Graphene-based long-range SPP hybrid waveguide with ultra-long propagation length in mid-infrared range

A graphene-based long-range surface plasmon polariton (LRSPP) hybrid waveguide, which is composed of two identical outer graphene nanoribbons and two identical inner silica layers symmetrically placed on both sides of a silicon layer, is investigated using the finite-difference time-domain method. By combining the simulated results with the coupled mode perturbation theory, we demonstrate that the LRSPP and short-range SPP (SRSPP) modes originate from the coupling of the same modes of the two graphene nanoribbons. For the LRSPP mode, an ultra-long propagation length (~10 μm) and an ultra-small mode area (~10^-7A₀, where A₀ is the diffraction-limited mode area) can be simultaneously achieved. This waveguide can be used for future photonic integrated circuits functional in the mid-infrared range.