# Multipolar Plasmonic Resonances of Aluminum Nanoantenna Tuned by Graphene
## 3 Results and Discussion  
Figure 1b shows the calculated absorption spectra of the proposed G-AINR structure (red solid line) and AINR structure (black solid line) under the transverse magnetic (TM) light with inclined incident angle (\(\theta\)) of 30\({}^{\circ}\). The period (\(P\)), width (\(w\)), thickness (\(t_{1}\)) of the  
Figure 1: (**a**) Schematic of the proposed hybrid graphene–Al nanoribbon (G–AINR) structure on Al\({}_{2}\)O\({}_{3}\) substrate. The parameters \(P\), \(w\), \(t_{1}\) and \(t_{2}\) represent the period, width of the AINR, thickness of the AINR and the vertical distance between graphene and AINR. The parameters \(\theta\) represents the inclined incident angle. The length of AINR is infinite along the \(y\) direction. (**b**) Absorbance of the G-AINR and AINR structures under TM light with inclined incident angle \(\theta\) of 30\({}^{\circ}\). AlNR and the vertical distance (\(t_{2}\)) between graphene and AlNR are set as 110, 90, 10 and 1 nm, respectively. For graphene embedded in the Al\({}_{2}\)O\({}_{3}\) substrate, there is a low absorption peak with a broad band centered at 265 nm, as shown in Figure S1, which is the optical dissipation mode of graphene [28]. For both the AlNR structure and G-AlNR structure, several absorption peaks are achieved, which range from 200 to 700 nm. These absorption peaks represent the multipolar plasmonic resonance modes of AlNR. The peaks depicted by \(l=1\), 2 and 3 denote the plasmonic fundamental mode (electric dipole mode), electric quadrupole mode and the third-order plasmonic mode of the AlNR structure. Such similar multipolar plasmonic resonance modes of Al nanoantennas have been experimentally investigated using electron energy loss spectroscopy [26]. The plasmonic fundamental mode (\(l=1\)) and the third-order plasmonic mode (\(l=3\)) are also called the plasmonic odd modes of AlNR that could be directly excited by incident light under normal incidence. On the contrary, the plasmonic even modes of AlNR such as the electric quadrupole mode (\(l=2\)) could not be excited by incident light under normal incidence due to its net electric dipole moment being zero in the quasistatic limit. However, under inclined incident light with \(\theta\) of 30\({}^{\circ}\), all these plasmonic odd modes and even modes are excited simultaneously. Compared to AlNR, the corresponding absorption peaks (\(l=1\) and \(l=2\)) of G-AlNR are located at the same position, while the position of corresponding absorption peak with \(l=3\) of G-AlNR slightly blueshifts, as shown in the inset of Figure 1b. It is shown that the absorbance at the plasmonic odd modes (\(l=1\) and \(l=3\)) of the G-AlNR structure are larger than those of AlNR structure. In particular, the third-order plasmonic mode (\(l=3\)) of AlNR is nothing more than a shoulder in the spectrum shown in the inset of Figure 1b, which is due to the low optical excitation efficiency for the metallic high-order plasmonic modes. Compared to AlNR, although only a small absorption peak is obtained under TM light with inclined incident angle (\(\theta\)) of 30\({}^{\circ}\), the \(l=3\) mode of G-AlNR with a narrow bandwidth is clearly enhanced. The full-width at half maximum (_FWHM_) and the corresponding \(Q\)-factor of the \(l=3\) mode of G-AlNR are extracted to be 8.5 nm and 27, respectively. The \(Q\)-factor of the \(l=3\) mode of G-AlNR is much larger than the \(Q\)-factor (\(Q=2\)) supported by the plasmonic fundamental mode (\(l=1\)) of the G-AlNR structure. The resonance strength of the \(l=3\) mode tuned by the inclined incident angle will be further discussed below. On the other hand, the absorbance at the plasmonic even mode (\(l=2\)) of the G-AlNR structure is smaller than that of AlNR structure. The absorption of multipolar plasmonic resonances of AlNR tuned by a monolayer graphene can be explained by analyzing the electric field distributions. Figure 2 shows the electric field distributions of \(E_{y}\) and surface charge distribution of each plasmon mode for G-AlNR and AlNR.