Fig. 1. Dispersions of polaritons. (a) Schematic showing α-MoO₃/Gr waveguide model. Distributions of magnetic fields, H_y'(z), are analytical results from waveguide model. Rotation coordinate transform is given in left bottom. (b)-(d) Dispersion relations of SPPs (b), PhPs (c), and HP³ (d) in monolayer graphene, pristine α-MoO₃ lamina, and α-MoO₃/Gr heterostructure, respectively. Blue dots indicate experimental data extracted from near-field optical measurements. Black squares are results obtained from finite element method numerical simulations. (e)-(m) In-plane dispersion contours of SPPs [(e)-(g)], PhPs [(h)-(j)], and HP³ [(k)-(m)]. Excitation frequencies are 700 cm^-1 [(e), (h), (k)], 920 cm^-1 [(f), (i), (l)], and 990 cm^-1 [(g), (j), (m)], respectively. Solid white lines shown in (b)-(m) are results calculated by waveguide model. Pseudo-colored images represent calculated imaginary part of complex reflectivity, Im(r_p), of multilayered structures. Dashed lines shown in (h), (i), (k), and (l) are asymptotes of hyperbolic dispersion contours. (n)-(p) Frequency-dependent dispersion contours of polaritons in monolayer graphene (n), pristine α-MoO₃ lamina (o), and α-MoO₃/Gr heterostructure (p), respectively. Colors represent different order modes: TM₀ (blue), TM₀ (green), TM₂ (yellow), TM₃ (red), and TM₄ (gray). Thicknesses of α-MoO₃ lamina and monolayer graphene are 115 nm and 0.5 nm, respectively. Fermi energy of graphene is set as 0.3 eV

Fig. 2. Finite element method simulations of polaritons in α-MoO₃/Gr heterostructure. (a)-(c) Calculated real parts of z-component of electric field, Re(E_z), excited by electric dipole, with excitation frequencies of 700 cm^-1 (Band 1), 920 cm^-1 (Band 2), and 990 cm^-1 (Band 3), respectively. (d)-(f) Fourier transformations of (a)-(c). Fermi energy of graphene is set as 0.3 eV

Fig. 3. Nano-optical imaging of polaritons. (a)-(d) Near-field optical intensity distributions of α-MoO₃/Gr heterostructure, with excitation frequencies of 920 cm^-1 (Band 2), 936 cm^-1 (Band 2), 990 cm^-1 (Band 3), and 995 cm^-1 (Band 3), respectively. Insets in (a) and (b) are enlarged images of regions marked with white dashed lines. (e)-(h) Near-field optical interference fringes of α-MoO₃/Gr heterostructure (dashed lines) and pristine α-MoO₃ (solid lines). Fringes are obtained along [100] (black line) and [001] (blue line) crystalline directions in (a)-(d)

Fig. 4. Influence of α-MoO₃ thickness on polaritons in α-MoO₃/Gr heterostructures. (a), (b) Dependence of propagation constants of PhPs and HP³ on thickness of α-MoO₃ lamina. Excitation frequency is 936 cm^-1 (Band 2). Solid lines are calculated using analytical waveguide model, and blue dots indicate experimental data extracted from s-SNOM. (c)-(e) Near-field optical images of heterostructures composed of α-MoO₃ laminas with different thicknesses of 58 nm, 142 nm, and 156 nm, respectively. Excitation frequency is 936 cm^-1 (Band 2). (f) Interference fringes of polaritons in α-MoO₃/Gr heterostructure (dashed lines) and pristine α-MoO₃ lamina (solid lines). Fringes are investigated along [100] crystalline direction of α-MoO₃ as indicated in (c)-(e). Fermi energy of graphene is set as 0.3 eV in theoretical calculations