The aim of this study is to theoretically investigate the loss function of ${\mathrm{layer}}_1$-hBN-${\mathrm{layer}}_2$ nanostructures, where layers 1 and 2 may be doped graphene, pristine graphene, or vacuum. This was achieved by comparing results obtained from the ab initio and massless Dirac fermion approaches and by examining how variations in the insulator thickness and system composition influence the loss function features relative to the reststrahlen bands of hexagonal boron nitride (hBN). It is shown that increasing the hBN thickness weakens plasmon coupling, leading to mode merging, while hBN's anisotropy causes phonon modes to diffuse within their reststrahlen bands, yet remain hybridized with plasmons in damping-free regions. Introducing an undoped graphene layer significantly suppresses both plasmon and phonon patterns, demonstrating that layer configuration and doping asymmetry play a key role in determining plasmon-phonon hybridization and spectral intensity.

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• Dielectric properties
• Phonons
• Plasmonics
• Plasmons
• Graphene
• Heterostructures
• van der Waals systems
• Electron energy loss spectroscopy
• Linear response theory