Bandwidth-tunable near-infrared perfect absorption of graphene in a compound grating waveguide structure supporting quasi-bound states in the continuum

Feng Wu; Feng Wu; Dejun Liu; Dejun Liu; Shuyuan Xiao; Shuyuan Xiao; Shuyuan Xiao

doi:10.1364/OE.446270

1. Introduction

In recent years, a kind of special bound states embedded in the continuous spectra called bound states in the continuum (BICs) have received increasing attention [1–3]. Genuine optical BICs cannot be directly excited since they possess infinite Q factors. However, as the parameters (such as geometric parameters or incident angle) slightly deviate from those for BICs, BICs turn into excitable quasi-BICs with ultra-high Q factors [4–6]. Various micro-structures have been proposed to realize quasi-BICs, including photonic crystal slabs [7–13], asymmetric metasurfaces [4,14–19], and dielectric disk chains [20–22], etc. In lossless and infinite micro-structures supporting quasi-BICs, Q factors can be arbitrarily high by delicately tuning the related parameters [4,23]. Owing to this extraordinary resonant property, quasi-BICs with ultra-high Q factors have been widely utilized in lasing [24], ultra-sensitive sensing [25–28], wireless power transfer [29], and high-efficiency second harmonic generation [30,31]. Unfortunately, compared with defect modes [32] and whispering-gallery modes [33], the modal volumes of quasi-BICs are much larger. Therefore, when taking the absorptive losses in micro-structures and the scattering losses caused by fabrication imperfections into consideration, the measured Q factors of quasi-BICs (on the order of 10⁴ [7,8] or 10⁵ [9]) are smaller than those of defect modes (can reach the order of 10⁶ [34]) and whispering-gallery modes (can reach the order of 10⁹ [35,36]). Nevertheless, the large modal volume of quasi-BIC turns into an advantage if we utilize quasi-BIC to enhance optical absorption. Up until now, most of works have focused on the transmission or reflection characteristic of quasi-BICs [4,7–12,15–19,24–29] but only a few works have focused on the absorption characteristic of quasi-BICs [37–39].

Over the past two decades, two-dimensional materials, such as graphene [40–44], black phosphorus [45–49], and transitional metal dichalcogenides [50–54], have attracted researchers’ great interest due to their unique electrical and optical properties. It is known that the optical absorptance of monolayer graphene is only 2.3% under normal incidence at visible and near-infrared wavelengths [55]. Hence, researchers proposed lots of micro-structures to enhance the optical absorptance of monolayer graphene [56–62]. Particularly, researchers utilized all-dielectric metasurfaces supporting quasi-BICs to enhance the optical absorptance of monolayer graphene [37,38]. Assisted by the high-Q resonant property of the quasi-BICs, the optical absorptance of monolayer graphene can be greatly enhanced. However, in the above works (Refs. [37] and [38]), there exists the following two shortcomings. One is that the fabrication of the proposed metasurfaces needs complex two-dimensional lithography technique, which poses a challenge in experimental realization. The other is that the maximum absorptance did not reach 100% (50% in Ref. [37] and 74% in Ref. [38]).

Very recently, based on the selective excitation of the guided mode, researchers found that all-dielectric compound grating waveguide structures can support quasi-BICs [63,64]. The proposed compound grating waveguide structure is composed of a four-part periodic dielectric grating layer and a dielectric waveguide layer. Compared with all-dielectric metasurfaces, the fabrication of all-dielectric compound grating waveguide structures only needs one-dimensional lithography technique. In this paper, we introduce graphene layer into an all-dielectric compound grating waveguide structure supporting quasi-BIC to realize near-infrared perfect absorption of graphene. The underlying physical mechanism of perfect absorption can be explained by the critical coupling theory. In addition, by tuning the Fermi level and the layer number of the graphene, the absorption rate of the system changes correspondingly. For the compound grating waveguide structure supporting quasi-BIC, the radiation coupling rate of the resonance mode can be tuned by the geometric parameter to maintain the critical coupling condition. Hence, the full width at half maximum (FWHM) of the perfect absorption peak can be flexibly tuned from 5.7 to 187.1 nm. Narrow-band perfect absorption would possess potential applications in the design of 2D material-based optical sensors [65] and electrical switchers [66], while broad-band one would possess potential applications in the design of 2D material-based solar thermophotovoltaic devices [67,68].

2. Quasi-BICs in compound grating waveguide structures

First, following the theory in Ref. [63], we realize quasi-BICs in a compound grating waveguide structure at near-infrared wavelengths. Figure 1(a) gives the schematic of the unit cell of the compound grating waveguide structure. The compound grating waveguide structure is composed of a four-part periodic dielectric grating layer (with the grating constant Λ = 747 nm and the thickness h_G = 515 nm) and a dielectric waveguide layer (with the thickness h_WG = 184 nm). Here the role of the dielectric grating layer is to provide the guided mode while that of the dielectric grating layer is to provide the additional tangential wave vector (the x component of the wave vector). Without the dielectric grating layer, the incident light cannot couple with the guided mode at any wavelengths since the dispersion relation of the guided mode lies below the light cone of the air. With the dielectric grating layer, the incident light can couple with the guide mode at some given wavelengths since the dielectric grating layer provides the additional tangential wave vector. For the unit cell of the dielectric grating, the first and the third parts are high-index medium Si (with the refractive index n_H = 3.48 [69]), while the second and the fourth parts are air. In addition, both the widths of the first and the third parts are d_A = 0.15Λ, while those of the second and the fourth parts are d_B = d + Δd = 0.35Λ + Δd and d_C = d ‒ Δd = 0.35Λ ‒ Δd, respectively. A geometric parameter δ = Δd/d [or δ = (d_B ‒ d_C)/(d_B + d_C)] is defined to describe the width difference between the second and the fourth parts. The media of the dielectric waveguide layer and the substrate are chosen to be Si and SiO₂ (with the refractive index n_S = 1.46 [69]), respectively. Suppose a TE-polarized light (the electric field is parallel to the y-axis) launches onto the structure at an incident angle θ.

Fig. 1. (a) Schematic of the unit cell of the compound grating waveguide structure. (b) Zero-order transmittance spectra with different geometric parameters δ at normal incidence under TE polarization.

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Based on the rigorous coupled wave analysis (RCWA) [70], we calculate the zero-order transmittance spectra with different geometric parameters δ at normal incidence (θ = 0°) under TE polarization, as shown in Fig. 1(b). RCWA is an exact solution of the Maxwell’s equations for the light diffraction in grating structures. The accuracy of the solution only depends on the number of terms retained in the space-harmonic expansion of the field [70]. To ensure the accuracy, the number of the harmonics is chosen to be 11 in our numerical calculations. When δ = 0.3, a sharp Fano resonance occurs at λ = 1896.6 nm due to the guided mode resonance (GMR). The corresponding line width can be calculated by Δλ = |λ_Peak ‒ λ_Dip| = 19.4 nm. As the geometric parameter δ decreases from 0.3 to near zero, the line width of the Fano resonance decreases rapidly. When δ = 0, the line width of the Fano resonance vanishes, which corresponds to a BIC. The underlying physical mechanism can be explained by the GMR theory [63].

When the geometric parameter δ is not equal to zero, the widths of the second and the fourth parts of the grating layer d_B and d_C are different. Therefore, the grating constant is Λ. The GMR condition can be expressed as [71]

(1)$${k_{x,i}} = {k_0}\sin \theta - i\frac{{2\pi }}{\Lambda } = {\beta _{}}(i ={\pm} 1{,_{}} \pm 2{,_{}}\ldots ),$$

where k₀sinθ = (ω/c)sinθ represents the tangential wave vector in the air, k_x,i represents the tangential wave vector in the grating layer, and β represent the propagating constant of the guided mode within the guided layer. In this work, we consider the TE₀ guided mode. The dispersion relation of the TE₀ guided mode within the guided layer can be given by [72]

(2)$${h_{\textrm{WG}}}\sqrt {k_0^2n_{\textrm{WG}}^2 - {\beta ^2}} = \arctan (\frac{{\sqrt {{\beta ^2} - k_0^2n_0^2} }}{{\sqrt {k_0^2n_{\textrm{WG}}^2 - {\beta ^2}} }}) + \arctan (\frac{{\sqrt {{\beta ^2} - k_0^2n_\textrm{S}^2} }}{{\sqrt {k_0^2n_{\textrm{WG}}^2 - {\beta ^2}} }}).$$

Based on Eq. (2), we calculate the dispersion relation of the TE₀ guided mode, as shown by the black solid line in Fig. 2(a). The normalized angular frequency is ω₀ = 2πc/h_WG. The dispersion relation of the TE₀ guided mode is cut off at ω_cutoff = 0.0247ω₀. Then, based on Eq. (1), we also calculate the tangential wave vectors in the grating layer k_x_,−1 and k_x_,−2 as a function of the angular frequency at normal incidence, as shown by the red and the green dashed lines in Fig. 2(a). One can see that there are two crossing points A₋₁ (ω₋₁ = 0.0978ω₀ or λ₋₁ = 1881.4 nm) and A₋₂ (ω₋₂ = 0.1669ω₀ or λ₋₂ = 1102.4 nm), which satisfy the GMR condition [i.e., Eq. (1)]. Therefore, around these two wavelengths, Fano peaks will occur due to the GMR.

Fig. 2. GMR in the compound grating waveguide structure for (a) δ ≠ 0 and (b) δ = 0 at normal incidence.

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As the geometric parameter δ decreases from a non-zero value to zero, the widths of the second and the fourth parts of the grating layer d_B and d_C become identical. Therefore, the four-part periodic grating reduces to a two-part periodic grating with a new grating constant Λ’ = Λ/2 and the grating-induced tangential wave vector becomes double. The GMR condition now becomes

(3)$$k{^{\prime}_{x,i^{\prime}}} = {k_0}\sin \theta - i^{\prime}\frac{{2\pi }}{{\Lambda ^{\prime}}} = {k_0}\sin \theta - i^{\prime}\frac{{4\pi }}{\Lambda } = {\beta _{}}(i^{\prime} ={\pm} 1{,_{}} \pm 2{,_{}}\ldots ).$$

Based on Eq. (2), we calculate the dispersion relation of the TE₀ guided mode, as shown by the black solid line in Fig. 2(b). Then, based on Eq. (3), we also calculate the tangential wave vector in the grating layer k'_x_,−1 as a function of the angular frequency at normal incidence, as shown by the red dashed line in Fig. 2(b). One can see that only one crossing point A'₋₁ (previous A₋₂) is remained. Therefore, as the geometric parameter δ changes from a non-zero value to zero, the GMR condition at A₋₁ (λ₋₁ = 1881.4 nm) is broken, leading to a BIC. The BIC wavelength predicted by the GMR theory (1881. 4nm) is quite close to the actual BIC wavelength calculated by the transmittance spectrum (1890. 4nm).

Then, Fig. 3(a) gives the relationship between the Q factor and the geometric parameter δ. For the Fano resonance, the Q factor can be calculated by Q = f_Peak/|f_Peak ‒ f_Dip| [73]. When δ = 1, the Q factor is only 1.2×10¹. As the geometric parameter δ decreases from 1 to near zero, the Q factor increases rapidly. When δ = 0.02, the Q factor reaches 2.0×10⁴. As the geometric parameter δ approaches zero, the Q factor becomes infinite, which corresponds to a BIC. In addition, the dependence of the Q factor and 1/δ² is also given in Fig. 3(b). One can see that the Q factor almost linearly depends on 1/δ², which is similar to that in Ref. [4].

Fig. 3. (a) Relationship between the Q factor and the geometric parameter δ. (b) Linear dependence of the Q factor and 1/δ².

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Next, we calculate the electric field distributions (|E_y|) in the unit cell for different geometric parameters δ at the corresponding Fano dips, as shown in Figs. 4(a) to 4(c). The magnitude of the incident electric field is normalized. One can see that the electric field is greatly enhanced in the dielectric waveguide layer, which confirms the GMR. In addition, as the geometric parameter δ approaches zero, the electric field becomes more localized in the dielectric waveguide layer since the resonance of the quasi-BIC becomes stronger. In the next section, we will utilize the field localization property of the quasi-BIC to greatly enhance the absorption of graphene.

Fig. 4. Electric field distribution |E_y| in the unit cell for different geometric parameters at the corresponding Fano dips: (a) δ = 0.3, (b) δ = 0.2, and (c) δ = 0.1.

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3. Bandwidth-tunable near-infrared perfect absorption of graphene assisted by quasi-BICs

In this section, we introduce graphene into the compound grating waveguide structure to realize bandwidth-tunable near-infrared perfect absorption. The relative permittivity of graphene ε_g can be determined by its optical conductivity σ_g [74,75]

(4)$${\varepsilon _\textrm{g}} = 1 + \frac{{{\sigma _\textrm{g}}{\eta _0}c}}{{\omega {h_{\textrm{g, eff}}}}},$$

where η₀ represents the vacuum wave impedance, c represents the light speed in vacuum, ω represents the angular frequency, and h_g,eff represents the effective thickness of monolayer graphene. It should be noted that the effective thickness of monolayer graphene h_{g, eff} = 0.5 nm is utilized to calculate the optical conductivity of monolayer graphene, which is not equal to the actual thickness of monolayer graphene [74]. According to the random phase approximation in the local limit, the optical conductivity of graphene can be given by the sum of the intra-band and the inter-band optical conductivities [42]

(5)$${\sigma _\textrm{g}} = {\sigma _{\textrm{intra}}} + {\sigma _{\textrm{inter}}}.$$

The intra-band and the inter-band optical conductivities can be further given by [42]

(6)$${\sigma _{\textrm{intra}}} = \frac{{2{e^2}{k_\textrm{B}}T}}{{\pi {\hbar ^2}}}\frac{i}{{\omega + i{\tau ^{ - 1}}}}\ln [2\cosh (\frac{{{E_\textrm{F}}}}{{2{k_\textrm{B}}T}})],$$

(7)$${\sigma _{\textrm{inter}}} = \frac{{{e^2}}}{{4\hbar }}[\frac{1}{2} + \frac{1}{\pi }\arctan (\frac{{\hbar \omega - 2{E_\textrm{F}}}}{{2{k_\textrm{B}}T}}) - \frac{i}{{2\pi }}\ln \frac{{{{(\hbar \omega + 2{E_\textrm{F}})}^2}}}{{{{(\hbar \omega - 2{E_\textrm{F}})}^2} + {{(2{k_\textrm{B}}T)}^2}}}],$$

where e, k_B, T, ħ, ω, τ, and E_F represent the charge of an electron, the Boltzmann constant, the temperature, the reduced Planck constant, the angular frequency, the relaxation time, and the Fermi level, respectively. Throughout this paper, the temperature is set to the room temperature T = 300 K. Here the relation time is determined by the Fermi level, i.e., τ = (μE_F)/(ev_F), where the electron mobility μ = 10000 cm²/(V·s) and the Fermi velocity v_F = 1.0×10⁶ m/s [42]. Based on Eqs. (4) to (7), we calculate the real and the imaginary parts of the relative permittivity of graphene with different Fermi levels, as shown in Figs. 5(a) and 5(b). One can see that the relative permittivity of graphene can be flexibly tuned by the Fermi level.

Fig. 5. (a) Real and (b) imaginary parts of the relative permittivity of graphene with different Fermi levels.

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Now, we introduce graphene into the compound grating waveguide structure to realize bandwidth-tunable near-infrared perfect absorption. The schematic of the unit cell of the proposed structure is shown in Fig. 6(a). Considering the difficulty in the fabrication process, we put the monolayer graphene at the bottom of the grating layer in the calculation [43,57]. To suppress the transmittance and realize perfect absorption, we add a metal (Ag) layer with the thickness d_M = 100 nm at the bottom of the waveguide layer. The relative permittivity of Ag ε_M can be described by the Drude model [76]

(8)$${\varepsilon _\textrm{M}} = {\varepsilon _{\inf }} - \frac{{\omega _\textrm{P}^2}}{{{\omega ^2} + i\Gamma \omega }},$$

where ε_inf = 5.0 represents the high-frequency relative permittivity, ω represents the angular frequency, ω_P = 1.3983×10¹⁶ Hz represents the plasma angular frequency, and Γ = 3.2165×10¹³ Hz represents the damping frequency [76].

Fig. 6. (a) Schematic of the unit cell of the proposed structure. (b) Absorptance spectra with different geometric parameters δ at normal incidence under TE polarization. The Fermi level is set to be E_F = 0.2 eV. (c) Absorptance spectra at different incident angles under TE polarization. The Fermi level is set to be E_F = 0.2 eV and the geometric parameter is set to be δ = 0.116.

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Then, based on the rigorous coupled wave analysis [70], we calculate the absorptance spectra of the proposed structure with different geometric parameters δ at normal incidence under TE polarization, as shown in Fig. 6(b). In the numerical calculations, the actual thickness of the monolayer graphene is h_g = 0.34 nm [43]. The Fermi level is set to be E_F = 0.2 eV. One can see that when δ = 0 (corresponds to BIC), the absorptance is quite low (lower than 3.4%). As δ slightly deviates from zero, the absorptance is enhanced due to the resonance of quasi-BIC. When δ = 0.05, an absorption peak with the maximum 55.1% occurs. It should be noted that the added metal layer changes the wavelength of the resonant peak. When δ increases from 0.05 to 0.116, the maximum absorptance increases to 100% (i.e., perfect absorption). When δ continues to increase to 0.2, the maximum absorptance decreases to 78.3%. This phenomenon can be explained by the critical coupling theory as follow.

According to Refs. [77] and [78], for a lossy resonant system, when the radiation coupling rate (i.e., leakage rate) of resonance mode is equal to the absorption rate of the system, the system is said to be critically coupled. Then, all the incident light can be absorbed. Here we detailedly derive the critical coupling condition in our system. Based on the temporal coupled-mode theory (CMT) [79], we consider a single-mode optical resonator with the amplitude a coupled with one port. The dynamic equations can be expressed as [80]

(9)$$\frac{{da}}{{dt}} = ( - i{\omega _0} - \gamma - \alpha )a + i\sqrt {2\gamma } {S_ + },$$

(10)$${S_ - } ={-} i{S_ + } + i\sqrt {2\gamma } a,$$

where ω₀ represents the resonance angular frequency, γ represents the radiation coupling rate of the resonance mode, α represents the absorption rate of the system, S₊ and S₋ represent the amplitude of the incoming and the outgoing waves, respectively.

For the resonance mode, we suppose a = a₀e^−iωt. Then, the solution of Eq. (9) can be given by

(11)$$a = \frac{{i\sqrt {2\gamma } {S_ + }}}{{ - i(\omega - {\omega _0}) + (\gamma + \alpha )}}.$$

Hence, the absorptance of this system can be derived as

(12)$$A = \frac{{S_\textrm{ + }^\mathrm{\ast }{S_\textrm{ + }} - S_ - ^\mathrm{\ast }{S_ - }}}{{S_\textrm{ + }^\mathrm{\ast }{S_\textrm{ + }}}} = \frac{{2\alpha {a^\ast }a}}{{S_\textrm{ + }^\mathrm{\ast }{S_\textrm{ + }}}} = \frac{{4\gamma \alpha }}{{{{(\omega - {\omega _0})}^2} + {{(\gamma + \alpha )}^2}}}.$$

One can see that Eq. (12) predicts a symmetric Lorentzian curve. It is clear that the maximum absorptance occurs at the resonance angular frequency ω = ω₀. The maximum absorptance A₀ is determined by the ratio between γ and α, i.e.,

(13)$${A_0} = \frac{{4\gamma \alpha }}{{{{(\gamma + \alpha )}^2}}} = \frac{4}{{\frac{\gamma }{\alpha } + \frac{\alpha }{\gamma } + 2}}.$$

When the critical coupling condition γ = α is satisfied, the maximum absorptance reaches 100% in this single-mode, one-port system. The FWHM of the absorption peak can be expressed as

(14)$${\Gamma ^{\textrm{FWHM}}} = 2(\gamma + \alpha ) = 4\alpha .$$

Therefore, as the geometric parameter δ changes, the radiation coupling rate of the resonance mode γ changes correspondingly. As shown in Fig. 6(b), when the geometric parameter δ = 0.116, the critical coupling occurs and the near-infrared perfect absorption is achieved. It should be noted that the perfect absorption is robust against the incident angle. Figure 6(c) gives the absorptance spectra of the proposed structure at different incident angles under TE polarization. The geometric parameter is kept to be δ = 0.116 and the Fermi level is also kept to be E_F = 0.2 eV. One can see that as the incident angle increases from 0° to 20°, the absorption peak shifts towards shorter wavelengths while the peak absorptance maintains near 100%.

Next, if we change the Fermi level of the monolayer graphene E_F, the absorption rate of the system α changes correspondingly. For the compound grating waveguide structure supporting quasi-BIC, the radiation coupling rate of the resonance mode γ can be tuned by the geometric parameter δ to maintain the critical coupling condition γ = α. According to Eq. (14), the FWHM of the perfect absorption peak Γ^FWHM = 4α will also changes, leading to the bandwidth-tunable near-infrared perfect absorption. Figures 7(a) and 7(c) show the absorptance (at normal incidence) as functions of the wavelength and the geometric parameter δ with different Fermi levels E_F = 0 eV and E_F = 1.2 eV, respectively. By adjusting the gate voltage applied to graphene, E_F = 0 eV can be realized in experiments [81]. The critical coupling points can be found by sweeping the wavelength and the geometric parameter δ. For E_F = 0 eV and E_F = 1.2 eV, the critical couplings occur at δ = 0.288 and δ = 0.096, respectively. Correspondingly, Figs. 7(b) and 7(d) give the absorptance spectra at critical couplings. One can see that when the critical coupling condition is satisfied for E_F = 0 eV, the FWHM of the perfect absorption peak reaches Γ^FWHM = 43.7 nm. However, when the critical coupling condition is satisfied for E_F = 1.2 eV, the FWHM of the perfect absorption peak is only Γ^FWHM = 6.0 nm. In the proposed structure, the grating layer and the waveguide layer are lossless while the graphene layer and the metal layer are lossy. To confirm that the absorptance is mainly originated from the monolayer graphene, the comparison between the absorptance spectrum of the structure with the lossy Ag layer (Γ = 3.2165×10¹³ Hz) and that with the lossless Ag layer (Γ = 0 Hz) is given in Appendix.

Fig. 7. Absorptance (at normal incidence) as functions of the wavelength and the geometric parameter δ with different Fermi levels: (a) E_F = 0 eV and (c) E_F = 1.2 eV. (b) and (d): corresponding absorptance spectra when the critical coupling conditions are satisfied.

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To investigate the bandwidth-tunable property of the near-perfect absorption, we calculate the FWHM of the perfect absorption peak as a function of the Fermi level of the graphene E_F, as shown in Fig. 8. One can see that as the Fermi level gradually increases from 0 to 1.6 eV, the FWHM of the perfect absorption peak rapidly decreases from 42.7 to 5.7 nm. The tuning amplitude of the FWHM reaches about one order.

Fig. 8. Relationship between the FWHM of the perfect absorption peak and the Fermi level of the graphene E_F.

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In addition to changing the Fermi level of the monolayer graphene, another method to tuning the FWHM of the perfect absorption peak is to replace the monolayer graphene with the few-layer graphene. Both the experimental measurements [82] and theoretical calculations [83] have confirmed that the interacting effect between adjacent monolayer graphene can be ignored as the layer number of few-layer graphene N < 6. Hence, the few-layer graphene can be viewed as a superposition of monolayer graphene. Figures 9(a) and 9(c) show the absorptance (at normal incidence) as functions of the wavelength and the geometric parameter δ with different layer numbers of the few-layer graphene N = 2 and N = 3, respectively. The Fermi level of the graphene is selected to be E_F = 0 eV. For N = 2 and N = 3, the critical couplings occur at δ = 0.450 and δ = 0.616, respectively. Correspondingly, Figs. 9(b) and 9(d) give the absorptance spectra at critical couplings. One can see that when the critical coupling condition is satisfied for N = 2, the FWHM of the perfect absorption peak reaches Γ^FWHM = 94.6 nm. When the critical coupling condition is satisfied for N = 3, the FWHM of the perfect absorption peak reaches Γ^FWHM = 187.1 nm. By tuning the Fermi level and the layer number of the graphene, the FWHM of the perfect absorption peak can be flexibly tuned from 5.7 to 187.1 nm. Narrow-band perfect absorption would possess potential applications in the design of 2D material-based optical sensors [65] and electrical switchers [66], while broad-band one would possess potential applications in the design of 2D material-based solar thermophotovoltaic devices [67,68]. It is known that by introducing graphene layers into graphene-based structures supporting conventional Fano resonances, one can realize perfect absorption when the critical coupling condition is satisfied [43,84]. However, the FWHMs of the perfect absorption peaks assisted by conventional Fano resonances are usually on the order of 10 nm (20 nm in Ref. [43] and 18 nm in Ref. [84]). Different from the above works, we introduce graphene layers into compound grating waveguide structures supporting quasi-BICs. The radiation rate of the quasi-BIC can be flexibly tuned by the geometric parameter. Therefore, the FWHM of the perfect absorption peak can be tuned in a broad range (from the order of 1 nm to the order of 100 nm).

Fig. 9. Absorptance (at normal incidence) as functions of the wavelength and the geometric parameter δ with different layer numbers of the few-layer graphene: (a) N = 2 and (c) N = 3. (b) and (d): corresponding absorptance spectra when the critical coupling conditions are satisfied. The Fermi level is set to be E_F = 0 eV.

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Finally, we discuss about how to fabricate the proposed compound grating waveguide structure. Following an experimental work [43], the fabrication process of the proposed compound grating waveguide structure requires four steps. First, deposit a 100 nm Ag layer by magnetron sputtering technique. Then, deposit a 184 nm Si layer on the Ag layer by chemical vapor deposition technique. Next, transfer the graphene layer on the top of the Si layer. Finally, a Si layer is spin coated on the substrate and the grating pattern is formed in the Si layer by E-beam lithography technique.

4. Conclusion

In conclusion, we realize bandwidth-tunable near-infrared perfect absorption by introducing graphene layer into an all-dielectric compound grating waveguide structure supporting quasi-BIC. The underlying physical mechanism of perfect absorption can be explained by the critical coupling condition derived from CMT in a single-mode, one-port system. By changing the Fermi level and the layer number of the graphene, the FWHM of perfect absorption peak can be flexibly tuned from 5.7 to 187.1 nm. This bandwidth-tunable perfect absorber may be useful in the design of 2D material-based optical sensors, electrical switchers, and solar thermophotovoltaic devices.

Appendix: comparison between absorptance spectrum of structure with lossy Ag layer and that with lossless Ag layer

In the proposed structure, the grating layer and the waveguide layer are lossless while the graphene layer and the metal layer are lossy. To confirm that the absorptance is mainly originated from the graphene, here we calculate the absorptance spectra of the proposed structures with the lossy Ag layer (Γ = 3.2165×10¹³ Hz) and the lossless Ag layer (Γ = 0 Hz) at normal incidence under TE polarization, as shown by the black and the red solid lines in Fig. 10. The parameters are set to be: N = 1, E_F = 0 eV and δ = 0.288. One can see that the peak absorptance still reaches 99.5% when the Ag layer is lossless, which indicates that the absorptance is mainly originated from the graphene.

Fig. 10. Absorptance spectra of the proposed structures with the lossy Ag layer (Γ = 3.2165×10¹³ Hz) and the lossless Ag layer (Γ = 0 Hz) at normal incidence under TE polarization. The parameters are set to be: N = 1, E_F = 0 eV and δ = 0.288.

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Funding

National Natural Science Foundation of China (12104105, 11947065); Natural Science Foundation of Jiangxi Province (20202BAB211007); Shanghai Pujiang Program (20PJ1412200); Interdisciplinary Innovation Fund of Nanchang University (2019-9166-27060003); Start-Up Funding of Guangdong Polytechnic Normal University (2021SDKYA033).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.

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Bandwidth-tunable near-infrared perfect absorption of graphene in a compound grating waveguide structure supporting quasi-bound states in the continuum

Abstract

1. Introduction

2. Quasi-BICs in compound grating waveguide structures

3. Bandwidth-tunable near-infrared perfect absorption of graphene assisted by quasi-BICs

4. Conclusion

Appendix: comparison between absorptance spectrum of structure with lossy Ag layer and that with lossless Ag layer

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (10)

Equations (14)

Optics Express