Group velocity modulation and wavelength tuning of phonon-polaritons by engineering dielectric-metallic substrates

In analogy to the observed for single plasmon-polaritons, we show that subdiffractional hyperbolic phonon-polariton (HP2) modes confined in hexagonal boron nitride (hBN) nanocrystals feature wave-particle duality. First, we use Synchrotron Infrared Nanospectroscopy to demonstrate modulation of the HP2 frequency-momentum dispersion relation and group velocity by varying the thickness of the SiO2 layer in the heterostructure hBN/SiO2/Au. These modulations are, then, exploited for the hBN crystal lying on a SiO2 wedge, with a gradient of thickness of such a dielectric medium, built into the Au substrate. Simulations show that a phonon-polariton pulse accelerates as the thickness of the wedge increases. This is explained by a parameter-free semi-classical approach considering the pulse as free quantum particle. Within this picture, an estimated average acceleration value of ~ 1.45 10^18 m.s^(-2) is determined using experimental inputs. This estimation is in good agreement with the value of 2.0 10^18 m.s^(-2) obtained from the theory directly.