A reformulation of coupled mode theory for multimode guides with application to a specialized graded-index optical fiber coupler.

摘要

Coupled mode theory for parallel dielectric waveguides is reformulated for the case of a multimode multiwaveguide system. This theory is derived on the basis of a generalized reciprocity theorem. Analytical relations among the coupling coefficients are derived and applied to the coupled mode equations. It is found that even for lossless identical fibers the coupling coefficients from the m{dollar}sp{lcub}th{rcub}{dollar} mode in fiber "a" to the n{dollar}sp{lcub}th{rcub}{dollar} mode in fiber "b" and from the n{dollar}sp{lcub}th{rcub}{dollar} mode in fiber "b" to the m{dollar}sp{lcub}th{rcub}{dollar} mode in fiber "a" described by K{dollar}sbsp{lcub}rm m,n{rcub}{lcub}rm(a,b){rcub}{dollar} and K{dollar}sbsp{lcub}rm n,m{rcub}{lcub}rm (b,a){rcub}{dollar}, respectively, are not related simply as complex conjugates. With the appropriate use of the overlap integrals, the new theory satisfies both the reciprocity and the power conservation relations exactly. The symmetric (hermitian) orthogonality of the supermode eigenvectors with a weighting matrix given by the overlap intergrals matrix is demonstrated in the lossy (and lossless) case.; A system consisting of two identical coupled graded-index slab fibers is studied. 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 for different graded-index slab fibers. This desired coupling length is shown to be independent of the incident light beam. To achieve control of the effective coupling length between the two fibers, special means for separating them at some point are needed for some applications. For this purpose, a tapered section is introduced. The stairwise approximation is used to compute the fields propagated through the tapered section, and mode matching method is used to connect the fields at the junctions between the successive segments. Both linear and curved tapers are considered. The electric fields are computed at the output of the system for incident optical beams with different axial displacements and beams launched on axis with a tilted wave front. On the basis of such computations an optimum taper to separated the coupled fibers, with minimal perturbation of the fields present at the right end of the coupling section, is selected.; This special coupler of two graded-index slab fibers can be used to examine the tilt or the roughness of a surface through the reflected beam. It may find applications as a mode filter, an alignment sensor or as a feed component of an optical monopulse tracking radar.