A high figure of merit of phonon-polariton waveguide modes with hbn/SiO2/graphene /hBN ribs waveguide in mid-infrared range

Natural hyperbolic materials can confine electromagnetic waves at the nanoscale. In this study, we propose a waveguide design that combines a high quality factor (FOM) with low loss, utilizing hexagonal boron nitride and graphene and gold substrate. The waveguide consists of a dielectric rib with a graphene layer sandwiched between two hBN ribs. Numerical simulations demonstrate the existence of two guided modes in the proposed waveguide within the second reststrahlen band (1360.0 cm(-1) <omega < 1609.8 cm(-1)) of hBN. These modes are formed by coupling the hyperbolic phonon polariton (HPhP) of two hBN rib in the middle dielectric rib and are subsequently modulated by a graphene layer. Interestingly, we observe variations in four transmission parameters, namely effective length, figure of merit, device length, and propagation loss of the guided modes, with respect to the operation frequency and gate voltage. By optimizing the waveguide's geometry parameters and dielectric permittivity, the modal properties were analyzed. Simulation results indicate that optimizing the waveguide size parameters enables us to achieve a high FOM of 4.0 x 10(7). The proposed waveguide design offers a promising approach for designing tunable mid infrared range waveguides on photonic chips, and this concept can be extended to other 2D materials and hyperbolic materials.