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• Four reststrahlen bands were observed in graphene-hBN hyperbolic metamaterials. • A "epsilon near zero and pole" can be got by adjusting the chemical potential and the filling ratio. • Dispersion properties are controlled by the chemical potential. The tunability can be improved by the filling ratio of hBN and graphene, respectively. • Ghost modes with the vibration attenuation character are presented at a special condition. We present a detailed study on the tunable propagation derived from the coupled surface plasmon–phonon polaritons (SPPPs) with the effective medium theory (EMT) in graphene-hBN metamaterials (MMs). Four reststrahlen bands (RBs) are observed, two of which mainly come from the hBN and the others originate from the effect of the graphene. The RBs frequency windows can be adjusted by the chemical potential and the filling ratio. An epsilon-near-zero-and-pole(ε NZP)hyperbolic metamaterial (HMM) is detected at the precise frequency, chemical potential and filling ratio where the HMM undergoes a completely inversion of anisotropy. We derive the relative dispersion relation and demonstrate that the propagation of SPPP modes can be regulated by modifying the chemical potential. In addition, the tunability of the graphene-hBN MMs also can be improved by changing the thicknesses of the hBN and the number of graphene sheets. The energy-flux density in the graphene-hBN MM seriously deviates from its wave vector and can be localized at a certain depth. Besides, the ghost SPPP modes with the oscillation-attenuation character are observed at some special conditions through checking the distribution of electric fields. The attenuation total reflection (ATR) measurement is established to examine these SPPP modes. The numerical results show that the observation of each SPPP modes requires different conditions dictated by material parameters and the polarization direction of the incident light. [ABSTRACT FROM AUTHOR]

• Found two highly confined Dyakonov-like polaritons. • Saw remarkable walk-off angle. • Dyakonov-like polaritons are very easily excited. • Energy-flux density of polariton is highly located at the surface. Two Dyakonov-like polaritons (DLPs) were found in the hexagonal boron nitride (hBN). DLP-I lies in the lower reststrahlen band (RB-I) where the hBN is a hyperbolic material, but DLP-II exists in a narrower frequency region where the hBN is an elliptical material, adjacent to the higher reststrahlen band (RB-II). After uniformly considering the DLP electromagnetic fields on the two sides of the hBN surface, we found that the two DLPs are highly confined in the hBN, and even are completely confined in a certain wave-vector. And also, the Poynting vector of either DLP in the hBN seriously deviates from its wave vector and the directional difference outside and inside the hBN dramatically changes with the distance from the surface. The above extraordinary results can support some potential applications in the mid-infrared range, such as high-efficient energy conduction, strictly manipulating infrared-ray direction and infrared-filtering as well as continuous light-splittingfrom micro-meter to nano-meter dimensions. [ABSTRACT FROM AUTHOR]