Propagating beam theory of optical fiber cross coupling

Evanescent field coupling between parallel optical waveguides is treated by the propagating beam method. This method utilizes Fourier analysis to generate the modal properties of optical waveguides from numerical solutions to the paraxial-wave equation. Previous applications have been for single waveguides. Detailed results are presented here for a variety of coupled waveguide pairs: identical slab waveguides, identical and nonidentical single-mode optical fibers, and identical few-mode optical fibers. Results include propatation constants and eigenfunctions for the normal modes of the coupled systems. The difference between the propagation constants of the corresponding normal modes determines the coupling length for the mode pair; whereas the eigenfunctions determine the extent of power transfer. The results obtained establish the applicability of the propagating beam method to the study of coupling in a general class of practical waveguides