Coupled-Mode Theory for Optical Fibers

A set of coupled-mode equations is derived to describe mode propagation in uniform and slightly nonuniform cylindrical optical-fiber systems. The coupling between fibers of an array made up of n identical fibers each at the vertex of a polygon and one at the center, which is not necessarily the same as its n neighbors, is determined. Examples of this array are two fibers, three fibers in a row, and a hexagonal array with a fiber in the center. Very simple expressions for the coupling coefficients are presented. Mode coupling on a lossy fiber is investigated and a simple expression for the loss of a HE11 mode is given.