Fig. 4. Real-space visualization of the general case of refraction between two anisotropic media using nanoscale-confined HPhPs passing through a bending-free planar prism.

a Experimental $\mathrm{Re}\left({\sigma }_3\left(\mathit{x},\mathit{y}\right)\right)$ near-field images of polaritons propagating in a 231-nm-thick α-MoO₃ flake at ${\mathrm{\lambda }}_0$ = 11.0 μm. The black contour line marks a triangular prism fabricated by etching an air cavity on the SiO₂ substrate below the α-MoO₃ flake. A first refraction takes place at boundary-1 (orange solid line) for incident polaritons with collinear $\mathbf{k}$ and $\mathbf{S}$ (black arrows), yielding refracted polaritons with non-collinear ${\mathbf{k}}_{\mathrm{R}}$ and ${\mathbf{S}}_{\mathrm{R}}$ (orange arrows). These polaritons then reflect at boundary-2 (green solid line), yielding polaritons with non-collinear ${\mathbf{k}}_{\mathrm{in}}$ and ${\mathbf{S}}_{\mathrm{in}}$ (green arrows). A second refraction at boundary-3 (violet solid line) yields polaritons with non-collinear ${\mathbf{k}}_{\mathrm{out}}$ and ${\mathbf{S}}_{\mathrm{out}}$ (violet arrows). b Simulated $\mathrm{Re}\left(E_z\left(x,y\right)\right)$ near-field images of HPhPs for the case shown in a. Dashed lines in experimental and simulated near-field images indicate the wavefronts of polaritons as they pass through the prisms. c–e Analytic IFCs of HPhPs in MoO₃/air (gray curve) and MoO₃/SiO₂ (black curve), predicting the directions of refraction or reflection of HPhPs at boundary-1 (c), boundary-2 (d), and boundary-3 (e) based on momentum conservation. The orange (c), green (d), and purple (e) solid lines represent the boundary-1, boundary-2, and boundary-3, while the corresponding dashed lines represent the normal to the boundary.