Nonlinear Tamm states in layered metaldielectric metamaterials

Surface modes appear as a special type of waves localized near an interface separating two different media. In optics, linear electromagnetic surface waves are known to exist at an interface separating homogeneous and periodic dielectric media [1] as well as in layered structures containing thin metal films [2–4]. The interest in the study of nonlinear electromagnetic surface waves has been renewed, and it was shown theoretically [5–7] and experimentally [8–11] that nonlinearity-induced self-trapping of light may become possible near the edge of a one-dimensional waveguide array leading to the formation of nonlinear Tamm states (see also the review paper [12]). In particular, it was found that the self-trapped surface modes acquire some novel properties in the nonlinear regime, and they can only exist above a certain threshold power and, for the same value of the power, up to two different surface modes can exist simultaneously. Recently, it was shown that strongly confined plasmonic surface modes can be formed at the termination of metal–dielectric metamaterials [13–15]. One of the requirement is to employ binary structures to reduce the lattice symmetry [15]. In this Letter we demonstrate that such terminated metal–dielectric metamaterials can support a variety of transverse electric (TE) polarized surface modes in the nonlinear regime, and we analyze the properties of the nonlinear Tamm states in such structures, including their stability. We also compare our results with the predictions of the effective medium approach. The structure we consider consists of a periodic metal– dielectric stack occupying half space at 0 z > with a thin nonlinear layer at 0 z = (see Fig. 1). To describe this structure, we employ Maxwell’s equations: