  Near-field mapping has been widely used to study hyperbolic phonon-polaritons
in van der Waals crystals. However, an accurate measurement of the polaritonic
loss remains challenging because of the inherent complexity of the near-field
signal and the substrate-mediated loss. Here we demonstrate that large-area
monocrystalline gold flakes, an atomically-flat low-loss substrate for image
polaritons, provide a platform for precise near-field measurement of the
complex propagation constant of polaritons in van der Waals crystals. As a
topical example, we measure propagation loss of the image phonon-polaritons in
hexagonal boron nitride, revealing that their normalized propagation length
exhibits a parabolic spectral dependency. Further, we show that image
phonon-polaritons exhibit up to a twice lower normalized propagation loss,
while being 2.4 times more compressed compared to the case of dielectric
substrate. We conclude that the monocrystalline gold flakes provide a unique
nanophotonic platform for probing and exploitation of the image modes in
low-dimensional materials.
