Fig. 3: Study of the propagation of PhPs in LiV₂O₅.

a Analytical 3D IFC (\({q}_{a},{q}_{b},\omega\)) for the real part of the polariton wavevector (\({{{Re}}}(q)\)) at frequencies \(\omega=\) 997 cm⁻¹ and \(\omega=\) 1007 cm⁻¹. b Analytical 3D IFC (\({q}_{a},{q}_{b},\omega\)) for the imaginary part of the polariton wavevector (\({Im}(q)\)) at frequencies \(\omega=\)997 cm⁻¹ and \(\omega=\)1007 cm⁻¹. c, Analytical 2D IFC extracted from combining \({{{Re}}}(q)\) (white) and \({Im}(q)\) (red) from (a and b) at \(\omega=\)997 cm⁻¹. \({{{Re}}}(q)\) is larger than \({Im}\left(q\right)\) along all directions. The color plot is obtained by Fourier Transforming (FT) a numerical simulation in real space of PhPs excited using a point dipole on a LiV₂O₅ layer with thickness \(d=\)200 nm at \(\omega=\)997 cm⁻¹. d Analytical 2D IFC extracted from combining \({{{Re}}}(q)\) (white) and \({Im}(q)\) (red) from (a and b) at \(\omega=\) 1007 cm⁻¹. \({{{Re}}}(q)\) is larger than \({Im(q)}\) only in a significant manner along the b direction, predicting canalization of PhPs along this axis. The color plot is obtained by Fourier Transforming (FT) a numerical simulation in real space of PhPs excited using a point dipole on a LiV₂O₅ layer with thickness \(d=\) 200 nm at \(\omega \) = 1007 cm⁻¹. The appearance of two flat bands at \(\omega \) = 1007 cm⁻¹ corroborates the existence of naturally canalized PhPs in LiV₂O₅. e Figure of Merit (FOM) for propagating PhPs, defined as \({{{Re}}}(q)/{Im}(q)\), along the \(a\) (blue) and \(b\) (green) crystal directions. The approximately 5× difference in the FOM between the \(b\) and \(a\) directions corroborates the canalization of PhPs along the former. The small insets show the real part of the electromagnetic field, \({Re}(E_{z})\), from numerical simulations, showing canalized PhPs at \(\omega \) = 1007 cm⁻¹. The blue shaded area indicates the Reststrahlen band a₂ (RB_a2). f, PhPs quality factor \(\left|\frac{{{{Re}}}\left(q\right)}{{Im}(q)}\right|\) as a function of in-plane propagation angle \(\varphi\) (°) and the permittivity ratio along the a direction \(\left|\frac{{Im}({{{{{{\rm{\varepsilon }}}}}}}_{{{{{{\rm{a}}}}}}})}{{{{Re}}}({{{{{{\rm{\varepsilon }}}}}}}_{{{{{{\rm{a}}}}}}})}\right|\). The white dashed lines correspond to the permittivity ratio value at \(\omega \) = 1003 cm⁻¹, \(\omega \) = 1006 cm⁻¹, and \(\omega \) = 1007 cm⁻¹, while the black dashed line traces the \(b\) direction.