Engineering of self-bending surface plasmon polaritons through Hermite-Gaussian mode expansion

Surface plasmon polaritons have received much attention over the last decades in photonics or nanotechnology due to their inherent high sensitivity to metal surface variations (e.g., presence of adsorbates or changes in the roughness). It is thus expected that they will find promising major applications in widely cross-disciplinary areas, from material science to medicine. Here we introduce a novel theoretical framework suitable for designing new types of structured paraxial surface plasmon beams and controlling their propagation. More specifically, this method relies on a convenient Hermite--Gaussian mode expansion, which constitutes a complete basis set upon which new types of structured paraxial plasmon beams can be generated. The family of beams generated in this way presents a rather peculiar feature: they exhibit local intensity maxima at different propagation distances, which enables the control over where to place the beam energy. This, thus, opens up worthwhile pathways to manipulate light propagation along metal surfaces at the nanoscale. As a proof-of-concept, we provide numerical evidence of the feasibility of the method by analyzing the propagation of Airy-based surface plasmon polaritons along an air--silver interface.