We present approximate analytical expressions describing the optical bistability phenomenon in a plasmonic-gap-waveguide-based nonlinear device. The device is formed by a metal–dielectric–metal (MDM) waveguide perpendicularly coupled to a stub structure that is filled with an optically nonlinear medium. Among the recently reported studies on nonlinearity-induced bistability in plasmonic nanostructures, our work stands out because of its pure analytic approach and the considered device geometry. The scattered-field technique that we employ here is hinged on the concepts of circuit theory and the characteristic-impedance model for single-mode MDM waveguides. By properly accounting for surface-plasmon damping, multiple reflections, and the Kerr effect, we obtain a fairly accurate parametric relation connecting the input and output intensities of the device. The impact of changing the operating wavelength and geometrical parameters of the stub on the bistable switching thresholds and the hysteresis loop width is demonstrated using a number of numerical examples. The derived relation is useful for rapid design optimization of plasmonic switches and memories.
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