Fig. 5

Volume vs. edge-localized hyperbolic polaritons. a EEL probability spectrum of 30-nm-thick semi-infinite slab for an on-edge electron trajectory (blue) and for a trajectory 5 nm outside the slab (thin purple) obtained using full-wave simulation (Comsol). b EEL probability spectrum for the beam passing through the h-BN slab away from the edge (off-edge trajectory) obtained using Comsol (solid green). Dashed green spectra in a and b are retarded theoretical calculations (see Supplementary Note 5) using Eq. (1). c Cross section of the induced electric fields (z-component) taken at ω = 1570 cm⁻¹ for the on-edge electron trajectory. d Same as in c but for the off-edge electron trajectory. e Momentum dependent probability П(q _y ,ω) for the on-edge electron trajectory. f Retarded calculation of P(q _y ,ω) for a 30-nm-thick, laterally infinite h-BN layer (see Supplementary Note 5), i.e. the sum of contributions depicted in Fig. 2a–c, but with retardation included. Dashed blue curve marks the dispersion of M0-HPhP mode. Insets in e and f illustrate the electron trajectories and the polariton propagation directions. In all plots, the vertical dashed lines mark the TO, SO, and LO phonon energies