Phonon polaritons (PhPs) in van der Waals (vdW) crystal slabs enable nanoscale infrared light manipulation. Specifically, periodically structured vdW slabs behave as polaritonic crystals (vdW-PCs), where the polaritons form Bloch modes. Because the polariton wavelengths are smaller than that of light, conventional far-field spectroscopy does not allow for a complete characterization of vdW-PCs or for revealing their band structure. Here, we perform hyperspectral infrared nanoimaging and analysis of PhPs in a vdW-PC slab made of h-BN. We demonstrate that infrared spectra recorded at individual spatial positions within the unit cell of the vdW-PC can be associated with its band structure and local density of photonic states (LDOS). We thus introduce hyperspectral infrared nanoimaging as a tool for the comprehensive analysis of polaritonic crystals, which could find applications in the reconstruction of complex polaritonic dispersion surfaces in momentum-frequency space or for exploring exotic electromagnetic modes in topological photonic structures.
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