Theoretical macrobending loss in single-mode transmission through a uniform index fiber-optic cable

Abstract

The macrobending loss of propagating waves in optical fibers is studied here by employing simple toroidal coordinates (r, θ, ϕ) for the governing Maxwell equations of electromagnetism, the solution for which is expressed by the central axial component Πϕ of the Hertz vector Π. The refractive indices of the core and its cladding are supposed uniform all along the length of the cable. Effects of coating, Jacketing and the effect of elastic strain in the fiber are not considered. Knowing that the bending losses are of different nature when the radius of curvature R exceeds or is less than a certain critical value Rc, the study is accordingly divided in to two parts. Firstly, when R > Rc wave guide action holds, and it is shown through an example that it is small, varying linearly with the bending angle ϕ of the cable and practically independent of R. On the other hand, when R < Rc, leaking waves are propagated and the problem is remodeled by a leaking ring source of EM waves in a medium consisting of the cladding only. The analysis of the model results in a bending loss formula that varies as ϕ3 and depends on R by a factor of the form e−αR/R.