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This investigation focuses on the Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts on the surface of the uniaxial hyperbolic material hexagonal boron nitride (hBN) based on the biaxial hyperbolic material alpha-molybdenum (α-MoO 3 ) trioxide structure, where the anisotropic axis of hBN is rotated by an angle with respect to the incident plane. The surface with the highest degree of anisotropy among the two crystals is selected in order to analyze and calculate the GH- and IF-shifts of the system, and obtain the complex beam-shift spectra. The addition of α-MoO 3 substrate significantly amplified the GH shift on the system's surface, as compared to silica substrate. With the p-polarization light incident, the GH shift can reach 381.76λ 0 at about 759.82 cm -1 , with the s-polarization light incident, the GH shift can reach 288.84λ 0 at about 906.88 cm -1 , and with the c-polarization light incident, the IF shift can reach 3.76λ 0 at about 751.94 cm -1 . The adjustment of the IF shift, both positive and negative, as well as its asymmetric nature, can be achieved by manipulating the left and right circular polarization light and torsion angle. The aforementioned intriguing phenomena offer novel insights for the advancement of sensor technology and optical encoder design.

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 <ω < 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 × 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., Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Sheng zhou reports financial support was provided by Guangzhou Maritime University., (© 2024 The Authors.)