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Abstract
We investigate the absorption enhancement of an unstructured graphene sheet in a broad frequency range from terahertz (THz) to mid-infrared regime. Ultra-multiband graphene absorption enhancement is observed by integrating graphene in a metal-dielectric-graphene (MDG) sandwich structure for polarized waves. Multiple order Fabry-Perot (FP) resonances are demonstrated to be responsible for the multiband absorption. Furthermore, perfect absorption is realized by introducing the MDG structure on a metal reflector to suppress the transmission channel. In addition, the absorption peaks can be easily tuned by changing the doping level of graphene. This work may have potential for improving the performance of graphene based optoelectrical devices and can be regarded as a demonstration of a tunable broadband near-perfect metamaterial absorber.
© 2017 Optical Society of America
1. Introduction
Graphene, a layer of carbon atoms arranged in a honeycomb lattice, has drawn tremendous attentions due to its exotic electrical and optical properties [1, 2], holding promising prospects in various fields of optoelectronics such as transparent electronics [3–5], optical modulators [6–8], photodetectors [9–12] or active plasmonic devices [13–15]. Specifically, graphene is desirable for terahertz (THz) band communication and THz wave manipulation, with applications in filters, oscillators, detectors, and modulators [16–19]. Graphene exhibits a weak absorption efficiency of 2.3% in the visible to infrared range [20], which limits its interaction strength with lights. Thus, to enhance the optical absorption of graphene is highly desired in order to improve the performance of graphene based devices.
Different approaches have been proposed to enhance the absorption of graphene according to different frequency ranges. In the far-infrared or THz regime, graphene possesses strong plasmonic response. Largely enhanced or even perfect absorption has been demonstrated by exciting the localized graphene plasmons in patterned graphene structures [21–24]. However, this method comes with difficulty in electrically changing the carrier density in patterned graphene, which is against to the tunable feature of graphene plasmons. In the near-infrared or visible regime, metal plasmonic structures [25–27], photonic crystals [28–30] or optical cavities [31–33] can be introduced to enhance the near fields proximate to graphene at resonances. The enhanced near fields increase the interaction strength between graphene and the incident electromagnetic (EM) waves and thus can improve the absorption. Strong resonance leads to a strong absorption enhancement but with a narrow bandwidth, which is unfavorable in broadband applications. Designing different plasmonic elements with various sizes in one unit can partially broaden the bandwidth [34, 35]. Nevertheless, multiband absorption enhancement in a broad frequency range remains a challenge.
In this letter, we investigate the absorption enhancement of an unstructured graphene sheet in a broadband range from mid-infrared to THz frequencies. Near-perfect multiband absorption of graphene is demonstrated theoretically by integrating graphene into a metal-dielectric-graphene (MDG) sandwich structure. Highly confined graphene plasmons (GPs) are excited in the MDG structure, and multiple order Fabry-Perot (FP) resonances, formed by interference of oppositely propagating GPs waves, account for the multiband absorption enhancement. The graphene used here is an unpatterned sheet, which indicates the doping level shall be easy to be tuned electrically. Combined with the tunability of graphene plasmons, one can expect near-perfect graphene absorption at arbitrary frequencies in a range of 2 THz to 60 THz given an appropriate graphene Fermi level. This work may have potential for improving the performance of graphene based optoelectrical devices and can be regarded as a demonstration of a broadband metamaterial absorber.
2. Results
The schematic view of the proposed structure is shown in Fig. 1. A dielectric layer with a thickness of s is sandwiched by a metal grating and a single layer graphene sheet. In one period, the metal grating element, the dielectric spacer and the graphene sheet compose the MDG sandwich structure. The complementary structure of the top metal grating is introduced under the MDG structure to improve the absorption of graphene, with the purpose of mimicking the tip enhancement effect (see Appendix A.1). Geometric parameters are given as W = 1 μm, P = 2 μm, t = 40 nm and s = 5 nm, respectively.
Fig. 1 Schematic view of the proposed structure. Parameters are given as W = 1 μm, P = 2 μm, t = 40 nm and s = 5 nm, respectively.
We used FDTD (Finite-Difference Time-Domain, Lumerical) method to calculate the absorption spectrum of the proposed structure. In the simulation, gold is chosen as the metal material with permittivity obtained from experiment data [36]. Graphene is modeled as a conductive surface with conductivity calculated from random phase approximation (RPA) [37–39]. The conductivity of graphene is given by
In Eq. (1), , kB is the Boltzmann constant, is the reduced Plank constant, e is the elementary charge, T = 300 K is the temperature, ω is the angular frequency, EF is the Fermi energy and τ is the relaxation time, respectively. Here the intrinsic relaxation time is used with expression [38], where μ = 10 000 cm2/V·s is the mobility and = 106 m/s is the Fermi velocity. For simplicity and not losing generality, all dielectric materials are assumed to be air. Plane waves are incident along z axis with electric field polarized along x axis. PML (Perfect Matched Layer) boundary condition is adopted in z direction and period boundary condition is adopted in x and y directions. As a starting point, the Fermi energy of graphene is set to be 0.5 eV.The absorption spectra of the proposed structure (gray line and shadow), the proposed structure but without the graphene sheet (black line) and a freestanding graphene sheet (blue line) are shown in Fig. 2(a), respectively. As one can see the absorption of a single graphene layer is poor. The absorption raise at low frequencies is due to the significant increase of graphene’s conductivity (see Appendix A.2). Besides, gold acts like a perfect electrical conductor (PEC) in the considered frequency range, so little absorption is expected when graphene is not included in the structure. However, when graphene is integrated in the complementary grating structure, ultra-multiband absorption enhancement covering the considered frequency range is observed, which is more than one order higher than the inherent absorption of a graphene layer. Here we emphasize that the observed absorption comes almost completely from graphene, a detailed discussion of which can be found in Appendix A.3.
Fig. 2 Absorption spectrum and field distribution of |E/E0|. (a) Absorption spectra of the proposed structure (gray line and shadow), the proposed structure but without the graphene sheet (black line) and a freestanding graphene sheet (blue line). (b) Field distribution of |E/E0| at the three absorption peaks “I”, “II” and “III” marked in (a). White rectangles indicate where metal exists.
3. Physical Interpretation of the Multiband Absorption
To explore the underlying physics for the absorption enhancement, we examine the field distributions under these peaks. For example, the electric fields corresponding to the three peaks marked as “I”, “II” and “III” are shown in Fig. 2(b). As can be seen, the electric fields exhibit standing wave patterns, which indicates the multiband absorption peaks originate from resonances with different orders. We come up with a FP resonance model to account for the observed multiband absorption. The formation of FP resonances can be explained as follows. As depicted in the inset of Fig. 3(a), oppositely propagating GPs waves are excited in the MDG sandwich structure, and they interfere with each other resulting in the FP resonances. If we define the order of FP resonance as the number of standing wave nodes, the marked three peaks in Fig. 2(a) correspond to 3rd, 17th and 25th order of FP resonances, respectively. We note that the GPs excited here have distinct characteristics from GPs existing in a suspend graphene sheet. For example, the GPs excited here have larger wavevectors (see Appendix A.4) and they are highly confined in the MDG structure in z direction. They are more like the counterpart of plasmons existing in metal-dielectric-metal (MDM) structures. Plasmons are traditionally excited by grating couplers with undesired narrow bandwidth. To excite the GPs in the MDG structure in a broadband manner, we introduce the complementary structure. The opposite edges act as electrical dipoles, and can effectively excite the GPs in the MDG structure.
Fig. 3 Verification of the FP resonance model. (a) Calculated effective refractive index of GPs waves travelling in the MDG sandwich structure. Inset is the schematic illustration of how FP resonances are formed. (b) Wavelength of GPs derived from the FP resonance model and numerical simulations.
In order to verify the FP resonance model mentioned above, the wavelength of GPs waves in the MDG sandwich structure is calculated in two ways. And the effectiveness of the FP resonance model lies in the fact that the result given by the FP resonance model agree with the result derived from numerical simulations. In one way, the wavelength of GPs in the MDG structure can be calculated using FP resonance condition, which can be expressed as λGP = 2W/M, where λGP is the wavelength of GPs at resonance, M is the FP resonance order and W is the length of MDG sandwich, respectively. It is worthy to note that, due to the symmetry of the MDG structure, M can only be odd numbers. In another way, the GPs wavelength can be derived by calculating the effective refractive index (ERI) of the eigen travelling waves in the MDG structure. Then the wavelength of GPs can be derived as λGP = λ0/neff, where λ0 is the wavelength in vacuum, neff is the calculated ERI, respectively.
We use finite element method (FEM) to calculate the neff numerically and show it in Fig. 3(a). In the simulation, eigenmodes in the proposed MDG structure at different frequencies are calculated. And neff is defined as neff = β/k0, where β is the propagation constant of the eigenmodes (i.e. GPs waves) and k0 is the wavenumber in vacuum. As can be seen, the neff increases monotonically as the frequency increases, with a typical value of several tens. This means the GPs excited in the MDG structure can concentrate EM energy far beyond the diffraction limit, which is a prominent issue of compact optics. The numerically calculated GPs wavelength is shown in Fig. 3(b), which is in good agreement with results derived from FP resonance model, indicating the FP resonance model can interpret the observed multiband absorption enhancement properly. The GPs wavelength is tens of times smaller than the incident wavelength, which explains why the MDG structure with a width of 1 μm can sustain multiple orders of FP resonances.
4. Discussion
It is notable that the absorption maximum is limited to 50% in the above context. A detailed analysis confirms this is because the scattered far field of the proposed structure is symmetric with respect to the xy plane [21]. Theory has shown that perfect absorption of a thin layer can be realized when the transmission channel is suppressed. A straightforward way to cut off the transmission is to put the proposed structure on a metal reflector. Figure 4(a) shows the schematic view of the structure with a gold substrate. A dielectric spacer is introduced to minimize the influence of the metal reflector on the plasmon modes in the MDG structure. The thickness of the dielectric spacer is 1 μm. And again, for simplicity, the dielectric material is assumed to be air. Other parameters are the same as in Fig. 1.
Fig. 4 Near-perfect absorption enhancement. (a) Schematic view of the proposed structure with a metal substrate. The thickness of the dielectric spacer is 1 μm. Other parameters are the same as in Fig. 1. (b) Absorption spectra of the structure in (a) at different graphene doping levels represented by Fermi energy EF. An offset of 1 between adjacent lines is included for clarification.
Tunability is a prominent advantage of graphene plasmons. The graphene used here is an unpatterned sheet, so electrical doping of graphene is expected to be facile. The absorption spectra of the structure with a metal substrate at different doping levels are shown in Fig. 4(b). One can see that multiband near-perfect graphene absorption is achieved after the introduction of the metal substrate. What’s more, the absorption peaks blue shift significantly upon a higher doping level. For example, the peaks circled by dashed ellipses in Fig. 4(b) correspond to the same order of FP resonance. However, the resonant frequency moves from 18.2 THz to 35.1 THz when the graphene Fermi level is increased from 0.3 eV to 1.1 eV. A large tunable bandwidth of 16.9 THz is achieved. This observation indicates that one can expect perfect graphene absorption at arbitrary frequencies in an ultrabroad frequency range, as long as an appropriate graphene Fermi level is applied.
5. Conclusion
In summary, we have integrated graphene in a MDG sandwich structure to enhance the optical absorption of a single layer graphene sheet for polarized waves. Multiband absorption enhancement in an ultrabroad frequency range is realized by exciting multiple order FP resonances of GPs waves in the MDG structure. The introduction of a metal reflector can make the absorption perfect. Moreover, the absorption can be largely tuned by changing graphene doping level. In this manner, an absorptive metamaterial operating at a broad frequency range of 2 THz to 60 THz is demonstrated.
Appendix
A.1 Tip enhancement effect in the complementary metal grating structure
The tip enhancement effect has been widely utilized in tip enhanced Raman spectrum (TERS) or to launch graphene plasmons efficiently [40–47]. The essence of tip enhancement effect is the greatly enhanced fields around the tip. Here, to launch surface plasmon waves in the MDG structure effectively, we introduce the complementary metal grating structure to mimic such a tip. In the complementary structure, the two pairs of opposite edges in the vertical direction act as two tips and the fields around the tips are greatly enhanced.
We demonstrate the field enhancement of the complementary structure in Fig. 5. The near fields of a simple metal grating and a metal grating with a complementary structure are compared. As one can see, the near fields around the tip experience more than one order enhancement in the complementary structure.
Fig. 5 Distributions of Ez component of a metal grating (a) and a metal grating with the complementary structure (b). Shaded rectangles mark the region where metal material exits.
A.2 Conductivity of graphene
The conductivity of graphene is shown in Fig. 6 at various Fermi energy. At low frequencies, it experiences significant increase.
A.3 Comparison of absorption in graphene and in gold
The absorption per unit volume can be calculated from the divergence of the Poynting vector as . Then the absorption in different materials can be calculated by integration of in the volume where the interested material exists. The absorption in gold is calculated using this method. The absorption in graphene, however, is calculated as the extraction of absorption in gold from the total absorption, since graphene is modeled as a conductive surface without thickness and the integration cannot be done. The absorption in graphene and in gold is compared in Fig. 7. Almost all absorption is from graphene.
A.4 Dispersion of GPs in the MDG structure
In Fig. 8, we calculate the dispersion relationship of plasmons at metal-air interface [48], suspended graphene sheet [49] and the proposed MDG structure. One can see the wavevector of graphene plasmons in our MDG structure is much larger than in a simple graphene sheet.
Funding
National Natural Science Foundation of China (NSFC) (61178047, 61575006).
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