Fig. 3: Tuning hybrid modes by WO_x/WSe₂ layer number and laser frequency.

Near-field amplitude images of, a WOx/graphene/α-MoO₃ with ~0.60 eV hole doping and, b WO_x/1L-WSe₂/graphene/α-MoO₃ with ~0.45 eV hole doping. [100] and [001] modes are visibly less anisotropic in the more highly doped sample. c Near-field line profiles showing that increasing doping level substantially increases the wavelength of [001] modes, but only marginally increases [100] mode wavelengths. Black dashed lines align the first peaks. d Line profiles extracted from the sample in b excited at different laser frequencies from 875–915 cm⁻¹. Note [001] modes in b are reflected from a physical boundary of the WO_x/graphene layer at 8° from the [001], which is practically equivalent to the [001] direction (Supplementary Fig. 6). e Momenta from fitting profiles in d are consistent with the dispersion calculated from the imaginary part of the p-polarized reflection coefficient. \({\omega }_{{TO}({LO})}^{j}\) are TO(LO) frequencies of \(j\)-axis phonons: values plotted as white dashed lines. Note that there is a splitting at \({\omega }_{{TO}}^{b}\) from the upper Reststrahlen band phonon not considered in Eq. 1. f Calculated dispersion of phonon polaritons in bare α-MoO₃ showing the absence of [001] modes for \(\omega\)=875–915 cm⁻¹.