Graphene-tuned EIT-like effect in photonic multilayers for actively controlled light absorption of topological insulators

Hua Lu; Hua Lu; Yangwu Li; Zengji Yue; Dong Mao; Jianlin Zhao; Jianlin Zhao

doi:10.1364/OE.397753

1. Introduction

Topological insulators, as novel quantum nanomaterials, have recently gained particular attention in electronics, optoelectronics and optics owing to unique electronic and optical characteristics [1–6]. Different from original insulators and metals, topological insulators exhibit a topologically-protected conducting surface (or edge) state and insulating bulk state simultaneously [1–3]. In 2006, Zhang et al. theoretically predicted the topological properties of two-dimensional (2D) HgTe quantum wells with the generation of the quantum spin Hall effect [5]. Next year, the prediction was verified experimentally by Molenkamp et al. [6]. In the 2D structured material, gapless Dirac fermions appear in the edge state because of strong spin-orbit coupling in the bulk state [5,6]. Subsequently, similar topological Dirac surface states were theoretically proposed and experimentally demonstrated in three-dimensional (3D) materials including Bi₂Se₃, Bi₂Te₃, Sb₂Te₃ and their composition Bi_2-xSb_xTe_3-ySe_y [7–10]. The time-reversal symmetry of the surface states in topological insulators renders the travelling electrons avoiding from the back scattering of non-magnetic impurities [1,2,5,6]. Until now, some attractive physical phenomena have been reported in topological insulators, including magnetoelectric effects, Majorana fermions and superconductivity [1–3]. Topological insulators with fascinating electronic features offer new routes to the development of quantum computing, spintronics and new electronic devices [11]. Furthermore, exciting optical characteristics were reported in 3D topological insulator materials, for instance ultrahigh optical nonlinearities [12], saturable absorption [13], photonic Weyl points [14], optical resonance [15], photothermal conversion [16], surface plasmon polaritons [17–20] and Tamm plasmon polaritons (TPPs) [21]. Taking advantage of these optical responses, a large number of high-performance functionalities were proposed based on topological insulators, such as all-optical switching [22], mode-locking fiber laser [23], nanometric hologram [15], optical modulation [19], angular-momentum nanometrology [24], light energy harvesting [25,26] and refractive index monitoring [27]. The light absorption of topological insulators is one of the most fundamental physical issues for optical nonlinearity and optoelectronic functionalities [23,25,26]. The dynamical tunability of light absorption is crucial for active optical and optoelectronic devices, especially modulators and switches [19,25,26,28]. The light absorption of topological insulators can be enhanced and tailored by TPPs [21]. But, how to realize active control of light absorption from topological insulators? The electrical control of Fermi level for topological insulators was used to modulate light transmission/reflection, which may offer a good method to tune light absorption of topological insulators [29]. The active tunability of light absorption without changing material properties is also significant.

We propose an effective method to actively control light absorption of topological insulators in a multilayer photonic system composed of a BSTS film and a dielectric Bragg mirror with a graphene-involved defect layer. TPPs generated between the BSTS film and Bragg mirror contribute to the strong light absorption of BSTS at near-infrared wavelengths. The introduction of a defect layer in the Bragg mirror enables the appearance of ultranarrow induced transparency in the absorption spectrum, derived from the formation of an electromagnetically induced transparency (EIT)-like effect. Particularly, we find that light absorption of a topological insulator can be effectively tuned by adjusting the gate voltage on graphene in the defect layer. The mechanism of light absorption control was reasonably analyzed using a two-oscillator model. The results will open a new route for topological insulator-based active electro-optic devices.

2. Structure and model

As depicted in Fig. 1, the multilayer photonic structure consists of a BSTS topological insulator film, a dielectric Bragg mirror with alternately stacked SiO₂/Si₃N₄ layers, and a defect layer. The defect layer contains a doped Si layer and an Al₂O₃ layer with an inserted single-layer graphene. The gate voltage V_b is exerted between the graphene and Si layers. The incident light impinges on the BSTS film with an angle of θ. d_t, d_s, d_a, d_b, d_g, and d_c stand for the thicknesses of BSTS, Si, Si₃N₄, SiO₂, graphene, and defect layers, respectively. d_i represents the thickness of the spacer between the graphene and Si layer. The period number of SiO₂/Si₃N₄ Bragg mirror is set as N. At the wavelengths of interest, the refractive indices of SiO₂, Si₃N₄, Al₂O₃, and Si can be set as 1.45, 2.2, 1.76, and 3.5, respectively. The refractive index of graphene can be derived from the Kubo formula [30,31]. According to the Kubo formula, the surface conductivity of single-layer graphene can be described as σ_g=σ_intra+σ_inter. Here, σ_intra and σ_inter correspond to the intraband and interband transitions of electrons in graphene, respectively. σ_intra can be described as

(1)$${\sigma _{intra}} = \frac{{i{\textrm{e}^2}{k_B}T}}{{\pi {\hbar ^2}(\omega + i{\tau ^{ - 1}})}}[\frac{{{\mu _c}}}{{{k_B}T}} + 2\ln (\textrm{exp} ( - \frac{{{\mu _c}}}{{{k_B}T}}) + 1)],$$

where e, k_B, T, and μ_c denote the electron charge, Boltzmann’s constant, temperature, and chemical potential of graphene, respectively. ω, ħ, and τ stand for the angular frequency of incident light, reduced Planck's constant, and momentum relaxation time of charge carrier scattering, respectively. When |μ_c|>>k_BT and ħω>>k_BT, σ_inter is governed by

(2)$${\sigma _{inter}} = \frac{{i{\textrm{e}^2}}}{{4\mathrm{\pi}\hbar }}\ln [\frac{{2|{{\mu_c}} |- \hbar (\omega + i{\tau ^{ - 1}})}}{{2|{{\mu_c}} |+ \hbar (\omega + i{\tau ^{ - 1}})}}].$$

Here, the relaxation time depends on the carrier mobility μ and can be expressed as τ=μμ_c/(ev_f²). The Fermi velocity can be set as v_f=10⁶ m/s [31]. As previously reported, the carrier mobility of single-layer graphene suspended in air could exceed 2×10⁵ cm²V⁻¹s⁻¹ [31]. The carrier mobility of graphene on a SiO₂ substrate could approach 4×10⁴ cm²V⁻¹s⁻¹ [32]. The carrier mobility can exceed 2×10³ cm²V⁻¹s⁻¹ for CVD-grown graphene on Al₂O₃ [33]. To ensure the credibility of results, the carrier mobility of graphene is set as μ=1×10⁴ cm²V⁻¹s⁻¹ in this work. The chemical potential of graphene can be described as μ_c=ħv_f(πn_s)^1/2 [34]. The doping level of graphene can be tailored by altering the gate voltage V_b on graphene through n_s=ε_aε₀|V_b|/(ed_i), where ε_a is the relative permittivity of Al₂O₃ layer. The single-layer graphene can be equivalent to an ultrathin film with a thickness d_g=0.34 nm, thus the relative permittivity of graphene can be described as ε_g=1 + iσ_g/(ωε₀d_g) [30]. The topological insulator can be regarded as a bulk insulator coated with a surface conductor [18,35]. The BSTS topological insulator has attracted special attention due to the good bulk interior and surface electronic transport [35]. The surface conductor can be treated as an ultrathin layer with a thickness of t = 1.5 nm [18]. The relative permittivities of the surface and bulk states in the near-infrared region can be obtained by fitting the measured data with the Drude and Tauc-Lorentz models, respectively [18]. The relative permittivity of the bulk state is mainly attributed to the interband transition, whose band structure can be governed by Kramers-Kronig relations [18,36]. The imaginary and real parts (ε_b'’ and ε_b’) of relative permittivity for the bulk state can be described as

(3)$$\varepsilon _b^{\prime\prime}(E )= \left\{ \begin{array}{ll} \frac{{A{E_0}C{{({E - {E_g}} )}^2}}}{{{C^2}{E^2} + {{({{E^2} - E_0^2} )}^2}}} \cdot \frac{1}{E}, &E > {E_g} \\ 0 &E \le {E_g} \end{array} \right.$$

(4)$$\varepsilon _b^{\prime}(E )= {\varepsilon _b}(\infty )+ \frac{2}{\pi}P\int_{E_g}^\infty {\frac{{\xi \varepsilon _b^{\prime\prime}}(\xi )}{{{\xi ^2} - {E^2}}}}d \xi ,$$

where A, E₀, E_g, and C denote the absorption peak amplitude, peak in joint density of states, band gap energy, and broadening factor, respectively; E=ħω is the energy of incident photons; ε_b(∞) and P represent the relative permittivity at high frequency and Cauchy principal part of the integral, respectively [36]. The relative permittivity of the surface state can be described using the classical Drude model: ε_s(ω)=ε_∞-ω² p/[ω(ω+iγ)], where ε_∞, ω_p, and γ are the relative permittivity at the infinite frequency, bulk plasma frequency, and electron collision frequency, respectively. The parameters for the BSTS material can be set as ε_∞=1.3, ω_p=7.5 eV, γ=0.05 eV, A = 65.9, E_g=0.25 eV, E₀=1.94 eV, C = 1.94, and ε_b(∞) = 0 [18]. The results in [18] show that the relative permittivity of the BSTS bulk state presents the lossy insulating characteristic in the near-infrared region. The BSTS surface state has negative real permittivities and exhibits a metal-like property. The transfer matrix method (TMM) is an effective theoretical method to study the light propagations in the multilayer structures [37,38]. Derived from Maxwell’s equations and boundary conditions of electric and magnetic fields, the transfer matrix equations of the multilayer structure can be described as

(5)$$\left[ \begin{array}{l} E_{up}^ - \\ E_{up}^ + \end{array} \right] = {M_1}{P_1}{M_2}{P_2} \cdots {M_{2N + 8}}\left[ \begin{array}{l} E_{down}^ - \\ E_{down}^ + \end{array} \right] = \left( {\begin{array}{cc} {{Q_{11}}}&{{Q_{12}}}\\ {{Q_{21}}}&{{Q_{22}}} \end{array}} \right)\left[ \begin{array}{l} E_{down}^ - \\ E_{down}^ + \end{array} \right],$$

where $E_{\rm{up}}^{+}$ and $E_{\rm{up}}^{-}$ are the electric fields of incident and reflection light on the top of the multilayer structure, respectively; $E_{\rm{down}}^{+}$ and $E_{\rm{down}}^{-}$ are the electric fields of output and input light at the bottom of the structure, respectively. Thus, the absorption spectra of the structure can be expressed as A = 1-|Q₂₁/Q₁₁|²-|1/Q₁₁|². For TM-polarized incident light, the transfer matrixes M_j (j = 1, 2, …, 2N + 8) and P_j (j = 1, 2, …, 2N + 7) can be described as

(6)$${M_j} = \frac{1}{{2{n_{j - 1}}\cos {\theta _{j - 1}}}}\left( {\begin{array}{cc} {{n_{j - 1}}\cos {\theta_j} + {n_j}\cos {\theta_{j - 1}}}&{{n_{j - 1}}\cos {\theta_j} - {n_j}\cos {\theta_{j - 1}}}\\ {{n_{j - 1}}\cos {\theta_j} - {n_j}\cos {\theta_{j - 1}}}&{{n_{j - 1}}\cos {\theta_j} + {n_j}\cos {\theta_{j - 1}}} \end{array}} \right),$$

(7)$${P_j} = \left( {\begin{array}{cc} {\textrm{exp} ( - i2\pi {d_j}{n_j}\cos {\theta_j}/\lambda )}&0\\ 0&{\textrm{exp} (i2\pi {d_j}{n_j}\cos {\theta_j}/\lambda )} \end{array}} \right),$$

where θ_j and n_j respectively stand for the propagation angle of light and refractive index of the j-th layer, which can be governed by Snell’s law: n_jsinθ_j=n_j₋₁sinθ_j₋₁ (θ₀=θ and n₀=1). d_j represents the thickness of the j-th layer. λ=2πc/ω denotes the incident wavelength.

Fig. 1. 3D diagram of the multilayer photonic system consisting of a thin BSTS topological insulator film, a Bragg mirror with stacked Si₃N₄/SiO₂ layers and a defect layer (containing Al₂O₃, graphene, and doped Si) in the middle of Bragg mirror.

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3. Results and analysis

The parameters of the BSTS film/Bragg mirror structure are originally set as d_t=58 nm, d_a=150 nm, d_b=240 nm, d_c=0 nm, N = 20, and θ=0° to explore the light propagation properties. The TMM theoretical calculations illustrate that the absorption spectrum of multilayer photonic structures presents a distinct peak at the wavelength of 1309.6 nm, as shown in Fig. 2(a). The strong light absorption is derived from the generation of TPP mode between the BSTS and Bragg mirror [21,37]. The topological insulators possess a metal-like surface state with negative permittivities, providing required condition for the formation of near-infrared TPPs [37]. To clarify the theoretical results, we employ the finite-difference time-domain (FDTD) method to simulate the light propagation [38,39]. In the simulations, the top and bottom of multilayer structures are set as the absorbing boundary conditions with perfectly matched layers. Periodic boundary conditions can be set on the other sides of computational space. The non-uniform mesh is used to simulate the response of all the layers. The mesh sizes of surface and bulk layers are set as 0.3 nm and 2 nm, respectively. The mesh size of graphene is set as 0.06 nm. The absorption spectra of multilayer structures can be obtained through A = 1-|P_t/P_i|-|P_r/P_i|, where P_t, P_r, and P_i stand for the transmitted, reflected, and incident light powers, respectively. The electric field amplitude of incident light is set as 1 V/m. As depicted in Fig. 2(a), the simulations are in good agreement with the TMM calculations. Figure 2(b) shows the electric field distribution and intensity profile in the multilayer structure at the wavelength of 1309.6 nm. An obvious TPP mode is observed between the BSTS film and Bragg mirror [21,38]. The field intensity of BSTS-based TPP mode is ∼20 times less than that of Au-based TPP mode [40]. Even so, the light absorption of a topological insulator can be significantly enhanced by the formation of TPPs [21].

Fig. 2. (a) Absorption spectrum of the multilayer structure with d_c=0 nm. (b) Corresponding electric field distribution and intensity profile in the structure at the absorption peak. (c) Absorption spectrum of the multilayer structure with an Al₂O₃ defect layer (d_c=154.5 nm and d_g=d_s=0 nm) in the Bragg mirror. The inset shows the prototype three-level model of the EIT effect. (d) Corresponding electric field distribution and intensity profile at the induced absorption wavelength (λ=1309.9 nm). Here, d_t=58 nm, d_a=150 nm, d_b=240 nm, θ=0°, and N = 20. The circles and curves in (a) and (c) denote the FDTD and TMM results, respectively.

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Subsequently, we study the light propagation characteristics of the multilayer structure with an Al₂O₃ defect layer in the middle of Bragg mirror. It shows in Fig. 2(c) that an ultranarrow dip appears in the broad absorption spectrum at the wavelength of 1309.9 nm when d_c=154.5 nm. This nonintuitive phenomenon can be reasonably attributed to the generation of optical effect in analogy to the EIT in atomic systems [41]. According to the prototype three-level model of the EIT effect, the TPP mode between the BSTS film and Bragg mirror can be analogous to the upper state 2>, and thus the excitation of the topological insulator-based TPP mode can be considered as the transition from the ground state 1 > to 2 > [41,42]. The incident light is regarded as the “probe light”. An optical mode formed in the defect layer can be in analogy to the upper state 3 > . The defect mode can be excited by the coupling of TPP mode, similar to the transition from the state 2 > to 3 > . Even though the distance between the BSTS and defect layers is ∼3.95 µm, the TPP field can be effectively coupled with the defect mode due to the relatively weak confinement of TI-based TPPs. The coupling from defect mode to TPP mode can be considered as “pump light”. The two transition pathways: 1>→2 > and 1>→2>→3>→2 > will destructively interfere with each other, resulting in the weakness of the TPP field, as shown in Fig. 2(d). The weakened TPP field gives rise to the reduction of light absorption from the topological insulator and the formation of ultranarrow induced transparency with a spectral width of 0.63 nm, as shown in Fig. 2(c). The numerical simulations are in excellent agreement with the theoretical calculations. Additionally, we investigate the dependence of the EIT-like response on the thickness of BSTS film d_t. As depicted in Fig. 3(a), the broad absorption peak possesses a red shift with increasing d_t, while the induced transparency wavelength keeps unchanged. The position of induced transparency is determined by the wavelength of defect mode [43]. The defect layer can be regarded as a Fabry-Pérot (FP) cavity, whose resonance wavelength can be described as λ=4πn_cd_c/(2kπ-φ₁-φ₂) [44]. Here, φ₁ and φ₂ are the phase shifts of reflection on the two sides of defect cavity, respectively; n_c is the refractive index of defect cavity; k is an integer, representing resonant order. The TPP wavelength exhibits a red shift with increasing d_t [21], while the wavelength of defect mode is unrelated with d_t. Therefore, we can observe a nearly unchanged induced transparency window in the red-shift absorption peak. As shown in Fig. 3(b), both the induced transparency window and the absorption peak present a red shift as the Bragg mirror layer thickness d_a increases. Moreover, the induced transparency has a linearly red shift in an invariant absorption peak with increasing d_c, as depicted in Fig. 3(c). According to the resonance condition, we can see that the wavelength of defect mode is proportional to d_c. However, the TPP mode is nearly independent on the defect layer. Thus, we can see the red-shift induced transparency in a fixed absorption peak with increasing d_c. In Fig. 3(d), the induced transparency in the middle of absorption peak presents a blue shift with increasing θ. Similar to the previous reports, the TPP wavelength possesses a blue shift as θ increases [21,37]. The wavelength of the defect mode in the Bragg mirror also has a blue shift with increasing θ [45]. Thus, we observe the blue shift of induced transparency window with increasing θ. The simulations agree well with theoretical calculations. Figure 4 depicts the electric field amplitudes of EIT resonances in multilayer structures with different d_t, d_a, d_c, and θ. It shows that the EIT electric field amplitude nearly keeps unchanged with altering d_t, d_a and d_c, while decreases with the increase of θ.

Fig. 3. Evolution of absorption spectrum from the multilayer structure with (a) the thickness of the BSTS film d_t when d_a=150 nm, d_c=154.5 nm, and θ=0°, (b) the thickness of Si₃N₄ layer d_a when d_t=58 nm, d_c=154.5 nm, and θ=0°, (c) the thickness of Al₂O₃ defect layer d_c when d_t=58 nm, d_a=150 nm, and θ=0°, and (d) the light incident angle θ when d_t=58 nm, d_a=150 nm, and d_c=154.5 nm. Here, d_b=240 nm and N = 20. The circles denote the induced transparency wavelengths obtained by numerical simulations.

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Fig. 4. (a)-(d) Electric field amplitudes of EIT resonances (defect modes) versus d_t, d_a, d_c, and θ in the multilayer structure with the same parameters as in Figs. 3(a)–3(d).

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The TPP excitation between the BSTS film and Bragg mirror can effectively boost light absorption of the topological insulator. The coupling between the TPP and defect modes in the multilayer structure enables the tailoring of light absorption from the topological insulator with the generation of the EIT-like effect. To realize the active control of light absorption, we integrate the graphene and Si layer into the defect layer, as shown in Fig. 1. The parameters are set as d_a=150 nm, d_b=240 nm, d_u=50 nm, d_i=5 nm, d_s=60 nm, θ=0°, and N = 20. The in-plane electric fields dominate in the TPP and defect modes of multilayer structure. Graphene can be simply treated as an isotropic material [46]. Figure 5(a) depicts the spectral evolution of light absorption in multilayer structure with the gate voltage V_b between the graphene and Si layers. An ultranarrow transparency window obviously appears as V_b exceeds about 4.8 V, at which the interband transition of electrons in graphene will be hindered as the photon energy of defect mode (λ≈1310 nm) is less than 2μ_c (i.e., ħω<2μ_c). Moreover, the induced transparency wavelength originally presents a red shift and then has a blue shift with increasing V_b, which derives from the alternation of graphene refractive index. Figure 5(b) shows the electric field intensity profiles in the structure at the wavelength of 1310 nm when V_b=0 V and 6 V. We can see that the electric field of defect mode is relatively low when V_b=0 V, compared with the case when V_b=6 V. This is due to that the dissipative loss of graphene is greatly reduced when V_b changes from 0 V to 6 V. The electric field of TPP mode is suppressed when V_b=6 V, giving rise to the weakening of light absorption from the BSTS film, as depicted in the insets of Fig. 5(b). Thus, the gate-modulated BSTS absorption can be realized at the induced transparency wavelength, as shown in Figs. 5(c) and 5(d). The modulation depth of light absorption from the topological insulator is ∼3.67 dB when V_b alters from 0 V to 6 V. When the carrier mobility of graphene is decreased to 2000 cm²V⁻¹s⁻¹ with V_b=6 V, the real permittivity of graphene is almost unchanged, but the imaginary permittivity increases from 0.067 to 0.33. The BSTS absorption dip has only a slight rise of 0.02.

Fig. 5. (a) Evolution of absorption spectrum from the multilayer structure with the gate voltage V_b on graphene. (b) Electric field intensity profile in the structure when V_b=0 V and 6 V. The insets depict the intensity profiles in the BSTS film when V_b=0 V and 6 V. (c)-(d) Absorption spectra of the BSTS film and graphene when V_b=0 V and 6 V. The parameters are set as d_a=150 nm, d_b=240 nm, d_u=50 nm, d_i=5 nm, d_s=60 nm, θ=0°, and N = 20.

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To clarify the physical mechanism of the tunability of light absorption in the multilayer structure, we theoretically investigate the dependence of the EIT-like response on the gate voltage on graphene. The EIT-like spectrum can be described by using a two-oscillator model. As mentioned above, the TPP structure composed of BSTS film and a Bragg mirror can be regarded as “oscillator 1”, where the TPP mode is directly excited by the incident light. The defect layer can be considered as “oscillator 2”, where the defect mode can be generated through coupling with the TPP mode. As depicted in the inset of Fig. 2(c), ω₀ and δ stand for the resonance frequency of oscillator 1 and the resonance frequency detuning between the oscillators 1 and 2, respectively; γ₁ and γ₂ are the decaying rates derived from the intrinsic loss of the oscillators 1 and 2, respectively; κe^iφ are the coupling coefficient between the oscillators 1 and 2. When ω₀>>γ₁>>γ₂, γ₁>>|δ| and ω₀>>|ω-ω₀|, the light absorption of multilayer structure can be described as [47]

(8)$$A\textrm{ = }{\mathop{\rm Im}\nolimits} \left\{ {\frac{{f(\omega - {\omega_0} + \delta + i{\gamma_2}/2)}}{{{{(\kappa {e^{i\varphi }})}^2} - (\omega - {\omega_0} + \delta + i{\gamma_2}/2)(\omega - {\omega_0} + i{\gamma_1}/2)}}} \right\},$$

where f is an amplitude coefficient. By using Eq. (8), we can achieve the light absorption spectra of a multilayer system with different gate voltages V_b by fitting the above calculated results. As shown in Fig. 6(a), the fitting results agree well with the TMM calculations. The fitted physical parameters f, ω₀, γ₁ and φ in Eq. (8) are about 0.892, 1.439×10¹⁵ rad/s, 1.55×10¹⁴ rad/s and π, respectively. The values of δ, γ₂ and κ change with V_b, as depicted in Figs. 6(b)–6(d). We can see in Fig. 6(b) that the resonance frequency detuning δ gradually increases when V_b is adjusted from 0 V to 4.8 V, then decreases when V_b continuously increases. This contributes to the evolution of induced transparency wavelength in Fig. 5(a). The decay rate γ₂ nearly remain constant when V_b<4.7 V, and then quickly alters when V_b is around 4.8 V. γ₂ decreases from 1.72×10¹² rad/s to 0.19×10¹² rad/s when V_b changes from 4.7 V to 5V. It illustrates that the dissipative loss of defect layer dramatically alters when the gate voltage approaches ∼4.8 V, which is well consistent with the above analysis. The spectra in Fig. 3 can also be fitted using the above equation. The fitting process is still valid when δ is much larger than γ₂. It is worth noting that the coupling strength κ is also related to the gate voltage V_b, as shown in Fig. 6(d). κ has unchanged value of 2.4×10¹² rad/s when V_b<4.7 V, and then quickly ascends to 3.4×10¹⁴ rad/s when V_b=5 V. These theoretical calculations show that the active tuning of the EIT-like effect derives from the alternation of the decaying rate for the defect mode and the coupling strength between the TPP and defect modes, which strongly depend on the gate voltage on graphene. This offers a new avenue for active tunability of light absorption of topological insulators.

Fig. 6. (a) TMM calculated (dots) and fitting (curves) results of light absorption spectrum from the multilayer structures with different gate voltages V_b on graphene. (b) Fitting values of resonance frequency detuning δ between the oscillators 1 and 2 with different V_b. (c) Fitting values of decay rate γ₂ in the oscillator 2 with different V_b. (d) Fitting values of coupling strength κ between the oscillators 1 and 2 with different V_b. Here, d_a=150 nm, d_b=240 nm, d_u=50 nm, d_i=5 nm, d_s=60 nm, θ=0°, and N = 20.

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4. Conclusions

We have investigated light propagation characteristics in multilayer photonic structures composed of BSTS topological insulator film and a SiO₂/Si₃N₄ Bragg mirror. The TPP mode can be generated between the BSTS film and Bragg mirror, inducing the strong light absorption of the topological insulator. When an Al₂O₃ defect layer is introduced in the Bragg mirror, an ultranarrow induced transparency can be realized in the absorption spectrum with the formation of the EIT-like effect in the multilayer structure because of the destructive interference between the TPP mode and defect mode. It is found that the EIT-like response is strongly dependent on the thicknesses of the BSTS film, Bragg mirror layer, defect layer and light incident angle. The theoretical results are in excellent agreement with numerical simulations. Especially, a single-layer graphene is integrated into the defect layer, and thus the dynamic tunability of light absorption in the topological insulator can be achieved by adjusting the gate voltage on graphene. According to two-oscillator model, we find that the tunability of light absorption is attributed to the graphene-controlled decaying rate of defect mode and coupling strength between the TPP and defect modes. Our results will pave a new pathway toward the active control of light absorption and novel topological insulator optoelectronic devices, especially modulators and switches.

Funding

National Key Research and Development Program of China (2017YFA0303800); National Natural Science Foundation of China (11974283, 11774290, 61705186, 11634010); Natural Science Basic Research Plan in Shaanxi Province of China (2020JM-130, 2018JM6013).

Disclosures

The authors declare no conflicts of interest.

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Graphene-tuned EIT-like effect in photonic multilayers for actively controlled light absorption of topological insulators

Abstract

1. Introduction

2. Structure and model

3. Results and analysis

4. Conclusions

Funding

Disclosures

References

Cited By

Figures (6)

Equations (8)

Optics Express