Theory of the circular harmonics expansion method for multiple-optical-fiber system

The circular harmonics expansion method that has been applied to solve the modal characteristics of multiple-core fiber structure is given a formal derivation. The validity of the field expansion expression in the method is rigorously proved by expanding the Green's function for the scalar wave equation in a surface integral equation into circular harmonics. It is found that for coupled round cores only the modified Bessel functions of the second kind are needed in the expansion, and that the modified Bessel functions of the first kind do not appear in the expansion.<
>