Modal evolution in asymmetric three- and four-layer plasmonic waveguides

Through the employment of a novel approach in solving the dispersion for the three-layer plasmonic waveguides, considering lossy metals, we demonstrate that, besides well-known modes, the complete dispersion always contains high-lossy periodic solutions. Consideration of these solutions is shown to be crucial for the understanding of every aspect of dispersion evolution at broad spectral range when the thickness of the middle layer is varied. In particular, we show that generally considered modes of the three-layer waveguide transform into the single interface modes via interaction with high-lossy periodic solutions. Furthermore, the negative index mode is shown to experience a transition between low- and high-lossy regimes depending on the waveguide's thickness. Our results, avoiding complicated analytical analysis, perfectly integrate and importantly complement past theoretical works.