# Multipolar Plasmonic Resonances of Aluminum Nanoantenna Tuned by Graphene
## 3 Results and Discussion
For \(l=1\), the electric field of the electric dipole mode of G-AlNR are slightly stronger than that of AlNR as shown in Figure 2a,d. For \(l=2\), the electric field of the electric quadrupole mode of G-AlNR are apparently smaller than that of AlNR, as shown in Figure 2b,e. For \(l=3\), the electric field of the plasmonic third-order mode of G-AlNR are apparently stronger than that of AlNR, as shown in Figure 2c,f. Therefore, the localized electric field and the absorbance of the plasmonic odd modes of AlNR are simultaneously enhanced, while the localized electric field and the absorbance of the plasmonic even mode of AlNR are simultaneously decreased by placing monolayer graphene in the dielectric substrate. Therefore, with the presence of the monolayer graphene below the AlNR, a change in the resonance strength of the multipolar plasmonic modes results from the near field interactions of the monolayer graphene with the electric fields of the multipolar plasmonic resonances of the AlNR. It is worth noting that the tunability of localized electric field of the plasmonic high-order mode (\(l=2\) and \(l=3\)) at UV range coupled by graphene is larger than that of the plasmonic fundamental mode (\(l=1\)) at visible range, owing to the optical broadband dissipation mode of graphene also centered at UV range. To comprehend the tunability of the absorption spectra of multipolar plasmonic resonances of AlNR tuned by a monolayer graphene, we simulated the absorption spectra of G-AINR and AlNR under TM light with incident angle (\(\theta\)) of 30\({}^{\circ}\) when the positions of the three plasmonic resonance modes (\(l\) = 1, 2 and 3) are fixed at 265 nm shown in the gray zone by choosing the proper structural parameters. In Figure 3a, the period (\(P\)), width (\(w\)), thickness (\(t_{1}\)) of the AlNR and the vertical distance (\(t_{2}\)) between graphene and AlNR are 110, 43, 20 and 1 nm, respectively. In Figure 3b, \(P\), \(w\), \(t_{1}\) and \(t_{2}\) are 110, 90, 15 and 1 nm, respectively. In Figure 3c, \(P\), \(w\), \(t_{1}\) and \(t_{2}\) are 160, 150, 15 and 1 nm, respectively. Figure 3a,c shows that the absorbance of the plasmonic odd modes (\(l\) = 1 and \(l\) = 3) at 265 nm of the G-AINR structure are larger than those of AlNR structure. Figure 3b shows that the absorbance at the plasmonic even mode (\(l\) = 2) at 265 nm of the G-AINR structure is smaller than that of AlNR structure, which exhibits the same variation tendency shown in Figure 1b. We also analyzed the influence of the incident angle (\(\theta\)) and the vertical distance (\(t_{2}\)) between graphene and AlNR on the absorption of the G-AINR structure under TM light. Figure 4a presents a series of absorption spectra of the G-AINR (thick lines) and AlNR (thin lines) structures, with the incident angle (\(\theta\)) increasing from 0\({}^{\circ}\) to 45\({}^{\circ}\) with a step of  
Figure 3: Absorbance of the G-AINR and AlNR structures under TM light with incident angle (\(\theta\)) of 30\({}^{\circ}\) with the three plasmon modes: (**a**) \(l\) = 1; (**b**) \(l\) = 2; and (**c**) \(l\) = 3. The resonant positions of the three plasmon modes of both the G-AINR and AlNR structures are fixed at around 265 nm (gray zone) by choosing the right structural parameters (see text). Figure 2: Electric field distributions of \(E_{y}\) and surface charge distribution from front view (in _xz_ plane) of each plasmon mode for G-AINR and AlNR: (**a**) \(l\) = 1, G-AINR; (**b**) \(l\) = 2, G-AINR; (**c**) \(l\) = 3, G-AINR; (**d**) \(l\) = 1, AlNR; (**e**) \(l\) = 2, AlNR; and (**f**) \(l\) = 3, AlNR. Subplots (**a,d**), (**b,e**) and (**c,f**) are in the same scale, respectively. \(15^{\circ}\). The absorption of multipolar plasmonic resonances (\(l=1\), \(2\) and \(3\)) of AlNR tuned by a monolayer graphene under different \(\theta\) shows the same variation tendency as that under \(\theta=30^{\circ}\) shown in Figure 1b.