Aberrations in curved graded-index fibers

Graded-index fibers can be efficiently used as image relays and therefore it is necessary to study the aberrations in the images transmitted through these media. Since curvature in fibers is inevitable, aberrations in curved graded-index fibers are also important. In this paper, we have obtained explicit expressions for the second- and third-order aberration coefficients in curved fibers which reduce to the ones for the straight fiber as the radius of curvature of the fiber tends to infinity. It is shown by numerical calculations that the total aberrations (up to third order) in a graded-index fiber depend critically on the values of grading parameters α and β. It is also shown that for small values of grading parameter, α ∼ 2 cm−1, curvature effects are significant for radii of curvatures less than ∼ 25 cm, whereas for larger values of the grading parameter, α ∼ 50 cm−1, curvature affects the aberrations for radii of curvatures less than about 10 cm.