Application of the coupled-mode theory to a specialized graded-index optical fiber coupler

A specialized coupler formed by two identical multimode graded-index slab fibers is described. This special coupler can be used to examine the tilt or the roughness of a surface through the reflected beam. It may also find applications as a mode filter, an alignment sensor, or a feed component of an optical monopulse tracking radar. Coupled-mode theory is generalized for this application. The coupling length for maximum power transfer of the higher-order modes from the excited to the coupled fiber, leaving as much power of the lowest mode as possible to continue in the excited fiber, is computed. The fields are computed at the output of the system for incident optical beams with different axial displacements and beams launched on axis with tilted wavefronts. This desired coupling length is shown to be substantially independent of characteristics of the incident light beam. To compute the fields propagated through the tapered section introduced to separate the slab fibers, the stairwise approximation is used, and mode matching is used to connect the fields at the junctions between the successive segments. An optimum taper to separate the coupled fibers, with minimal perturbation of the fields, is present at the right-hand end of the coupling section.