A unified approach to coupled-mode phenomena

A unified approach is presented for the treatment of various coupled-mode phenomena in two parallel waveguides, This approach is summarized in a set of four coupled equations [see (8) or (12) in the paper], which is derived directly from Maxwell's equations. The equations are further simplified when applied to special cases such as evanescent coupling and grating-assisted coupling between parallel waveguides [e.g., reduced to a set of two equations], In particular, for evanescently coupled waveguides, the equations reduce to the familiar vectorial coupled-mode equations. For grating-assisted waveguides the equations agree with earlier treatments, although, in some cases, may include extra terms which were omitted previously. Considering the special case of perturbations in a single waveguide, the equations in the examples coincide with those given elsewhere in earlier works. The reduction to scalar equations or extension to multiwaveguide systems is straightforward.