Transmission line resonance technique for eccentric core optical fibers

Abstract

In several cases optical fibers in telecommunications have cores of non circular geometry. Fibre optic deformations appear in optical fibres for many reasons. Optical fibre core ellipticity for example where the fibre optic core is not perfectly circular due to fibre optic manufacturing tolerances, is measured and often is a problem. Optical fibre core eccentricity, where the fibre core is not on the axis of the fibre, but it is offset by a small length. This is another issue and very important for ensuring performance low loss splices and connector losses. Both of ellipticity and eccentricity are specified in accordance to international standards for fibre optic manufacturing telecommunications grade fibres.The present paper studies ellipticity and core eccentricity specifically and presents a new method for analysing their effect. We present an extension of the transmission line technique as a means of studying such fibers and deriving necessary parameters. Conformal mapping on the other hand is a simple mathematical tool by which we can generate sets of orthogonal two-dimensional coordinate systems. Shortly a conformal map of Cartesian two-dimensional space is defined by any analytical function W(z) where z, w, are: z = x + jy, W = θ + j φThe function deriving by the conformal mapping transformation h(θ,φ)=| ∂w∂z |=1| ∂z∂w |, can be used in order to define ∇A→ and ∇×A→ where A→ is the magnetic or electric field in the derived orthogonal coordinate system. Useful conformal maps for fiber optics applications should have the property that the equation θ(x, y) = constant, is forming closed curves in a Cartesian two-dimensional space (x,y).If θ(x, y) = constant represents a set of co-eccentric circles, we obtain the normal case of conventional fibers with circular cores. If θ(x, y) = constant represents a set of eclipses, we are have the formation of elliptic core optical fibers. If θ(x, y) = constant represents a set of eccentric circles, we are led to the formation of optical fibers with eccentric core. The method presented in the current paper uses the transmission line technique together with conformal mapping as tools for the study of various shaped optical fiber cores and the effect of eccentricity on the fundamental modes of eccentric core fibers.