Power-law index profile 41570 86589195 2006-11-08T22:46:41Z Sanguinity 297967 Disambig link repair 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]], 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== *[[Federal Standard 1037C]] [[Category:Fiber optics]] {{optics-stub}}