Fig. 2. Real-space visualization of refraction between two anisotropic media using highly confined polaritons with collinear incident k and S.

a, b Experimental $\mathrm{Re}\left({\sigma }_3\left(x,y\right)\right)$ (a) and simulated $\mathrm{Re}\left(E_z\left(x,y\right)\right)$ (b) near-field images of HPhPs propagating in a 160-nm-thick α-MoO₃ flake at ${\lambda }_0$ = 11.3 μm. The white and black dashed lines mark triangular prisms fabricated by etching an air cavity on the SiO₂ substrate below the α-MoO₃ flake. ${\mathbf{S}}_{\mathrm{in}}$ and ${\mathbf{k}}_{\mathrm{in}}$ display the direction of propagation and the wavevector of incident polaritons in α-MoO₃/air, respectively. Horizontal propagation of non-refracted polaritons is marked as ${\mathbf{k}}_{\mathrm{p}}$ and ${\mathbf{S}}_{\mathrm{p}}$. Upon refraction at a boundary of the prism with an angle ${\theta }_{\mathrm{in}}$ ~ 55°, HPhPs bend away from the normal, ${\mathbf{S}}_{\mathrm{out}-\exp }$ (blue arrow), with a tilted wavevector ${\mathbf{k}}_{\mathrm{out}-\exp }$ (green arrow). Compared to non-refracted HPhPs, indicated by ${\mathrm{\lambda }}_{\mathrm{p}}$, the refracted HPhPs are stronger confined (with a wavelength about 1.6 times shorter. c Analytic IFCs of α-MoO₃/SiO₂ (black hyperbolas) and α-MoO₃/air (gray hyperbolas) effective media in a, b, and considering momentum conservation at the boundary (orange line), the extracted wavevector and direction of the refracted polaritons, ${\mathbf{k}}_{\mathrm{out}}$ and ${\mathbf{S}}_{\mathrm{out}}$, respectively, are in good agreement with both experiment and simulation. d, e Experimental $\mathrm{Re}\left({\sigma }_3\left(x,y\right)\right)$ (d) and simulated $\mathrm{Re}\left(E_z\left(x,y\right)\right)$ (e) near-field images of HPhPs propagating in a 160-nm-thick α-MoO₃ flake at ${\mathrm{\lambda }}_0$ = 11.1 μm. The refracted HPhPs propagate almost parallel to the boundary with a wavelength 2.1 times smaller than ${\mathrm{\lambda }}_{\mathrm{p}}$. f Analytic IFCs of α-MoO₃/SiO₂ (black hyperbolas) and α-MoO₃/air (gray hyperbolas) effective media in d, e. The orange dashed lines in a–f represent the normal to the boundary.