  We report on a theoretical and numerical investigation of the switching of
power in new hybrid models of nonlinear coherent couplers consisting of optical
slab waveguides with various orders of nonlinearity. The first model consists
of two guides with second-order instead of the usual third-order
susceptibilities as typified by the Jensen coupler. This second-order system is
shown to have a power self-trapping transition at a critical power greater than
the third-order susceptibility coupler. Next, we consider a mixed coupler
composed of a second-order guide coupled to a third-order guide and show that,
although it does not display a rigorous self-trapping transition, for a
particular choice of parameters it does show a fairly abrupt trapping of power
at a lower power than in the third-order coupler. By coupling this mixed
nonlinear pair to a third, purely linear guide, the power trapping can be
brought to even lower levels and in this way a satisfactory switching profile
can be achieved at less than one sixth the input power needed in the Jensen
coupler.
