Application of coupled-mode theory to nonparailel sections of directional couplers

Coupled-mode theory is widely used for the analysis of directional couplers (see, e.g. Ref. 1) as well as diode laser arrays (see, e.g. Ref. 2). In this type of analysis one usually considers a section consisting of two (or more) parallel waveguides situated close enough so that the power transfer among neighboring guides can occur. However, in many cases, such as in Y-coupled arrays3 or as In directional couplers, where the guides must be brought together before the parallel section and then separated at the output end of the coupler, it is also important to consider nonparallel sections of the device.