Graphene is a two-dimensional (2D) carbon sheet with a honeycomb lattice^[1], because of its outstanding optical, mechanical and electronic characteristics^[2–4], it has aroused the interest of scientific researchers. The absorption efficiency of monolayer graphene is 2.3% within visible and near-infrared regions^{[5, 6]}, even though the absorption efficiency is considered to be large to a thin film^[7], but still can’t meet the requirements of practical applications, such as solar cells or photodetectors^{[8, 9]}.

In order to improve monolayer graphene absorption efficiency, several physical mechanisms have been proposed including one-dimensional photonic crystals^[10], surface plasmon^[11], dielectric multilayer^[12], magnetic dipole^[13] and so on. However, these methods only improve the absorption efficiency of graphene in the narrowband spectral ranges, which restrict their potential applications^[14]. For broaden bandwidth of graphene absorption, attenuated total reflection^{[7, 15]}, multi-resonator approach^{[13, 14, 16]}, periodical arrays of dielectric bricks^[17] and so on are applied. However, most of the studies are concentrated in THz band^[16–18], there are few studies in the visible and near-infrared regions, Ref. [16] achievs enhanced absorption of graphene in visible band, but the bandwidth only 0.1 μm, Ref. [14] achieves enhanced optical absorption of graphene in the wavelength range from 0.45 to 0.8, but its structure is more complicated to manufacture.

In this letter, we propose a novel hybrid nanostructure and numerically demonstrate the graphene absorption efficiency over 30% and absorption bandwidth more than 0.3 μm in near-infrared region. The calculation unit of the hybrid structure is a sandwich structure, in which the monolayer graphene is sandwiched between the three gratings and the SiO₂ spacer on the Ag substrate, and the three individual Ag gratings and the Ag substrate can excite three independent magnetic dipole resonances, which leads to monolayer graphene absorption enhancement over three different wavelength bands, in addition the proposed hybrid nanostructure manufacturing process is simple. By finely tuning the structure parameters, we can make the three independent magnetic dipole resonances overlapped, which leads to broadened absorption bandwidth. We also figure out that thickness of SiO₂ and widths of gratings are critical parameters to the position of absorption peaks.

Fig. 1 shows the representation of the proposed hybrid nanostructure, which consists of silver (Ag) metal grating, monolayer graphene layer, silica (SiO₂) layer and Ag substrate from top to bottom. In the unit cell of the hybrid nanostructure, w₁, w₂ and w₃ are three gratings widths, respectively, s is grating spacing, h is the thickness of grating, d is the thickness of SiO₂ spacer, h_s is the thickness of Ag substrate and P is the period of unit cell.

In numerical calculations, the computational model is three-dimensional (3D), and the length in the y direction is 3 μm. The refractive index of SiO₂ is set to be 1.45, and the relative dielectric constant of Ag is expressed by drude model^[19], as shown in Eq. (1), ε_Ag is the relative dielectric constant of Ag, ω_p = 1.39 × 10¹⁶ rad/s is plasma frequency, γ = 2.7 × 10¹³ s^–1 is attenuation rate, ω is the angular frequency of incident light. In order to enhance the absorption of graphene, the Ag substrate thickness must be greater than its skin depth in near-infrared region^[20], so in this letter, h_s is taken to be 0.1 μm.

${\varepsilon _{{\rm{Ag}}}}={\rm{ 3.4}}-\frac{{\omega _{\rm{p}}^{\rm{2}}}}{{{\omega ^{\rm{2}}}-{\rm{ i}}\omega \gamma }}.$ (1)

Under the random-phase approximation, the complex frequency-dependent surface conductivity σ can be expressed as the sum of the intraband σ_intra and interband conductivity σ_inter^{[21, 22]}:

${\sigma _{\operatorname{intra}}}{\rm{ = }}\frac{{{\rm{i}}{{\rm e}^2}{k_{\rm B}}T}}{{\pi {\hbar ^2}(\omega +\ {\rm{i}}\varGamma )}}\left[ {\frac{{{\mu _{\rm c}}}}{{{k_{\rm B}}T}} + 2\ln ({{\rm e}^{\frac{{ - {\mu _{\rm c}}}}{{{k_{\rm B}}T}}}} + 1)} \right],$ (2)

${\sigma _{\rm inter}} = \frac{{i{e^2}}}{{4\pi \hbar }}\ln \left[ {\frac{{2{\mu _{\rm c}} - \left( {\omega + {\rm{i}}{\rm{2}}\varGamma } \right)\hbar }}{{2{\mu _{\rm c}} + (\omega + {\rm{i}}{\rm{2}}\varGamma )\hbar }}} \right],$ (3)

where e is electron charge, ħ is reduced Planck’s constant, μ_c is chemical potential, Γ = 1/2τ is phenomenological scattering rate^[23], τ is momentum relaxation time, i is the imaginary unit, k_B is Boltzmann constant, T is temperature in K. On the basis of surface conductivity σ, the graphene’s effective permittivity ε_g can be express as^[24]:

${\varepsilon _g} = 1 + {\rm{i}}\frac{\sigma }{{\omega {\varepsilon _0}{t_g}}},$ (4)

where ε₀ is vacuum dielectric constant, t_g is the thickness of monolayer graphene layer. In our calculations, T = 300 K, μ_c = 0.1 eV, t_g = 0.5 nm.

Fig. 2 shows the calculated absorption spectra of monolayer graphene at normal incidence, under single-width and triple-widths conditions. These results are calculated by FDTD (finite-difference time-domain) simulation, FDTD can directly simulate the distribution of field and has high accuracy, and it is one of the most widely used numerical simulation methods at present. In single-width case, black, red and blue lines represent absorption efficiencies of graphene at grating width 0.14, 0.16, and 0.18 μm respectively. It can be clearly seen from Fig. 2 that for such single-width gratings, absorption bandwidth is very narrow, the bandwidth only 0.086 μm. The three absorption peaks are caused by magnetic dipole resonances.

If we put these three different gratings stripe in a period, forming a triple-widths grating, the graphene absorption bandwidth with absorption efficiency over 30% can reach 0.311 μm, as denoted by the gray line in Fig. 2. The broadening of graphene absorption bandwidth is due to the spectrally overlapping of magnetic dipole resonances caused by the three different gratings. However, it should be noticed that absorption peaks of triple-widths grating is slightly shifted from single-width gratings.

By calculating Maxwell's equations and combining with boundary conditions, the magnetic field distribution at resonance wavelength is obtained. The magnetic field distribution of the hybrid nanostructure at resonance wavelength of λ₁₁, λ₂₂, λ₃₃ are shown in Fig. 3, which are related to magnetic dipole resonances. At resonance wavelength λ₃₃, the magnetic fields are mainly confined to the SiO₂ spacer under the third Ag grating with a width w₃ (see Fig. 3(c)), whereas at the resonance wavelength λ₁₁, the magnetic fields are not only highly limited to SiO₂ spacer under the first Ag grating with a width w₁, but also some magnetic fields are confined to the SiO₂ spacer under the second Ag grating with a width w₂ (see Fig. 3(a))^{[14, 21]}. When the resonance wavelength is λ₂₂, although most of he magnetic fields are confined to the SiO₂ spacer under the second Ag grating with a width w₂, but also there are some magnetic fields in the SiO₂ spacer under the first and third Ag gratings with width w₁ and w₃ (see Fig. 3(b)). Briefly speaking, the wide absorption bandwidth of graphene is caused by the three magnetic dipole resonances overlapped.

Fig. 4 shows effect of grating width on absorption peaks. From Fig. 4(a) to Fig. 4(c), the width w₁, w₂ and w₃ of Ag gratings are increased gradually. It can be seen from Fig. 4 that when the widths of gratings are decreased, the absorption peaks will be blue-shifted. This phenomena can be explained by formula^[19,25]:

$ {\lambda _{{\rm{MP}}}}={\rm{ 2}}\pi {c_0}\sqrt {({L_{\rm m}} + {L_{\rm e}})C} , $  (5)

where c₀ is the speed of light in free space, λ_MP is magnetic dipole resonance wavelength, C is the capacitance, which is introduced by the Ag grating and Ag substrate, the capacitance is determined by SiO₂ spacer thickness, contact area between grating and substrate , electronic distribution on metal surface. L_m and L_e are mutual inductance and self-inductance, which are also introduced by the Ag grating and Ag substrate^{[19, 24]}. When the widths of gratings reduced or increased, the capacitance C will reduce or increase, for the contact area between grating and substrate is smaller or larger. Therefore as the widths of gratings increase, the graphene absorption peaks will be red-shifted, as depicted in Fig. 4.

Not only widths of gratings can affect graphene absorption peaks, but also the SiO₂ spacer thickness, as shown in Fig. 5. In Fig. 5 we can clearly see as the SiO₂ spacer thickness increases, the graphene absorption peaks will be blue-shifted, the phenomenon can also be explained by Eq. (5): when the SiO₂ spacer thickness increases, the spacing between Ag gratings and Ag substrate will get larger, which leads to capacitance C gets smaller, therefore λ_MP will be blue shifted.

We then investigate the influence of grating spacing s on graphene absorption peaks. From Fig. 6 we can find that the grating spacing almost has no effect on the graphene absorption peaks, owing to the fact that most of magnetic fields are almost confined to the SiO₂ spacer directly under the Ag gratings, only small magnetic fields is concentrated near the left and right edges of the Ag gratings (see Fig. 2).

In summary, a hybrid nanostructure consisting of a monolayer graphene sandwiched between three Ag gratings with different widths and a SiO₂ spacer on an Ag substrate is proposed to broaden monolayer graphene absorption bandwidth. The wide absorption bandwidth is related to the magnetic dipole resonances, which are excited between the three different widths Ag grating and Ag substrate. Absorption bandwidth of 0.311 μm in near-infrared region is demonstrated with the absorption efficiency over 30% and the dependence of absorption peaks on Ag grating widths and SiO₂ spacer thickness is also studied.