Analysis of modal cutoffs of radially inhomogeneous two-core optical fibers by circular harmonics expansion method

A scalar theory based on generalization of the circular harmonics expansion method combined with the finite element method is formulated to determine cutoff values for higher order normal modes on the two-core fiber with radially inhomogeneous core index profiles under the weakly guiding approximation. The validity of the field expansion expression in the derived generalized circular harmonics expansion method is proved rigorously by expanding the Green's function for the Laplace equation in a surface integral equation into generalized circular harmonics. Numerical examples are given for the two identical-core cases with power-law core index profiles. Our method is shown to be able to provide exact cutoff values for the touching-core case.