A comparison of beam propagation and coupled-mode methods: application to optical fiber couplers

We analyze the instantaneous power in the local normal modes of an optical fiber coupler with both various three-dimensional paraxial electric field propagation methods and coupled-mode theory. Our calculations show that large improvements in speed result if a low-order, split-operator, finite-difference propagation algorithm is substituted for the standard split-step fast Fourier transform technique. Further, as field evolution procedures incorporate higher-order modes, the calculated power transfer ratios agree far better with experiment than the corresponding coupled-mode predictions. The coupled-mode results however, can be improved by taking into consideration the exact shape of the refractive index profile and higher-order modes, while the approach is simple to program, and yields qualitatively correct predictions for performance trends