parabolic refractive-index profile

In round optical fibers, a refractive-index profile in which the refractive index of the core is a quadratic function of the distance from the optical fiber axis, i.e., the variation is such that the refractive index within the core at any distance from the axis, r, is given by the relation n_r = n_I(1 − br²)^1/2 where n₁ is the refractive index at r = 0, i.e., at the axis, r is the radial distance from the axis, and b is a constant given by the relation b = 2 Δ/a² where a is the value of r for which the refractive index becomes uniform, i.e., the radius of the core or half of the core diameter, and Δ is given by the relation Δ = (n²₁ − n²₂)/2n²₁ where n₁ again is the refractive index at r = 0, i.e., at the axis, and n₂ is the refractive index at the outer edge of the core, i.e., at r = a. Note: For most optical fibers, the refractive indices n₁ and n₂ are nearly equal. Therefore, Δ is also given by the relation Δ = 1 − (n₂/n₁) where the parameters are as defined above. Because n_r = n₂...