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It is well known that the absorption efficiency of a suspended monolayer graphene in the optical wavelength rang is only 2.3%, which limits its optoelectronic applications. In this work, we numerically demonstrate dual-band absorption enhancement of monolayer graphene at optical frequency, with the maximum absorption efficiency reaching to about 70% under optimum conditions. The dual-band absorption enhancement arises from the excitations of surface plasmon polaritons and magnetic dipole resonances in metamaterials. The monolayer graphene is sandwiched between a periodic array of Ag nanodisks and a SiO2 spacer supported on an Ag substrate. The resonance wavelengths of two absorption bands arising from surface plasmon polaritons and magnetic dipole resonances can be easily tuned by the array period and the diameter of the Ag nanodisks, respectively. Our designed graphene light absorber may find some potential applications in optoelectronic devices, such as photodetectors.
© 2017 Optical Society of America
1. Introduction
Monolayer graphene, a two-dimensional honeycomb lattice of carbon atoms, has been drawing increasing attentions in recent years, thanks to its outstanding electrical, mechanical and chemical properties [1]. The complex surface conductivity of graphene can be tuned by doping or gating, which has a wide variety of applications such as photodetection, photovoltage, photocatalyst, and so on [1]. The potential of graphene is also rising in photonics and optoelectronics, plasmonics, and metamaterials [1]. The inter-band optical absorption in a suspended monolayer graphene characterized by its fine-structure constant is known to have a universal value of 2.3% at a normal angle of incidence [2]. Such a poor optical absorption limits the applications of graphene in optoelectronics. Recently, there have been many efforts to enhance the electromagnetic wave absorption of graphene in a wide spectra range including GHz [3, 4], THz [5–20], infrared [21–45], and optical frequency [46–57]. The physical mechanisms behind the absorption enhancement of graphene include propagating or localized surface plasmon resonances [5, 15, 17, 18, 23, 24, 30, 31, 33, 37, 38, 40, 42, 44, 45, 54], guided-mode resonances [22, 28, 29, 50, 51, 55–57], Fabry-Perot cavity resonances [3, 6, 8, 10, 11], interference effects [4, 13, 16, 32], total internal reflection [20, 21, 47–49], magnetic dipole resonances [14, 25, 27, 36, 41, 53], etc. At the same time, there is also increasing interest to make graphene absorbers of electromagnetic waves as efficient and effective as possible through carefully engineering their versatile properties like tunability [8, 10, 12–14, 16, 18, 19, 30–32, 36, 45], broad bandwidth [3, 11, 15, 17, 18, 25, 40, 42, 46, 47], broad incident angle [9, 12, 14, 21, 23, 33, 36, 39, 40, 45, 53,54], and polarization independence [12, 14, 21, 23, 33, 39, 40, 43]. Dual-band or multi-band is also one of the most important performances of graphene absorbers, which has been investigated in THz and infrared regions [5, 9, 11, 14, 15, 17, 18, 23, 25, 27, 32, 33, 36, 40, 42]. However, in visible region, there are only a few researches on dual-band light absorption enhancement of monolayer graphene.
In this work, we will numerically investigate dual-band absorption enhancement of monolayer graphene in visible region, with the maximum absorption efficiency reaching to about 70% under optimum conditions. The dual-band absorption enhancement arises from the excitations of surface plasmon polaritons and magnetic dipole resonances in metamaterials. The monolayer graphene is sandwiched between a periodic array of Ag nanodisks and a SiO2 spacer supported on an Ag substrate. The influences of geometrical parameters on the light absorption of the monolayer graphene are studied in detail. It is found that the resonance wavelengths of two high-absorption bands arising from surface plasmon polaritons and magnetic dipole resonances can be easily tuned by the array period and the diameter of the Ag nanodisks, respectively. Our designed graphene light absorber may find some potential applications in optoelectronic devices such as photodetectors.
2. Results and discussions
Figure 1 shows schematically the unit cell of the designed metamaterials for dual-band light absorption enhancement of monolayer graphene. The monolayer graphene is sandwiched between the Ag nanodisk and the SiO2 spacer supported on an Ag substrate. The Ag nanodisk is supposed to lie on the xy plane, with the coordinate origin located at the center of the SiO2 spacer. Light is normally incident in the negative z-axis direction, with its polarization along the x-axis direction. The commercial software package“EastFDTD”, which is based on finite difference time domain (FDTD) method [58], is used to calculate the reflection and absorption spectra, and the electromagnetic field distributions. In numerical calculations, the frequency-dependent relative permittivity of Ag is taken from experimental data [59], and the refractive index of SiO2 is taken to be 1.45. Under the random-phase approximation, the surface conductivity σ of graphene includes the intraband term σintra and the interband term σinter [60, 61], where
Here, ω is the frequency of the incident light, e is the electron charge, ħ is the reduced Planck’s constants, Ef is the Fermi energy (or chemical potential), τ is electron-phonon relaxation time, kB is the Boltzmann constant, and T is a temperature in K. The graphene’s effective permittivity εg could be written as εg = 1 + iσ/(ε0ωtg), where ε0 is the permittivity in the vacuum, tg is the thickness of graphene sheet. In our calculations, Ef = 0.50 eV, τ = 0.50 ps, T = 300 K, tg = 0.35 nm. Although this work focuses on numerical investigation, the designed graphene metamaterials may be realized experimentally by the following procedures [62]: the SiO2 spacer is first coated on the Ag substrate through thermal evaporation, and then the monolayer graphene is coated on the top of the SiO2 spacer after a chemical vapor deposition (CVD), finally the Ag nanodisk array is fabricated on the monolayer graphene with sufficiently high quality factors.
Fig. 1 Schematic of metamaterials for dual-band light absorption enhancement of monolayer graphene. px and py are the array periods along the x and y directions. t is the thickness of the SiO2 spacer. d and h are the diameter and the height of the Ag nanodisk. Ein, Hin, and Kin are the electric field, magnetic field, and wave vector of the incident light, which are along the x, y, and z axes, respectively.
Figure 2 shows the calculated absorption spectra of graphene, Ag, and total metamaterials, under normal incidence of light. Two resonance modes are found, which are centered at wavelengths of λ1 = 545.5 nm and λ2 = 784.5 nm. For resonance mode λ1, the normalized absorptions of graphene, Ag, and total metamaterials are 0.35, 0.55, and 0.90, respectively. For resonance mode λ2, the corresponding normalized absorptions are 0.72, 0.15, and 0.87, respectively. It is well-known that the absorption efficiency of a suspended monolayer graphene in the optical wavelength rang is only 2.3%, which limits its optoelectronic applications [2]. Obviously, the absorption efficiency of the monolayer graphene in our designed metamaterials is enhanced noticeably. We hope that the designed graphene light absorber could find some potential applications in optoelectronic devices, such as photodetectors. However, for practical applications of photodetectors, high light absorption in graphene is only a necessary condition, there are still many steps ahead [63, 64]. For example, the electrodes must be deliberately integrated into the graphene absorbers.
Fig. 2 Normal-incidence absorption spectra of graphene (black square), Ag (red circle), and total metamaterials (green triangle) in the wavelength range from 500 to 1000 nm. Geometrical parameters: d = 150 nm, h = 50 nm, t = 30 nm, px = py = 500 nm.
In order to well understand the physical mechanisms underlined two resonance modes, in Fig. 3 we plot the electric and magnetic field distributions at the resonance wavelengths of λ1 and λ2. For resonance mode λ1, in Figs. 3(a) and 3(b) one can see that parallel electromagnetic field bands stretching along the y-axis direction are formed, although they are disturbed near the Ag nanodisk. In fact, such electromagnetic field distributions correspond to the excitation of surface plasmon polaritons [65]. For resonance mode λ2, in Figs. 3(c) and 3(d) it is clearly seen that the electric fields are mainly concentrated near the edge of the Ag nanodisk, with two field “hotspots” on the left and right sides extending into the SiO2 spacer; and the magnetic fields are highly confined within the SiO2 spacer, with a maximum under the Ag nanodisk. Such distribution properties of electromagnetic fields are the typical characteristics of a magnetic dipole resonance [66].
Fig. 3 Normalized electric field intensity (E/Ein)2 and magnetic field intensity (H/Hin)2 on the xoz plane across the center of the SiO2 spacers, at the resonance wavelengths of λ1 and λ2 labeled in Fig. 2. Red arrows represent the field direction, and colors show the field strength.
In the following, we will investigate in detail the influences of geometrical parameters on the graphene absorption. We firstly investigate the influences of the size of the Ag nanodisk. For this purpose, Fig. 4 presents the normal-incidence absorption spectra of a series of graphene metamaterials, with the diameter d of the Ag nanodisk decreased from 150 to 110 nm in steps of 10 nm. When d is decreased, resonance mode λ2 will have an obvious blue-shift, while resonance mode λ1 almost has no shift. This is because resonance mode λ2 is related to a magnetic dipole resonance whose position depends strongly on the diameter of the Ag nanodisk, and resonance mode λ1 origins from surface plasmon polaritons whose excitation wavelength is determined by the period of the Ag nanodisk array. At the same time, the monolayer graphene retains the light absorptions of about 35% and 70% for two resonance modes, respectively.
Fig. 4 Normal-incidence absorption spectra of monolayer graphene in the wavelength range from 500 to 1000 nm. The diameter d of the Ag nanodisk is varied from 150 to 110 nm, and the other geometrical parameters are the same as those in Fig. 2.
Then, we investigate the influences of the period of the Ag nanodisk array on the light absorption of the monolayer graphene. To do this, in Fig. 5 we present the normal-incidence absorption spectra of a series of graphene metamaterials, with the period px along the x-axis direction increased from 500 to 700 nm in steps of 50 nm. With increasing period px, resonance mode λ1 will be red-shifted noticeably because the excitation wavelength of surface plasmon polaritons becomes larger, and the light absorption of the monolayer graphene is enhanced from 35% to 60%. For the period px to be increased continuously, however, resonance mode λ2 is only red-shifted slightly, since the excitation wavelength of the magnetic dipole resonance is insensitive to the period of the Ag nanodisk array. Simultaneously, the graphene absorption has a slight enhancement when the period px is increased.
Fig. 5 Normal-incidence absorption spectra of monolayer graphene in the wavelength range from 500 to 1000 nm. The period px along the x-axis direction is varied from 500 to 700 nm, and the other geometrical parameters are the same as those in Fig. 2.
To further confirm that resonance mode λ1 is closely related to the excitations of surface plasmon polaritons, in Fig. 6 we compare the resonance wavelengths of surface plasmon polaritons and absorption peak λ1 for the period along the x-axis direction px = 500, 550, 600, 650, and 700 nm. It is clearly seen that surface plasmon polaritons are also red-shifted when px is increased, which are on the whole consistent with absorption peak λ1 in resonance positions. The differences of the resonance wavelengths of surface plasmon polaritons and absorption peak λ1 are mainly because of the inhomogeneous superstrate of Ag substrate.
Fig. 6 The resonance wavelengths of surface plasmon polaritons (SPPs) and absorption peak λ1 labeled in Fig. 5. The period px along the x-axis direction is varied from 500 to 700 nm in steps of 50 nm, and the other geometrical parameters are the same as those in Fig. 2.
3. Conclusion
In summary, we have numerically investigated dual-band absorption enhancement of monolayer graphene at optical frequency, origining from surface plasmon polaritons and magnetic dipole resonances in metamaterials. The monolayer graphene is sandwiched between a periodic array of Ag nanodisks and a SiO2 spacer supported on an Ag substrate. We have studied in detail the influences of geometrical parameters on the light absorption of the monolayer graphene. The resonance wavelength of the absorption peak origining from surface plasmon polaritons can be easily tuned by the array period, and the light absorption of the monolayer graphene can be enhanced from about 35% to 60%. The resonance wavelength of the absorption peak origining from magnetic dipole resonances can be easily tuned by the diameter of the Ag nanodisk, and the monolayer graphene retains the light absorptions of about 70%. We hope that our designed graphene metamaterials could find some potential applications in optoelectronic devices, such as photodetectors.
Funding
National Natural Science Foundation of China (NSFC) (11304159 and 11104136); Natural Science Foundation of Zhejiang Province (LY14A040004); Natural Science Foundation of Jiangsu Province (BK20161512); Qing Lan Project of Jiangsu Province; Specialized Research Fund for the Doctoral Program of Higher Education of China (20133223120006); NUPTSF (NY217045); Open Project of State Key Laboratory of Millimeter Waves (No. K201821).\
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