Perfect ultraviolet absorption in graphene using the magnetic resonance of an all-dielectric nanostructure

The enhancement of light-matter interaction for monolayer graphene is of great importance on many photonic and optoelectronic applications. With the aim of perfect ultraviolet trapping on monolayer graphene, we adopt the design of an all-dielectric nanostructure, in which the magnetic resonance of optical field is combined with an ultraviolet mirror. The physics inside is revealed in comparison with the conventional plasmonic perfect absorber, and various influence factors of absorption bands are systematically investigated. In the ultraviolet range, an optimized absorbance ratio up to 99.7% is reached, which is 10 times more than that of the suspended graphene, and the absorption bands are linearly reconfigurable by angular manipulation of incident light. The scheme for perfect ultraviolet trapping in a sub-nanometer scale paves the way for developing more promising ultraviolet devices based on graphene and potentially other 2D materials. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (260.7190) Ultraviolet; (240.0310) Thin films; (350.4238) Nanophotonics and photonic crystals. References and links 1. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012). 2. Z. Yin, J. Zhu, Q. He, X. Cao, C. Tan, H. Chen, Q. Yan, and H. Zhang, “Graphene-based materials for solar cell applications,” Adv. Energy Mater. 4(1), 1300574 (2014). 3. C.-H. Liu, Y.-C. Chang, T. B. Norris, and Z. Zhong, “Graphene photodetectors with ultra-broadband and high responsivity at room temperature,” Nat. Nanotechnol. 9(4), 273–278 (2014). 4. C. T. Phare, Y.-H. Daniel Lee, J. Cardenas, and M. 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Introduction
The family of 2D materials has attracted a lot of interest in the field of device research, because they show exceptional electronic and optical properties compared with their 3D counterparts.As the most popular 2D material, graphene is regarded as a promising alternative to silicon for future development of optoelectronics, due to its high carrier mobility, fast optical response, extraordinary band structure, and unique mechanical strength and flexibility [1].In the past few years, many graphene-based photonic devices have been investigated, including solar cells, photonic detectors, optical modulators and optical sensors [2][3][4][5].In these investigations, graphene has shown poor light-matter interaction for its extremely small thickness, and weak spectral selectivity for its wavelength-independent absorption in the visible and near-infrared ranges [6].These drawbacks limit the performance of graphene-based devices, so optical absorption enhancement in graphene has been intensively studied.A lot of photonic nanostructures have been adopted to trap light on monolayer graphene in the spectral range from visible to infrared, such as plasmonic nanoantennas, plasmonic metamateirals, optical waveguides, and photonic crystals [7][8][9][10][11].Despite of these research achievements, there is few research about the routes to approaching perfect ultraviolet (UV) absorption in monolayer graphene, which has a variety of promising UV applications on photodetectors, light emitters, Raman microscopy, optical sensing and flame monitoring [12][13][14][15].A previous effort has been focused on achieving high UV absorption in graphene by using a multilayer structure without any nanostructure patterning [16].However, this method is limited by specific angular manipulation of incident light and intrinsic optical loss in the metal.In many practical circumstances, complete UV absorption of graphene with normal incident light on the substrate is quite in demand for highperformance devices.Therefore, an efficient design of photonic structure for normal incidence is essential for developing optoelectronic devices based on graphene.
In this study, we aim to achieve perfect UV absorption in monolayer graphene by using an all-dielectric photonic nanostructure.Lossless dielectric materials are adopted to avoid unexpected optical dissipation beyond graphene.The UV magnetic resonance of dielectric nanostructure is combined with the perfect reflection of a UV mirror, in order to form a gap trapping mode for perfect UV absorption in graphene.

Methods
The design of proposed photonic nanostructure is shown in Fig. 1.The structure consists of periodic silica (SiO 2 ) nanoribbons, a graphene monolayer, a calcium fluoride (CaF 2 ) layer, a UV mirror with a stack of dielectric layers of alternate zirconia (ZrO 2 ) and cryolite (Na 3 AlF 6 ), and a transparent substrate.In view of the fabrication process, the UV mirror and CaF 2 layer can be deposited by ion plating and plasma ion-assisted deposition high energetic technologies [17], graphene can be transferred onto the CaF 2 surface [18], and SiO 2 nanoribbons can be fabricated by soft UV nanoimprint [19].In our design, the dielectric layers of SiO 2 , CaF 2 , ZrO 2 , Na 3 AlF 6 and substrate are assumed to be nonmagnetic (μ = μ 0 ) and optically lossless with the refractive index of 1.48, 1.45, 2.6, 1.33 and 1.48, respectively.The thickness of each layer and the layer number for the UV mirror are optimized for UV perfect reflection under normal incidence.Based on the many-body effects for UV excitation, the graphene monolayer is considered as a two-dimensional conductive surface with a wavelength-dependent conductivity σ, which can be described by the equations of Fano model [20], where λ, h and c represent the free space wavelength, Plank constant, speed of light in vacuum, respectively; σ CB (λ) is the continuum background from the calculation of a manybody system and denotes the response away from the singularity [21]; the Fano parameter q = −1 determines the strength of the excitonic transition to the unperturbed band transitions and the asymmetry of the conductivity line shape; ɛ is the normalized energy by width Г = 0.78 eV relative to the resonance energy E r = 5.02 eV of the perturbed exciton.Optical simulations based on the finite element method (FEM) are performed in order to optimize the structure for complete UV absorption [22].
Fig. 1.Schematic drawing of the perfect UV absorber for graphene.The symbols w, p, t 1 and t 2 represent the width of nanoribbon, the period of nanoribbon, the thickness of silica and the thickness of calcium fluoride, respectively.

Results and discussions
Initially, we illuminate the role of the UV mirror and its design.The UV mirror is built up by an optimized stack of all-dielectric layers without optical loss, in order to perfectly reflect the UV light toward the substrate.Based on the characteristic matrix method for multilayer dielectric coatings [23], we adopt a stack of quarter-wave dielectric layers of alternate high index (ZrO 2 ) and low index (Na 3 AlF 6 ).On the condition of using quarter-wave dielectric layers under normal incidence, the optical admittance of the stack and its reflectance in air can be expressed by Eq. ( 3) and Eq. ( 4) as below,

2
, Here, n H , n L and n s denote the refractive index of ZrO 2 , Na 3 AlF 6 and substrate, respectively.The odd number m represents the amount of dielectric layers.These two equations imply the greater the number of layers the greater the reflectance.The band width of high reflectance Δλ = λ max -λ min can be determined by the following equation, 0 0 min max 4 arc sin , where λ 0 is the critical free space wavelength for the design of quarter-wave dielectric layers in the UV mirror, and λ max and λ min are the maximum and the minimum wavelengths of the high reflection band, respectively.Through above analysis, we adopt λ 0 = 280nm as the critical wavelength, and the UV mirror is optimized with 5 layers of ZrO 2 (26.9nm thick) and 4 layers of Na 3 AlF 6 (52.6nm thick), and a nearly-perfect reflection band is formed in the UV range, as shown in Fig. 2(a).Even if there might be some thickness deviations from λ 0 in practical fabrication, a broad UV band with near unity reflectance can be generated according to Eq. (5).In this broad UV band, optical transmission is almost blocked.In Fig. 2(a), the analytical result demonstrates good agreement with the simulation result based on FEM, which confirms the reliability of FEM simulations for further study on the photonic nanostructure with graphene.After elucidating the function of the UV mirror, we discuss the general effects of the proposed photonic structure for perfect UV absorption in graphene.As observed in Fig. 2(b), the absorbance of suspended graphene is very low in the UV-visible range, and the maximum UV absorbance is less than 9% based on the experimental data and FEM simulation [24].In the photonic nanostructure, the UV absorption in graphene depends on the polarization of normal incident light.The p-polarized light brings about less than 30.1% of maximum UV absorbance at λ = 267nm in the UV range, besides this, there are three obvious peaks of absorbance in the visible range, which are prominent compared with the UV absorbance peak.On the contrary, the use of s-polarized light suppresses the visible absorbance significantly (the maximum visible absorbance is less than 5.3%), and achieves a maximum UV absorbance up to 99.7% at λ = 270nm, which is 10 times more than that of the suspended graphene.This absorbance ratio has approached the reflectance utmost limit of the designed UV mirror, and the full wave at half maximum (FWHM) is as narrow as 9.7nm, which shows a good spectral selectivity.Therefore, the result in Fig. 2(b) demonstrates that the s-polarized light is evidently more advantageous than the p-polarized light for perfect UV absorption in graphene, so we mainly focus on the use of s-polarized light excitation for the next investigations.
In order to further unveil the physics, the distributions of magnetic field and electric field are plotted in Fig. 2(c) and 2(d) for further discussions.As shown in Fig. 2(c), compared with the magnetic field at λ = 332nm, the dielectric nanostructure has a remarkable magnetic dipole resonance at λ = 270nm, which traps the UV magnetic field between the silica nanoribbon and the UV mirror.The magnetic resonance is excited along the direction of incident magnetic field, and it leads to the concentration and enhancement of magnetic field compared to the off-resonance state at λ = 332nm.The confinement of magnetic field is mainly inside the CaF 2 layer and close to the triple frontiers of air, SiO 2 and CaF 2 .Simultaneously, as shown in Fig. 2(d), the electric field for λ = 332nm is extremely low, especially in the region of graphene, whereas the electric field for λ = 270nm is confined and enhanced in the region between each silica nanoribbon and the UV mirror, and also guided along the direction vertical to the incident plane.The significant field reduction on graphene at λ = 332nm is attributed to the superposition of electric fields between the incident light and the reflective light, which have almost the same amplitude and the opposite phases.The optical absorption depends on the electric field intensity on the graphene surface, so, at the resonance state of λ = 270nm, the enhancement of local electric field on the atomic layer of graphene results in extraordinary high UV absorption.For both Fig. 2(c) and 2(d), the UV mirror acts like a perfect magnetic/electric conductor to entirely reflect the UV wave, and to strengthen the resonant effects and UV absorption enhancement in graphene.The proposed perfect absorber is mainly based on the magnetic resonance mode for the dielectric nanostructure [25,26], and this mechanism is very similar to the metal/dielectric/metal plasmonic perfect absorber induced by the electric resonance mode under p-polarized light, which has been reported in our previous work [27].In these two kinds of perfect absorber, the roles of magnetic field and electric field are exchanged.Nevertheless, the all-dielectric perfect absorber indicates an overwhelming advantage for complete UV trapping in graphene versus the plasmonic perfect absorber.This is because the proposed nanostructure exempts considerable optical loss of using metals, and the enhanced electric field is always parallel to the graphene surface, which is quite important for complete optical absorption in 2D materials [28].Next, we consider the effects of CaF 2 thickness and nanoribbon period on UV absorption of graphene.It is observed in Fig. 3(a), when the thickness of CaF 2 is below 73nm, the maximum UV absorbance is less than 30%.As the thickness of CaF 2 increases from 73nm to 165nm, the central wavelength of UV absorption band has a red shift from 248nm to 287nm.This is because the resonance for the maximum UV absorbance has a dominant mode area in the CaF 2 , and it shifts to longer wavelengths as the thickness of CaF 2 is extended.For the size range of t 2 from 112nm to 133nm, the maximum UV absorption is maintained above 98%.In addition, the influence of the period of silica nanoribbons on UV absorbance of graphene is plotted in Fig. 3(b).As the period changes from 189nm to 300nm, the central wavelength of UV absorption band has a red shift from 240nm to 326nm.When the filling factor of w/p gets too small (e.g.p = 300nm) for a fixed size of w, the density of enhanced electric field is too low on graphene and insufficient for high absorption enhancement on the entire monolayer of graphene.Within the size range of p from 210nm to 250nm, the absorbance ratios are above 95.5%, and a maximum absorbance of 99.7% can be achieved at λ = 270nm by using the period of 221nm.The results in Fig. 3 illuminate that one can perform the engineering on the nanoribbon period and the thickness (or refractive index) of the dielectric layer between the nanoribbons and the UV mirror, in order to tune the absorption band of graphene in the UV range.
Furthermore, the effects of nanoribbon width w and thickness t 1 on UV absorption of graphene are also investigated.As shown in Fig. 4(a), when the filling factor of w/p is too small, the density of enhanced electric field is low on graphene and leads to insufficient absorption enhancement.As w becomes larger, the absorbance increases significantly.For the width range from 83nm to 137nm, the maximum absorbance ratios are kept above 99%.As the value of w continues to increase and nearly approach the value of p, the absorption goes down severely due to the attenuation of the resonance mode in the photonic structure.The SiO 2 nanoribbon with a sufficient width acts as a dielectric nanoantenna to excite the magnetic resonance mode, which mainly confines the magnetic field in the CaF 2 layer but not the SiO 2 nanoribbon itself.The magnetic resonance mode has a relatively large mode area in the CaF 2 layer, and this makes the wavelength of this mode weakly depend on w and strongly depend on p. Figure 4(b) indicates that the thickness of silica should not be less than 19nm for a maximum absorbance ratio of higher than 86% in graphene.As t 1 is getting larger enough, the magnetic resonance surrounding graphene can be well kept for sufficient electric field enhancement on graphene, and lead to high UV absorption.For the certain size ranges of t 1 from 23nm to 43nm and from 130nm to 150nm, the maximum absorbance ratios are above 95%.There is a relatively-low absorption enhancement around λ = 307nm due to the effect of diffraction order in Fig. 4(b), the similar effect is also observed in Fig. 3(a), and this can be immensely avoided by optimized the thickness of CaF 2 and SiO 2 , as implied in these two figures.Both of the results in Fig. 4(a) and 4(b) demonstrate that the size change of w and t 1 slightly influences the central wavelength around 275 nm for the UV absorption band of graphene.Based on above discussions about Fig. 4, for a large structural size range, our design has a high fabrication tolerance to the width and thickness of nanoribbons for complete UV absorption in graphene.This is quite important for practical photonic applications in authentic nanostructures and devices based on graphene.Finally, we study the influences of oblique light incidence.In the UV-visible range, graphene monolayer acts as a broadband optical absorbing material, and it is unlike the conventional semiconductor materials, which can be utilized for optoelectronic applications by certain band engineering through doping or gating.In order to make the UV absorption band actively tunable, one can manipulate the incident angle for the all-dielectric nanostructure with a specific size, as shown in Fig. 5(a).As the incident angle changes from 0° to 10°, the UV absorption of graphene gradually splits to two bands away from the central absorbing wavelength of normal incidence, and the two bands vary almost linearly with the value of incident angle.As seen in Fig. 5(b), the evolution of absorption band is attributed to the emergence of new electromagnetic modes in the all-dielectric perfect absorber.This property demonstrates that the optical response of the dielectric nanostructure is sensitive to the incident angle, which is totally different from the plasmonic perfect absorber [27].It is observed by Fig. 5, as the incident angle continues to increase, there is only a primary absorption band with a relatively-low peak and a large FWHM in the UV range (e.g.28°), and the UV absorption is significantly reduced when the incident angle is getting large.These results implies that one can tune the absorption band flexibly by changing the incident angle, which is promising for developing reconfigurable UV devices based on graphene.

Conclusion
In summary, we have demonstrated an all-dielectric perfect absorber for complete UV trapping in monolayer graphene.By using the magnetic resonance and the UV mirror, an optimized nanostructure with a total thickness of no more than 500nm can achieve a UV absorbance up to 99.7%.Our work provides a promising method for perfect UV absorption in sub-nanometer 2D materials, which is very important for developing high-performance UV devices.

Fig. 2 .
Fig. 2. (a) Reflectance of the UV mirror in the air.(b) Absorbance of suspended graphene, and absorbance of graphene in the nanostructure by using s-and p-polarized light under normal incidence, (c) magnetic field distributions and (d) electric field distributions for p = 221nm, w = 111nm, t 1 = 29nm and t 2 = 126 nm.

Fig. 3 .
Fig. 3. (a) Absorbance in graphene as a function of λ and t 2 , where p = 226.4nm,w = 117.3nmand t 1 = 28.9nm.(b) Absorbance in graphene as a function of λ and p, where w = 111 nm, t 1 = 29nm and t 2 = 126nm.All results are for s-polarized light under normal incidence.

Fig. 4 .
Fig. 4. (a) Absorbance in graphene as a function of λ and w, where p = 226.4nm,t 1 = 28.9nm and t 2 = 126nm.(b) Absorbance in graphene as a function of λ and t 1 , where p = 226.4nm,w = 111 nm and t 2 = 126nm.All results are for s-polarized light under normal incidence.

Fig. 5 .
Fig. 5. (a) Absorbance in graphene as a function of λ and the incident angle.(b) UV absorbance in graphene for three incident angles and the electric field distributions for two absorbance peaks at the incidence of 5°.All results are for s-polarized light incidence.