Bending loss of propagation modes in arbitrary-index profile optical fibers.

A bending loss formula for optical fibers with an axially symmetric arbitrary-index profile is derived by approximating the refractive-index profile with a staircase function. The permissible bending radius R* defined for a given value of bending loss is derived. It is deduced that R* is nearly proportional to wavelength lambda when the normalized frequency nu and the refractive-index difference Delta are fixed. The ratio of R* at two different values of nu depends only on the ratio of nu. The influence of an index dip and profile smoothing on R* is numerically evaluated.