Modulation of hybrid plasmon phonon polaritons mode in circular cylindrical three-layer graphene waveguide

In this present research article, we have investigated analytically the characteristics of the fundamental mode of hybrid surface plasmon phonon polariton (HSPPhPs) mode in a circular cylindrical three-layer graphene (CTLG) waveguide structure. The dispersion equation of HSPPhPs is derived by using Maxwell’s equations and continuity conditions of tangential components of electric and magnetic fields in cylindrical geometry. The dispersion curve has been illustrated and thoroughly examined in relation to the effects of temperature and chemical potential (${\mu }_c$) of graphene, as well as variations in the thickness of silicon dioxide (SiO₂) and hexagonal boron nitride (hBN) layers, and found that in the presence of hBN, the effective mode index exhibits hyperbolic behavior with wave number. Up to the first Reststrahlen band (∼830.57 cm⁻¹), it varies slightly with graphene temperature; increasing graphene's (${\mu }_c$) lowers the index, while a thicker hBN layer reduces it, whereas the index increases with SiO₂ layer thickness. Also, we looked at how the CTLG waveguide structure is affected by the electric field distribution, phase speed, and propagation length.