Power-law index profile

For optical fibers, a power-law index profile is an index of refraction profile characterized by

:$$n(r) = egin{cases} n_1 sqrt{1-2Deltaleft({r over alpha} ight)^g} & r le alpha\ n_1 sqrt{1-2Delta} & r ge alpha end{cases}where$$Delta = {n_1^2 - n_2^2 over 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 mathrm{ for } r ge alpha), $$alpha is the core radius, and $$g is a parameter that defines the shape of the profile. $$alpha is often used in place of $$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.

ee also

*Graded-index fiber

References

*Federal Standard 1037C