Combined directional and contradirectional coupling in athree-waveguide configuration

A three-waveguide coupler, combining directional and contradirectional coupling between the central and side waveguides, respectively, is discussed. Coupled-mode formalism is used to examine the superposed processes both in synchronism and near synchronism. The nature of the solution is shown to depend on the relative coupling strengths of the individual processes. For stronger contradirectional coupling, the power is divided among the three output ports, at ratios closely related to the ratio of the coupling coefficients, and with a nonperiodic, slowly varying length dependence. The coupler can thus be used as a power divider without the need for a precisely special case where the directional and contradirectional coupling coefficients are equal