The fascinating optical properties of graphene are usually concluded in theory under the assumption that graphene is freestanding. However, in experimentally realizable devices, graphene is usually supported by a substrate, which may influence the optical properties of the graphene. Choosing the right substrate is therefore critical for graphene electromagnetic (EM) devices. In this paper, we studied the influence of two types of two-dimensional (2D) insulating substrates, hexagonal boron nitride (h-BN) and fluorographene (FG), on the graphene optical properties at room temperature. Our work shows that both substrates can preserve well the optical properties of graphene from 0.6 eV to 3.5 eV and the FG substrate can retain graphene’s original properties much better than the h-BN substrate when the photon energy is <0.6 eV or >3.5 eV. Besides, by analyzing the Kubo formula, the relaxation time of non-freestanding graphene, which can reflect the substrate–graphene interaction, is highly dependent on the substrate type and its stacking pattern. A THz graphene surface plasmonic modulator is used to further explain the substrate effect on graphene EM device design. Our results demonstrate that the h-BN substrate may degrade or fail the performance of THz (<0.1 eV) graphene modulator originally designed from freestanding graphene properties, while replacing h-BN with FG substrate or increasing the working frequency (>0.2 eV) can overcome the performance degradation. Finally, the substrate effects on graphene properties are also studied by examining the electronic properties of double-layer structures. Our results on the sensitivity issue that are caused by the stacking pattern and inter-layer distance may provide a reasonable explanation on the inconsistency of substrate-induced bandgap opening in graphene/h-BN heterostructures discussed in recent experimental and theoretical studies.
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