At times, the above rigorous approach may not be intuitive. Direct applications of the numerical methods do not provide much insight into the functioning of the devices in terms of their ``special structures''. For devices made of directional couplers, i.e. formed by several more or less parallel waveguides in close vicinity, the above approaches play down the coupling viewpoint. To model such devices, a more pragmatic approximation technique - ``Coupled mode theory'' (CMT) is used [42,50,51,52]. CMT has been quite successfully employed for the analysis of wave interaction in straight waveguides [35,107] and fibers [108]. To our knowledge, most of the studies [21,54,109,110] on CMT based modeling of interaction between bent/cavity waveguides and straight waveguides (in optical regime) are based on Ref. [44], where a complex eigenfrequency model of the cavity waveguides is used. Also the interaction between the cavity and the straight waveguide is treated with a rather heuristic ``coupled point'' argument (see Eq.(48) in Ref.[44]).
Capitalizing on the availability of the real frequency analytical model of 2-D bent waveguides discussed in Chapter 2, in the subsequent sections we address the problem of wave interaction in bent-straight waveguide couplers in terms of a frequency domain spatial coupled mode theory model. This model is consistent with standard physical notions, and the coupling is modeled with systematically and rigorously derived coupled mode equations.