Fig. 4: Thickness dependence and dispersion of hyperbolic exciton polaritons.
From: Hyperbolic exciton polaritons in a van der Waals magnet
a \(T=20{{{{{\rm{K}}}}}}\) near-field image of the corner of a \(107{{{{{\rm{nm}}}}}}\) CrSBr microcrystal at \(E=1.376{{{{{\rm{eV}}}}}}\). The hyperbolic exciton polariton (HEP) fringe appears only along the b-axis as expected from its hyperbolic isofrequency contour (left inset). b Averaged \(b\)-axis line profile (blue) compared to a line profile at the same \(T\) and \(E\) on a \(200{{{{{\rm{nm}}}}}}\) crystal (purple). Air mode wavelengths do not change with thickness (aligned by vertical dashed lines) while the HEP fringe (black arrow) blueshifts with decreasing thickness (diagonal dashed line). c Experimental HEP and air mode momenta at various energies overlaid on \(20{{{{{\rm{K}}}}}}\) \({{{{{\rm{Im}}}}}}{r}_{p}\) loss function (dashed orange line corresponds to \(\max {{{{{\rm{Im}}}}}}{r}_{p}\)). \({{{{{{\rm{X}}}}}}}^{*}\) sideband causes backbending of HEP dispersion (white line). d HEP does not appear in near-field image at \(E=1.387{{{{{\rm{eV}}}}}}\), but, (e) appears in image at \(E=1.376{{{{{\rm{eV}}}}}}\) (black arrow). Scale bars are \(1{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\). f Theoretical propagation length \({L}_{p}\) with and without \({{{{{{\rm{X}}}}}}}^{*}\) in orange and black, respectively. \({{{{{{\rm{X}}}}}}}^{*}\) causes significant \({L}_{p}\) reduction.
