is an [[index of refraction]] profile characterized by 

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

and <math> n(r)</math> is the nominal refractive index as a function of distance from the [[fiber axis]], <math>n_1</math> is the nominal refractive index on axis, <math>n_2</math> is the refractive index of the [[Cladding (fiber optics)|cladding]], which is taken to be homogeneous (<math>n(r)=n_2 \mathrm{\ for\ } r \ge \alpha</math>), <math>\alpha</math> is the [[Fiber_optics#Principle_of_operation|core]] radius, and <math>g</math> is a parameter that defines the shape of the profile. <math>\alpha</math> is often used in place of <math>g</math>. Hence, this is sometimes called an '''alpha profile'''. 

For this class of profiles, [[multimode distortion]] is smallest when <math>g</math> takes a particular value depending on the material used. For most materials, this optimum value is approximately 2. In the [[Limit of a function|limit]] of infinite <math>g</math>, the profile becomes a [[step-index profile]].

==See also==
*[[Graded-index fiber]]

==References==
*{{FS1037C}}

[[Category:Fiber optics]]


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