# Graphene-Based Cylindrical Pillar Gratings for Polarization-Insensitive Optical Absorbers
## 3 Results  
Figure 2 shows the reflection, transmission, and absorption spectra of the device with and without graphene layer for the TE and TM polarizations at normal incidence. The absorption spectrum shows resonant peaks at the 0.7 \(\upmu\)m, 0.9 \(\upmu\)m, and 0.96 \(\upmu\)m wavelengths. These correspond to absorption of 20%, 50%, and 40%, respectively. The absorption is zero when the structure has no graphene layer. It is noted that the optical response is insensitive to the polarization of the incoming light wave due to the symmetry of the device (2D square lattice). The electromagnetic field distributions are shown in Figure 3a,b at the resonant wavelength of 0.9 \(\upmu\)m (maximum absorption) for the TE and TM polarizations, respectively. It clearly illustrates that the fields are concentrated around monolayer graphene. The white lines represent the device structure  
Figure 1: (a) Sketch of a 2D graphene-based dielectric grating with an array of cylindrical pillars and (b) the cross-sectional (x,z) view of the single period of the device used for simulations. Figure 2: Optical reflectance (dashed blue line), the transmittance (dotted black line), and absorption (solid red line) spectra (**a**,**b**) without and (**c**,**d**) with graphene layer for both (**a**,**c**) TE and (**b**,**d**) TM plane waves at normal incidence. The device period p, waveguide Ta\({}_{2}\)O\({}_{5}\) thickness tr\({}_{2}\)O\({}_{5}\), and PMMA pillars height tr\({}_{\text{PMMA}}\) for this simulation result are set as 600 nm, 150 nm, and 600 nm, respectively. where the monolayer graphene is positioned at \(z=0.15\)\(\upmu\)m (that corresponds to the thickness of the Ta\({}_{2}\)O\({}_{5}\)). The comparison between Figure 3 (with graphene) and Figure 4 (without graphene) shows the difference between the values of field magnitudes of about a factor two. Next, we studied the effects of device geometrical parameters. Figure 5 describes the absorption (A) spectra at different grating periods (p) while Ta\({}_{2}\)O\({}_{5}\) layer thickness \(t_{\text{Ta2O5}}\) and PMMA pillar height \(t_{PMMA}\) are kept constant. It is evident that absorption peak wavelength is tuned over the visible and near-infrared wavelengths by changing the grating period. The sliding of the resonant wavelengths with increasing device period agrees well with the analysis presented in [6]. Each absorption spectrum shows multiple peaks which result from multiple guided-mode resonances. In addition, there is an increase in absorption with increasing period length as is observed in Figure 5a-d. Since our device is polarization independent for normally incident plane waves, we have shown the absorption spectra for TE polarized plane waves only. The effects of variations of Ta\({}_{2}\)O\({}_{5}\) layer thickness \(t_{\text{Ta2O5}}\) and PMMA pillar height \(t_{PMMA}\) on the absorption spectrum have also been investigated. Figure 6a depicts the effect of change of \(t_{\text{Ta2O5}}\) on the absorption spectrum. There is a red shift in the resonant wavelength as the thickness of the Ta\({}_{2}\)O\({}_{5}\) waveguide is increased from 80 nm to 160 nm. Multiple resonances appear among which the prominent ones are shown in the absorption map. Figure 6b depicts the effect of change of \(t_{PMMA}\) on the absorption spectrum revealing no changes when the PMMA thickness is varied in the range of 300 nm to 900 nm. Figure 4: Field profiles (**a**) amplitude of Ey component and (**b**) amplitude of Ex component at 0.9 \(\upmu\)m without the graphene layer. The white lines show the device structure. Figure 3: Field profiles (**a**) amplitude of Ey component and (**b**) amplitude of Ex component at 0.9 \(\upmu\)m for the device parameters of Figure 2. The white lines show the device structure where the monolayer graphene is positioned at \(z=0.15\)\(\upmu\)m (marked by the black line). We further analyze the optical response of the proposed device under the oblique incidence of the plane wave source.