Rigorous analysis of the coupling between two nonparallel optical fibers

The rigorous electromagnetic analysis of the coupling between two nonparallel optical-fiber waveguides is developed for the first time. Green´s theorem, involving the dyadic Green´s function of the fiber guiding the incident mode, is used to formulate the electric-field integral equation inside the second fiber. By applying the entire-domain Galerkin technique and by utilizing the generalized addition theorem for cylindrical waves for nonparallel axis translation, which is derived by the authors, this equation is analytically transformed into a system of coupled integral equations for the spectral weights of the field on the basis of TE and TM cylindrical vector wave functions. The Neumann-series iterative procedure is adopted to solve this system and obtain analytical expressions for the field scattering coefficients, which are sufficiently accurate for weakly coupled fibers