Near-Perfect Narrow-Band Tunable Graphene Absorber with a Dual-Layer Asymmetric Meta-Grating

Abstract

A near-perfect narrow-band graphene-based absorber was fabricated using a resonant system integrated with an asymmetric meta-grating at a wavelength of 1550 nm. By optimizing the gap between the two grating strips, the absorption of monolayer graphene can be increased to 99.6% owing to the strong field confinement of the bottom zero-contrast grating (ZCG). The position of the absorption spectrum could be adjusted by tailoring the grating period or the thickness of the waveguide layer. Interestingly, absorption spectrum linewidth can be tailored by changing the thickness of the spacer layer. The accidental bound states in the continuum (BICs) are then demonstrated in the structure. Moreover, the designed structure realizes the dynamic adjustment of the absorption efficiency at a specific wavelength, which has excellent potential in integrated optical devices and systems.

1. Introduction

Graphene is a promising two-dimensional material for ultrafast optoelectronic devices owing to its unique photoelectric properties [1,2,3,4]. It is widely used in photodetectors [5,6,7,8], modulators [9,10,11,12,13], tunable optical filters [14], polarizers [15], and sensors [16,17]. However, the performance of graphene-based optoelectronic devices is limited by the low absorption efficiency of monolayer graphene in the near-infrared (NIR) region [18,19]. Therefore, it is essential to engineer light-graphene interactions in this region. Generally, some graphene-based absorbers have been reported using dielectric or resonant metal structures, such as Fabry–Perot cavities [20], metal gratings [21], resonant waveguide grating [22,23,24,25], photonic crystals [26,27], and quasi-bound states in the continuum (quasi-BICs) resonance [28].

With the proposal of various types of graphene absorbers such as multi-band absorbers [29,30,31], broadband absorbers [32], and polarization-insensitive wide-angle metamaterial absorbers [33], the dynamic control of graphene absorbers has become an important issue. For instance, Wu et al. investigated the tunable near-infrared perfect absorption of graphene with bandwidth ranging from 5.7 to 187.1 nm in the compound grating waveguide structure supporting the quasi-BICs [34]. Xiao et al. proposed a two-port resonant structure to achieve a significant bandwidth manipulation of the absorption bandwidth from ultra-narrow to broadband by integrating graphene with a lossless photonic crystal slab [35]. Zhang et al. designed a subwavelength grating coupled hybrid structure to realize the dynamically switchable triple-band absorption enhancement of graphene [36]. In brief, most researchers have studied graphene absorbers using two approaches. One approach involves identifying and proposing methods to enhance the absorption efficiency of graphene, and the other involves studying the characteristics of the absorption spectrum to improve the performance of the absorber.

Herein, we investigated the dynamic absorption tuning of monolayer graphene at communication wavelengths with a dual-layer asymmetric meta-grating structure comprising a compound grating, spacer layer, and zero-contrast grating (ZCG). Monolayer graphene was embedded between the compound grating and the spacer layer. A nearly perfect absorption with a bandwidth of 0.4 nm was achieved at 1550.6 nm because of the strong localization ability of the ZCG to the light field in the designed structure. The results show that changing the thickness of the spacer layer in the dual-layer asymmetric meta-grating can control the linewidth of the absorption peak and can excite an accidental BICs state which may occur in any structure but requires careful tuning of the parameters. Furthermore, the position of the absorption peak can be adjusted by changing the thickness of the grating waveguide layer and the grating period. More importantly, the absorption efficiency of graphene can be dynamically adjusted according to the requirements of the actual situation by changing its chemical potential. This research will be helpful for designing graphene-based high-performance optoelectronic devices, such as optical detectors, modulators, and optical switches, which also show great potential for realizing advanced hybrid platforms in integrated optical systems.

2. Structure and Theory

Figure 1a shows a diagram of the proposed graphene absorber, which comprises compound grating (top grating), monolayer graphene, SiO₂ spacer layer, and ZCG (bottom grating). Monolayer graphene was sandwiched between the top grating and the SiO₂ spacer layer. The bottom grating was deposited on the back of the SiO₂ spacer layer to prevent the transmission of the incident light at 1550 nm. As a demonstration, the refractive indices of Si and SiO₂ were considered to be 3.47 and 1.44, respectively [37]. The structural parameters were assumed as follows: d_c = 430 nm, t_g = 0.34 nm, d_h = 355 nm, d_g = 415 nm, P = 696 nm, d_s = 128 nm, g = 21 nm, w₁ = 200 nm, w₂ = 150 nm, and w₃ = 430 nm. Here, the input light was assumed to be TE-polarized at normal incidence. The structure is finitely periodic in the x direction and uniform along the y direction.

Monolayer graphene was modeled as an ultrathin dielectric layer with a thickness of t_g = 0.34 nm. The material properties of graphene can be described by its surface conductivity, which can be obtained using the Kubo equation [38,39]:

$$\begin{array}{ll}{\sigma }_{\mathrm{gra}}& ={\sigma }_{\mathrm{intra}}(\omega )+{\sigma }_{\mathrm{inter}}(\omega )\\ & =i\frac{e^2{k}_{B}T}{\mathsf{\pi }{\hslash }^2\left(\omega +i2\Gamma \right)}\left\{\frac{{\mu }_c}{k_{B}T}+2\mathrm{In}\left[\exp (-\frac{{\mu }_c}{k_{B}T})+1\right]\right\}+i\frac{e^2}{4\mathsf{\pi }\hslash }\mathrm{In}\left[\frac{2\left|{\mu }_c\right|-(\omega +i2\Gamma )\hslash }{2\left|{\mu }_c\right|+(\omega +i2\Gamma )\hslash }\right],\end{array}$$

(1)

where σ_intra(ω) and σ_inter(ω) represent the intra- and inter-band transition conductivities, ω is the angular frequency, e is the charge of an electron, $\hslash$ is the reduced Planck constant, and k_B is the Boltzmann constant. T = 300 K is the Kelvin temperature, Γ = 1/2τ is related to the electron–phonon relaxation time τ, chemical potential of graphene µ_c = 0.3 eV, Fermi velocity υ_F = 10⁶ m/s, and carrier mobility μ = 10⁴ cm²/(V·s) [40]. The relationship between the surface conductivity σ_gra and the relative permittivity of monolayer graphene can be expressed by the following formula: ε_gra = 1 + iσ_gra/ωε₀t_g, where ε₀ is the vacuum permittivity [41]. Figure 1b shows the relationship between the chemical potential and permittivity of the monolayer graphene at 1550 nm. The permittivity of graphene strongly depends on its chemical potential, and the imaginary part of the permittivity decreases sharply when the chemical potential is approximately 0.4 eV.

The proposed resonant system based on a dual-layer asymmetric meta-grating structure can be considered a single-port lossless resonator. According to coupled-mode theory (CMT), the absorption efficiency of the proposed device can be calculated as follows [27,42]:

$$A=\frac{4\delta \gamma }{{\left(\omega -{\omega }_0\right)}^2+{\left(\delta +\gamma \right)}^2},$$

(2)

where γ and δ represent the external leakage rates and inherent losses of materials in the proposed structure, respectively, and ω and ω₀ represent the working frequency and the central resonant frequency, respectively. When the intrinsic loss of the material is equal to the external leakage rate, that is δ = γ, the system reaches the critical coupling condition, and the total absorption of monolayer graphene can be realized at the resonant frequency ω₀.

3. Results and Discussion

Theoretically, maintaining δ = γ of the resonance is critical for achieving critical coupling, and the intrinsic loss δ is almost constant. Therefore, controlling the external leakage rate γ plays a key role in achieving critical coupling. We first demonstrate the relationship between various structural parameters and the external leakage rate, and the influence of the structural parameters on the absorption of the proposed structure. Figure 2a shows the calculated absorption as a function of the wavelength for the proposed structure as the gap g increases from 0 to 84 nm. The efficiency of the absorption peak first increases gradually, owing to the enhanced excitation intensity of the resonant mode. For g = 21 nm, the maximum light absorption of the monolayer graphene reached 99.6%. As g further increased, the absorption efficiency became relatively weak, and the bandwidth of the absorption peak gradually increased. To better explain the effect of the spacing g on the entire resonant system, the phase diagrams at different g values were calculated, as shown in Figure 2b. The sharp π-phase transition at g = 21 nm indicates that a critical coupling condition is achieved [43,44]. A nearly perfect absorption peak with a bandwidth of 0.4 nm is achieved at 1550.6 nm, as shown in Figure 2c. We then compared the theoretical results from the CMT with the simulation results from the rigorous coupled-wave analysis (RCWA) and finite element method (FEM) methods. The total quality factory of the entire structure can be expressed as Q_CMT = Q_δQ_γ/(Q_δ + Q_γ), where Q_δ = ω₀/2δ and Q_γ = ω₀/2γ represent the intrinsic loss and external leakage, respectively. The fitted δ = γ = 1.2477 × 10¹⁰ Hz was obtained when critical coupling occurred, and the value of Q_CMT was 3876.5328.

By contrast, the total quality factor Q can be acquired from Q = λ₀/FWHM, where the full width at half maximum (FWHM) is only 0.4 nm at the resonant wavelength of 1550.6 nm. Thus, we obtained Q = 3876.5. The value of Q_CMT and Q are almost the same, indicating that the theoretical results agree with the simulation results. To better explore the physical mechanism of the narrow-band absorption peaks, Figure 2d shows the electric field amplitude distribution of the designed structure on the x-z plane at a resonant wavelength of 1550.6 nm. One can see that most of the electric field is concentrated on the bottom grating of the designed structure. In other words, the strong localization ability of ZCG in the designed structure significantly enhances the interaction between light and graphene.

Furthermore, we studied the dependence of the absorption spectrum on the spacer layer thickness in the designed structure, as shown in Figure 3. The absorption map of the proposed system for different spacer layers d_s is shown in Figure 3a. The results show that the absorption peak blue-shifts with increasing spacer thickness when the thickness of the spacer layer is less than 100 nm. A near-perfect absorption spectrum is achieved at the wavelength of 1550.6 nm when d_s = 128 nm. However, the position of the absorption peak keeps unchanged when d_s is greater than 150 nm. To further investigate this phenomenon. We calculate the reflection spectra of the designed structure under different d_s, as shown in Figure 3b. One can see that the reflection spectrum at the wavelength of 1550.6 nm gradually disappears when d_s gradually increased from 0 to 250 nm. Here, an accidental BICs’ state that can occur in any structure but requires careful adjustment of the parameters is excited [45]. In addition, the bandwidth of the absorption peak decreases rapidly as d_s increases from 0 to 300 nm. The FEM can rigorously calculate the eigenvalues of the structure, and the complex eigenvalues N can be described with the formula N = N_real − iN_imag [46]. To further explain the regulation mechanism of spacer layer thickness on the absorption spectra, we use the FEM to calculate the complex eigenvalue N of the proposed structure without graphene at different d_s, as shown in

Table 1. Complex eigenvalues N corresponding to different thicknesses of the spacer layer.

ds (nm)	N	Nreal/(2 × Nimag)
50	1.21441 × 1015 − 2.3160 × 1011i	2621.8
100	1.21473 × 1015 − 1.1039 × 1011i	5502.2
150	1.21479 × 1015 − 4.9016 × 1010i	12,393
200	1.21479 × 1015 − 2.0509 × 1010i	29,616

. The imaginary part of the complex eigenvalue decreases with an increase in d_s, and the real part increases gradually and then remains unchanged. As a result, the complex eigenvalue plays a key role in determining the absorption performance in the designed graphene absorbers with difficult d_s.

Subsequently, we studied the influence of waveguide thickness d_h and grating period P on the absorption spectra. According to Figure 4a, the central resonant wavelength exhibits a red-shifts as d_h varies from 335 to 375 nm. The absorption efficiency of the proposed dual-layer asymmetric meta-grating structure is high, which differs from our previous work [29]. Figure 4b shows the absorption spectra of the designed structure when the period P increases from 666 to 726 nm. The results show that the absorption wavelength shifts to the long-wave direction as the period increases because the successful excitation of guided-mode resonance must satisfy the phase-matching condition [47]. Meanwhile, the absorption spectrum maintained a high absorption efficiency when the period varied in the range of 60 nm. The results in Figure 4 show that the spectral position of the absorption peak can be controlled by tailoring the grating waveguide layer thickness or grating period. The realization of adjustable and switchable functions that satisfy the requirements of actual equipment has become the main direction of current research [48]. In our proposed graphene absorber with a dual-layer asymmetric meta-grating structure, the resonant wavelength can be adjusted by adjusting the thickness of the waveguide layer or grating period, which meets the requirement of wavelength tunability.

In the above analysis, we adjusted the absorption efficiency and the spectral position of the absorption peak by changing the structural parameters. However, it is undesirable to change the size of the absorber or further adjust the wavelength of the absorption peak by refabricating a new structure for practical applications. The chemical potential of graphene can be controlled by external gate voltage [49]. The relative permittivity of graphene changes with the chemical potential as shown in Figure 1b. Therefore, the influence of the chemical potential μ_c of monolayer graphene on the absorption response of the structure was studied based on the tunable properties of graphene [50]. Figure 5a shows that the absorption efficiency of the absorption peak can be flexibly tuned by changing the chemical potential. The absorption efficiency and resonant wavelength change simultaneously when the structural parameter g is changed. Here, a dynamic adjustment of the graphene absorption efficiency is realized at a specific wavelength by controlling the chemical potential μ_c. Figure 5b shows the absorption of graphene as a function of μ_c at a wavelength of 1550.6 nm. When μ_c increases from 0.2 to 0.34 eV, the absorption of graphene remains unchanged, and the corresponding modulation depth is minimal [50]. When u_c changes from 0.34 to 0.51 eV, the absorption efficiency of graphene can be flexibly regulated, and the position of the absorption peak remains unchanged. As μ_c increases from 0.51 to 0.8 eV, the absorption efficiency of graphene is finally modulated to very close to zero. Moreover, according to reference [37], the absorption of graphene can exhibit the characteristics of electrical switches when μ_c changes from 0.34 to 0.51 eV. Among them, high absorption efficiency is marked as an “on” state, and low absorption efficiency is marked as an “off” state. Unlike the wired control method, we can control the driving signal in a noncontact manner by adjusting the optical signal with the designed dual-layer asymmetric meta-grating structure, which shows great potential in integrated optical systems [51].

4. Conclusions

In this study, using a dual-layer asymmetric meta-grating structure, we obtained a narrow-band tunable graphene absorber in the communication band. The calculation results show that the absorption ability of monolayer graphene is dramatic owing to the strong localization ability of the ZCG at the bottom of the structure to the light field. By adjusting the structural parameters of the grating, the designed graphene-based absorber exhibited excellent wavelength tunability. Interestingly, accidental BICs can be realized while adjusting the linewidth by changing the thickness of the spacer layer. Moreover, based on the tunable properties of graphene, the proposed structure achieved a dynamically tunable absorption efficiency at a specific wavelength after changing the chemical potential of graphene. This research has great potential for application in high-performance optical detection, modulation, sensing, and advanced integrated optical systems.