Application of the Multipole Theory Method to the Optical-Fiber System

In this paper, the circular harmonics expansion that has been applied to solve the modal characteristics of various optical fiber structures is given a formal derivation. The multipole theory (MT) method is applied to prove that there are analytical circular harmonic expansions of infinite series convergence in each core and the cladding for the system consisting of multiple round core fibers, and there are also analytical circular harmonics expansions in some non-round cores, but there are only approximate circular harmonic expansions in the cladding of all non-round core fiber systems and the other non-round cores. The validity of the circular harmonics expansion is rigorously analyzed by the MT method.