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

a, b Experimental \({\rm{Re}}({\sigma }_{3}(x,y))\) (a) and simulated \({\rm{Re}}({E}_{z}(x,y))\) (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. \({{\bf{S}}}_{{\rm{in}}}\) and \({{\bf{k}}}_{{\rm{in}}}\) 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 \({{\bf{k}}}_{{\rm{p}}}\) and \({{\bf{S}}}_{{\rm{p}}}\). Upon refraction at a boundary of the prism with an angle \({\theta }_{{\rm{in}}}\) ~ 55°, HPhPs bend away from the normal, \({{\bf{S}}}_{{\rm{out}}-{\rm{exp }}}\,\) (blue arrow), with a tilted wavevector \({{\bf{k}}}_{{\rm{out}}-{\rm{exp }}}\) (green arrow). Compared to non-refracted HPhPs, indicated by \({{\rm{\lambda }}}_{{\rm{p}}}\), 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, \({{\bf{k}}}_{{\rm{out}}}\) and \({{\bf{S}}}_{{\rm{out}}}\), respectively, are in good agreement with both experiment and simulation. d, e Experimental \({\rm{Re}}({\sigma }_{3}(x,y))\) (d) and simulated \({\rm{Re}}({E}_{z}(x,y))\) (e) near-field images of HPhPs propagating in a 160-nm-thick α-MoO₃ flake at \({{\rm{\lambda }}}_{0}\) = 11.1 μm. The refracted HPhPs propagate almost parallel to the boundary with a wavelength 2.1 times smaller than \({{\rm{\lambda }}}_{{\rm{p}}}\). 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.