Plasmonic Tamm states in periodic stubbed MIM waveguides: analytical and numerical study

Abstract

We investigate both analytically and numerically the existence of localized surface modes, the so-called plasmonic Tamm states (PTSs), in a new and versatile platform based on a periodic array of metal-insulator-metal (MIM) stubs grafted along a MIM waveguide. By considering a semi-infinite structure in which we modify the length of the segment at the surface, we show the existence of surface states inside the bandgaps of the periodic structure and investigate the dependence of the localized modes as a function of the geometrical parameters and the boundary conditions applied at the surface. Three types of surface boundary conditions are considered, namely, two limiting cases of zero surface impedance (or perfect electric conductor), infinite surface impedance (or perfect magnetic conductor), and a third case where the structure is in contact with a real metal. In the latter case, we show that the existence of the interface state can be demonstrated based on topological arguments using the Zak phase. We also demonstrate that if a finite size comb-crystal is vertically grafted along a horizontal waveguide, the PTSs can be detected from the dips in the amplitudes of transmission and reflection coefficients as well as from the peaks in their delay times and the local density of states (LDOS). Our theoretical study is first performed analytically with the help of a Green’s function method, which allows the calculation of the dispersion relations of the bulk and surface modes and the LDOS, as well as the transmission and reflection coefficients of the plasmonic comb-like structure. Then, these results are confirmed by a numerical simulation utilizing a 2D finite element method. Besides providing a deep physical analysis of the PTSs, our work demonstrates the capability of the analytical method as a predictive approach in more complex structures. The proposed designs in this paper can be useful to realize highly sensitive plasmonic nanosensors.