Vector normal modes on two-core optical fibers. I. The normal mode solutions

A vector theory based on the circular harmonics expansion method combined with the finite-element method is formulated to solve the guided normal modes on the two-core fiber with radially inhomogeneous core index profiles. Numerical examples are given for the two-identical-core cases with power-law core index profiles. Polarization patterns for the vector modes on the strongly guiding two-core fiber structure, such as that of a fused coupler made with biconical tapering technology under weakly fusing condition, are presented.