Bistable optical systems are of considerable interest to produce high-speed optical signal-processing devices. Among them, those that use a nonlinear optical medium are attractive because they allow the lowest possible switching time. By the use of a suitable electromagnetic resonance, the bistability threshold can be lowered to a reasonnable value, for the incident power. Keeping in mind that a bistable optical system should be well adapted to optical integration in a planar geometry, one is naturally confronted to a corrugated waveguide filled with a nonlinear (Kerr) medium.