Emergence of Negative Dispersion of Electromagnetic Waves on a Solid-State Structure Containing a Plasma-Like Medium and Plasmonic Metasurfaces
Abstract
This study provides a detailed theoretical and numerical account of the dispersion properties of p-polarized electromagnetic waves in a complex multilayered solid-state structure. The system under investigation is a six-layer stack featuring two isotropic plasmonic metasurfaces, separated by dielectric spacers and supported by a semi-infinite plasma-like substrate—either a heavily doped semiconductor or a metal. By combining the transfer-matrix formalism with Maxwell’s equations and rigorous boundary conditions, we derive exact dispersion relations for both surface and bulk-surface eigenmodes. Our numerical results point to a cascaded hybridization process between the fundamental metasurface resonances and the surface plasmon-polariton (SPP) modes inherent to the substrate. A particularly significant finding is that adjusting the effective oscillator strengths of the metasurfaces triggers a pronounced dispersion asymmetry. This occurs when one metasurface exhibits a capacitive response while the other becomes effectively inductive. Such an electrodynamic imbalance leads to an anomalous negative frequency dispersion regime characterized by the propagation of backward waves. Furthermore, we demonstrate that modifying the dielectric environment or swapping the semiconductor substrate for a metallic one shifts the regions of resonant interaction, offering a versatile means of controlling the spectral intervals of mode splitting. These findings establish a solid theoretical groundwork for the design of tunable nanophotonic devices and the generation of distributed internal feedback, which is essential for the emergence of absolute electromagnetic wave instabilities in beam-coupled systems.
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