We present an improved analytical model describing transmittance of a metal-dielectric-metal (MDM) waveguide coupled to an arbitrary number of stubs. The model is built on the well-known analogy between MDM waveguides and microwave transmission lines. This analogy allows one to establish equivalent networks for different MDM-waveguide geometries and to calculate their optical transmission spectra using standard analytical tools of transmission-line theory. A substantial advantage of our model compared to earlier works is that it precisely incorporates the dissipation of surface plasmon polaritons resulting from ohmic losses inside any metal at optical frequencies. We derive analytical expressions for transmittance of MDM waveguides coupled to single and double stubs as well as to N identical stubs with a periodic arrangement. We show that certain phase-matching conditions must be satisfied to provide opt al filtering characteristics for such waveguides. To check the accuracy of our model, its results are compared with numerical data obtained from the full-blown finite-difference time-domain simulations. Close agreement between the two suggests that our analytical model is suitable for rapid design optimization of MDM-waveguide-based compact photonic devices.

We derive an exact dispersion relation for the surface plasmon polaritons of a nonlinear plasmonic waveguide using exact field decomposition of TM waves. Our approach generalizes the known linear dispersion relations to the case of a medium nonlinearity of the form ε NL = ε L + α|E| 2n. We apply the unique dispersion relation to a plasmonic waveguide with a Kerr-type nonlinearity (n = 1) and show that it enables backward-propagating modes. It also introduces critical points in the energy spectrum of surface plasmon polaritons that result in enhanced interaction of nonlinear modes with each other and external electromagnetic fields.

We present the first (to our knowledge) exact dispersion relation for the transverse-magnetic surface plasmon polariton (SPP) modes of a plasmonic slot waveguide, which is formed by a nonlinear Kerr medium sandwiched between two metallic slabs. The obtained relation is then simplified to the case of small field intensities, while retaining nonlinear terms, to derive approximate dispersion equations for the symmetric and antisymmetric SPP modes.

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We present approximate analytical expressions describing the optical bistability phenomenon in a plasmonic-gapwaveguide-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.

The design and realization of chip-scale plasmonic devices have been considerably facilitated by computational electromagnetic simulations and sophisticated nanofabrication techniques. For rapid device optimization, numerical simulations should be supplemented by simple analytical expressions capable of providing a reasonable estimate of the initial design parameters. In this paper, we develop an analytic approach and derive approximate expressions for the transmittance of metal-dielectric-metal (MDM) waveguides coupled to single, double, and periodic stub structures. Our method relies on the well-known analogy between MDM waveguides and microwave transmission lines, and enables us to use standard analytical tools in transmission-line theory. The advantage of our analytic approach over the previous studies is in accounting for the plasmon damping due to Ohmic losses and reflection-induced phase shift at the stub end. We found that the analyzed waveguide configurations can exhibit the characteristics of nanoscale filters and reflectors. We validate our analytical model by comparing its predictions with numerical simulations for several MDM waveguides with different stub configurations. The proposed theoretical results are particularly useful to reduce lengthy simulation times and will prove valuable in designing and optimizing MDM-waveguide-based photonic devices.

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