Analysis of hybrid plasmon-phonon-polariton modes in hBN/graphene/hBN stacks for mid-infrared waveguiding.

Guiding mid-infrared (mid-IR) signals provide wide-ranging applications including chemical sensing, thermal imaging, and optical waveguiding. To manipulate mid-IR signals on photonic chips, it is critical to build a waveguide that provides both sub-diffraction field confinement and low loss. We present a mid-IR waveguide made up of a multilayer graphene/hexagonal boron nitride (hBN) stacking (MLGhS) and a high-refractive index nanowire. The guided mode of the proposed waveguide structure is formed by coupling the fundamental volume plasmon polariton with the fundamental hyperbolic phonon polariton in hBN, and is then modulated by a high-index nanowire. Interestingly, we found that the effective index, propagation length, and mode area of the guided mode vary as the dependences of N-1, N, and N3/2, where N is the number of graphene layers. In addition, an anomalous result, which reveals Lp and Am monotonously decrease as Fermi energy increases that is not observed in conventional graphene plasmon waveguides, occurs in the present structure. The modal properties are analyzed by altering geometry effects and material parameters, and by crossing the upper Reststrahlen band of hBN from the wavevector k = 1,300 to 1,500 cm-1. Furthermore, crosstalk between adjacent waveguides are investigated to assess the degree of integration. The proposed idea not only provides a potential approach for designing tunable and large-area photonic integrated circuits, but it also has the potential to be extended to other 2D materials such as silicone, germanene, and stanene.