Power coupling between step-index optical fiber sections with different refractive indices

In this paper, the guided modes as well as the radiation modes for step index optical fibers are obtained. The problem of scattering of a dominant mode in an optical fiber section due to a step transition to another fiber section of different refractive index is treated rigorously using the mode-matching technique. This technique employs the complete spectrum of modes and results in a system of singular integral equations. Using a numerical method that accounts for the kernel singularities, the system of the singular equations is converted into a finite system of linear equations, which is amenable for exact numerical solution. The radiation power due to the discontinuity as well as the power coupled to the second fiber section are evaluated. The power balance is verified, where the summation of the reflected and radiated power together with that coupled to the second fiber section are found equal to the power of the incident mode.