  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.
