Graphene-Based Cylindrical Pillar Gratings for Polarization-Insensitive Optical Absorbers

: In this study, we present a two-dimensional dielectric grating which allows achieving high absorption in a monolayer graphene at visible and near-infrared frequencies. Dielectric gratings create guided-mode resonances that are exploited to e ﬀ ectively couple light with the graphene layer. The proposed structure was numerically analyzed through a rigorous coupled-wave analysis method. E ﬀ ects of geometrical parameters and response to the oblique incidence of the plane wave were studied. Numerical results reveal that light absorption in the proposed structure is almost insensitive to the angle of the impinging source over a considerable wide angular range of 20 ◦ . This may lead to the development of easy to fabricate and experimentally viable graphene-based absorbers in the future.


Introduction
Graphene has emerged as an attractive two-dimensional material due to its exceptional mechanical, electrical, and optical properties [1]. Monolayer graphene exhibits better absorbance than different dielectric and metals of the same thickness. A considerable amount of theoretical and experimental work has been published in recent years to explore the potential of graphene in optical and microwave absorbers in different spectral ranges of the electromagnetic spectrum for various applications such as biosensors, optical filters, modulators, and efficient photodetector [2][3][4].
Monolayer graphene shows a constant absorption of about 2.3% over the visible and near-infrared wavelengths [5]. However, in the context of optical absorbers, this value is not enough which substantially limits its use in photonic devices. Therefore, enhancement of light absorption by monolayer graphene has drawn significant attention from researchers and several solutions have been proposed in the technical literature to achieve the perfect absorption. One-and two-dimensional dielectric gratings exploit guided-mode resonance (GMR) to increase light-matter interaction. Light is effectively coupled to graphene if incorporated with such gratings [6]. By varying geometrical parameters of the grating structure, the resonant wavelength and the bandwidth of absorption are tuned. A number of numerical studies [7][8][9][10] report perfect absorption of light in graphene incorporated dielectric gratings over diverse spectral ranges. Recently, near total absorption in monolayer graphene based on critical coupling was presented at a visible wavelength of 605 nm [11]. In some other recent studies, multilevel structures were investigated and enhanced graphene absorption was reported [12][13][14]. The main drawback of the multilevel structures is the complexity of the fabrication process since it requires the deposition of multiple material layers. Experimental and measured results for several fabricated graphene-based structures have also been presented [15][16][17][18]. The maximum experimentally measured values of absorption reported are 35% at 0.73 µm [15], 40% at 0.7 µm [16], 45% at 10 µm [17], and 99% at 1.48 µm [18]. Apart from grating-based structures, perfect absorbers based on metamaterials have also been reported [19][20][21][22].
However, perfect, broadband, tunable and polarization-independent absorption of light in monolayer graphene for photonic applications is still a challenging problem and needs further research and exploration. In this framework, it is worth pointing out that the absorption spectra of resonant gratings are highly sensitive to the angle of incident light.
In previous work, we demonstrated that graphene-based gratings are exploited to modulate the Fano-like signature of GMRs [23]. Moreover, two-dimensional arrays of rectangular gold nanopatches grown on monolayer graphene were used to experimentally demonstrate the polarization dependence of plasmonic gratings at normal incidence [24].
In this study, we numerically investigate a two-dimensional (2D) dielectric grating through the rigorous coupled-wave analysis (RCWA) method. We demonstrate the effects of geometrical parameters of the 2D grating on its spectral characteristics of interest. We further study the response of the proposed device for the oblique incidence of a plane wave source. We show that it has a stable optical absorption of around 40% over a considerable wide angular range of 20 • . Electromagnetic field distributions at resonant frequencies are presented to explain the underlying physical phenomenon for optical absorption. Figure 1a shows the sketch of the proposed 2D dielectric grating. It consisted of a periodic array of polymethyl-methacrylate (PMMA) cylindrical pillars deposited on a tantalum pentoxide (Ta 2 O 5 ) waveguide. A slab of silicon dioxide (SiO 2 ) was used as a substrate. The monolayer graphene was placed on top of the waveguide under the PMMA pillars. The proposed 2D dielectric grating can be realized using nanoimprint lithography (NIL). This technology enables the faster fabrication of polymeric-based dielectric gratings at a low cost. The choice of the proposed 2D configuration was based on the possibility of an insensitive polarization behavior at normal incidence for the GMRs that are excited in the Ta 2 O 5 dielectric waveguide. A 20 nm thick buffer layer of PMMA was added on top of the graphene layer (and under the cylinder) to take into account the fabrication tolerances introduced by the NIL fabrication step.

Materials and Methods
The thickness of the monolayer graphene was equal to 0.34 nm. A thin buffer layer of PMMA (20 nm thick) was also placed over the monolayer graphene considering the quality of graphene was not affected by pillar fabrication. The geometrical parameters of the device are detailed in Figure 1b. The thickness t Ta2O5 of the Ta 2 O 5 slab and the PMMA pillar height t PMMA were initially set equal to 150 nm and 600 nm, respectively. The PMMA pillars have symmetric periodicity both in xand ydirections and the value chosen was equal to 600 nm at the start. The radius r of the cylindrical PMMA pillars was chosen as 250 nm. The 2D graphene-based dielectric gratings were simulated by means of RSoft-DiffactMOD that implements a Fourier-space method, the rigorous coupled-wave analysis (RCWA), to solve scattering from periodic structures. The refractive indices for PMMA, Ta2O5, and SiO2 were retrieved from Palik et al. [25]. For monolayer graphene, we used the complex refractive index n = 3 + jC1 * λ/3 reported in [26] at visible frequencies where C1 was equal to 5.446 µm −1 and λ was the free space wavelength to take into account the losses. 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 µm, 0.9 µm, and 0.96 µm 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 µm (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 The 2D graphene-based dielectric gratings were simulated by means of RSoft-DiffactMOD that implements a Fourier-space method, the rigorous coupled-wave analysis (RCWA), to solve scattering from periodic structures. The refractive indices for PMMA, Ta 2 O 5, and SiO 2 were retrieved from Palik et al. [25]. For monolayer graphene, we used the complex refractive index n = 3 + jC 1 * λ/3 reported in [26] at visible frequencies where C 1 was equal to 5.446 µm −1 and λ was the free space wavelength to take into account the losses. 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 µm, 0.9 µm, and 0.96 µm 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 2D graphene-based dielectric gratings were simulated by means of RSoft-DiffactMOD that implements a Fourier-space method, the rigorous coupled-wave analysis (RCWA), to solve scattering from periodic structures. The refractive indices for PMMA, Ta2O5, and SiO2 were retrieved from Palik et al. [25]. For monolayer graphene, we used the complex refractive index n = 3 + jC1 * λ/3 reported in [26] at visible frequencies where C1 was equal to 5.446 µm −1 and λ was the free space wavelength to take into account the losses. 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 µm, 0.9 µm, and 0.96 µm 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 µm (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 where the monolayer graphene is positioned at z = 0.15 µm (that corresponds to the thickness of the Ta2O5). 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 Ta2O5 layer thickness tTa2O5 and PMMA pillar height tPMMA 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.

Results
The effects of variations of Ta2O5 layer thickness tTa2O5 and PMMA pillar height tPMMA on the absorption spectrum have also been investigated. Figure 6a depicts the effect of change of tTa2O5 on the absorption spectrum. There is a red shift in the resonant wavelength as the thickness of the Ta2O5 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 tPMMA on the absorption spectrum revealing no changes when the PMMA thickness is varied in the range of 300 nm to 900 nm. structure where the monolayer graphene is positioned at z = 0.15 µm (that corresponds to the thickness of the Ta2O5). 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 Ta2O5 layer thickness tTa2O5 and PMMA pillar height tPMMA 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 Ta2O5 layer thickness tTa2O5 and PMMA pillar height tPMMA on the absorption spectrum have also been investigated. Figure 6a depicts the effect of change of tTa2O5 on the absorption spectrum. There is a red shift in the resonant wavelength as the thickness of the Ta2O5 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 tPMMA on the absorption spectrum revealing no changes when the PMMA thickness is varied in the range of 300 nm to 900 nm. 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 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 Ta2O5 and PMMA pillar height t PMMA on the absorption spectrum have also been investigated. Figure 6a depicts the effect of change of t 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.  We further analyze the optical response of the proposed device under the oblique incidence of the plane wave source. Figure 7 shows the absorption maps when the incidence angle is changed from 0° to 90° for both TE and TM polarizations. The maps show that the resonance at normal incidence splits into two arms for angular incidence. This behavior is typical of a grating structure that is derived by the absorption spectra. It is interesting to note that the absorption spectra do not split into two arms for certain resonant wavelengths and absorption is nearly independent of the source angle for specific angular ranges.  We further analyze the optical response of the proposed device under the oblique incidence of the plane wave source. Figure 7 shows the absorption maps when the incidence angle is changed from 0° to 90° for both TE and TM polarizations. The maps show that the resonance at normal incidence splits into two arms for angular incidence. This behavior is typical of a grating structure that is derived by the absorption spectra. It is interesting to note that the absorption spectra do not split into two arms for certain resonant wavelengths and absorption is nearly independent of the source angle for specific angular ranges. We further analyze the optical response of the proposed device under the oblique incidence of the plane wave source. Figure 7 shows the absorption maps when the incidence angle is changed from 0 • to 90 • for both TE and TM polarizations. The maps show that the resonance at normal incidence splits into two arms for angular incidence. This behavior is typical of a grating structure that is derived by the absorption spectra. It is interesting to note that the absorption spectra do not split into two arms for certain resonant wavelengths and absorption is nearly independent of the source angle for specific angular ranges. To further elaborate these important results, the absorption spectra of the device for both TE and TM polarizations are shown in Figure 8 in an angular range of 0-20° for two different device periods. The absorption is limited within narrow bandwidths of ~15 nm and ~20 nm for the maps in (a,b) and (c,d) respectively over a considerable wide angular range of 20°. The slope is about 0.5 nm/degree in the 0-10° range.
Another important result is depicted in Figure 9 which shows absorption spectra in an angular range of 70-90°. It is noted that the absorption is limited in narrow bandwidths of ~25 nm and ~10 nm for the angular ranges of 70-90° and 75-90°, respectively in both (a) and (b) maps. Furthermore, the device behavior is similar under both TE and TM polarizations. In short, the observations in Figure 8; Figure 9 prove the near insensitivity of the proposed device to the angle and polarization of the incident light in multiple angular ranges of around 20°. Angular response of our device shows clear improvement as compared with results reported in [15] for a To further elaborate these important results, the absorption spectra of the device for both TE and TM polarizations are shown in Figure 8 in an angular range of 0-20 • for two different device periods. The absorption is limited within narrow bandwidths of~15 nm and~20 nm for the maps in (a,b) and (c,d) respectively over a considerable wide angular range of 20 • . The slope is about 0.5 nm/degree in the 0-10 • range.
Another important result is depicted in Figure 9 which shows absorption spectra in an angular range of 70-90 • . It is noted that the absorption is limited in narrow bandwidths of~25 nm and~10 nm for the angular ranges of 70-90 • and 75-90 • , respectively in both (a) and (b) maps. Furthermore, the device behavior is similar under both TE and TM polarizations. To further elaborate these important results, the absorption spectra of the device for both TE and TM polarizations are shown in Figure 8 in an angular range of 0-20° for two different device periods. The absorption is limited within narrow bandwidths of ~15 nm and ~20 nm for the maps in (a,b) and (c,d) respectively over a considerable wide angular range of 20°. The slope is about 0.5 nm/degree in the 0-10° range.
Another important result is depicted in Figure 9 which shows absorption spectra in an angular range of 70-90°. It is noted that the absorption is limited in narrow bandwidths of ~25 nm and ~10 nm for the angular ranges of 70-90° and 75-90°, respectively in both (a) and (b) maps. Furthermore, the device behavior is similar under both TE and TM polarizations. In short, the observations in Figure 8; Figure 9 prove the near insensitivity of the proposed device to the angle and polarization of the incident light in multiple angular ranges of around 20°. Angular response of our device shows clear improvement as compared with results reported in [15] for a In short, the observations in Figure 8; Figure 9 prove the near insensitivity of the proposed device to the angle and polarization of the incident light in multiple angular ranges of around 20 • . Angular response of our device shows clear improvement as compared with results reported in [15] for a graphene-based absorber based on a one-dimensional grating where absorption spectra split into two arms from 0-20 • under similar simulation conditions. Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 9 graphene-based absorber based on a one-dimensional grating where absorption spectra split into two arms from 0-20° under similar simulation conditions.

Discussion
In our previous work [15,16], we experimentally demonstrated light absorption in graphenebased one-dimensional dielectric gratings based on PMMA rectangular strips. However, the response of the structures is sensitive to the oblique incidence of light. In this study, we propose a device based on a 2D grating of cylindrical PMMA pillars that exploit GMRs to enhance light absorption in the monolayer graphene. Our proposed structure achieved light absorption of more than 40% at multiple wavelengths for both TE and TM polarizations over narrow bandwidths in the visible and nearinfrared ranges. The device performance is insensitive to variation in the PMMA pillar height which is an important measure in terms of device stability and fabrication tolerances.
Our simulations further revealed that the device has a considerable stable angular response. The absorption spectra are nearly independent of the angle of the impinging light up to 20° with a slope of ~0.5 nm/degree. Moreover, the response is less sensitive to the polarization of the incident plane waves.
In conclusion, the proposed optical absorber is less sensitive to geometrical parameters variations, polarization, and angle of the incident light which can be easily realized using nanofabrication technologies such as nanoimprint lithography.
These results pave the way to the realization of polarization-insensitive optical absorbers that can be efficiently exploited in several applications and photonic devices such as biosensors, optical filters, modulators, and efficient photodetectors.

Discussion
In our previous work [15,16], we experimentally demonstrated light absorption in graphene-based one-dimensional dielectric gratings based on PMMA rectangular strips. However, the response of the structures is sensitive to the oblique incidence of light. In this study, we propose a device based on a 2D grating of cylindrical PMMA pillars that exploit GMRs to enhance light absorption in the monolayer graphene. Our proposed structure achieved light absorption of more than 40% at multiple wavelengths for both TE and TM polarizations over narrow bandwidths in the visible and near-infrared ranges. The device performance is insensitive to variation in the PMMA pillar height which is an important measure in terms of device stability and fabrication tolerances.
Our simulations further revealed that the device has a considerable stable angular response. The absorption spectra are nearly independent of the angle of the impinging light up to 20 • with a slope of 0.5 nm/degree. Moreover, the response is less sensitive to the polarization of the incident plane waves.
In conclusion, the proposed optical absorber is less sensitive to geometrical parameters variations, polarization, and angle of the incident light which can be easily realized using nanofabrication technologies such as nanoimprint lithography.
These results pave the way to the realization of polarization-insensitive optical absorbers that can be efficiently exploited in several applications and photonic devices such as biosensors, optical filters, modulators, and efficient photodetectors.