Surface plasmon polaritons (SPPs) are surface electromagnetic waves coupling to collective electron oscillation and propagating along the interface between the conductor (e.g., noble metals) and dielectric material.^[1,2] Nowadays, SPPs provide a significant platform for promoting the development of advanced optical physics and technologies because of their excellent capabilities of subwavelength light confinement, light field enhancement, and beyond diffraction limit.^[1–5] Based on these special properties of SPPs, some novel plasmonic activities were proposed theoretically and demonstrated experimentally, such as extraordinary optical transmission,^[6] optical activity,^[7] nonlinear optical effect,^[8] Fano resonance,^[9] and electromagnetically induced transparency (EIT) like effect.^[10–12] The plasmonic behaviors are also explored in new emerging materials, including grapheme,^[13,14] black phosphorus,^[15,16] topological insulators,^[17] etc. A large number of plasmonic devices have been proposed and investigated numerically and experimentally, such as nanoscale filters,^[2] all-optical switches,^[18] wavelength demultiplexers,^[19] solar cells,^[20] logical gates,^[21] modulators,^[22] photodetectors,^[23] waveguides,^[24] and nanolasers.^[25] Particularly, the applications of SPPs in optical sensors have attracted broad attention due to the high sensitivity of SPPs to the external environment.^[9,26-31] Surface plasmon resonance (SPR) sensors were demonstrated for gas detection, biosensing, and refractive index measurement in the simple prism-coupling systems (e.g., Kretschmann configuration).^[27,32] To improve the sensing performance, several special plasmonic responses were proposed to promote the spectral features. Fano resonance presents asymmetric spectral profile, contributing to the 7-fold improvement of the sensitivity for plasmonic sensors.^[9,33] The plasmonic effect analogue to EIT in atomic systems was proposed to promote the spectral width for improving the sensitivity of sensors.^[34,35] Reducing the width of resonant spectrum in SPR system is a challenge to us for the improvement of plasmonic sensing capability.

Here we propose a new plasmonic multilayer configuration consisting of stacked Al₂O₃ and SiO₂ layers, a thin metal film, and a dielectric prism substrate (Fig. 1). This Kretschmann configuration based multilayer system enables the realizing of the EIT-like spectral splitting through the coupling and interference between the SPR on the metal and GMR in the Al₂O₃ layer. When another Al₂O₃ layer is coated on the multilayer structure, the induced reflection peak can be further split because of the reintroduced GMR, resulting in the ultra-narrow reflection spectral dip. It is found that the coupling-induced splitting spectrum facilitates the achievement of plasmonic sensors with an ultra-high figure of merit (FOM) of 583, which is about 5 times larger than that of traditional SPR sensors.^[36] Our results will pave a new way for realizing the light manipulation and high-performance plasmonic sensing.

Fig. 1.

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Fig. 1. (color online) Schematic diagram of the multilayer configuration with an incident angle θ of light. Here, n0: refractive index of dielectric prism substrate, d1 (n1: thickness (refractive index) of gold film, d2 (n2): thickness (refractive index) of the first SiO2 layer, d3 ( n3): thickness (refractive index) of the first Al2O3 layer, d4 (n4): thickness (refractive index) of the second SiO2 layer, d5 (n5): thickness (refractive index) of the second Al2O3 layer, and n6: refractive index of the environment.

As shown in Fig. 1, the proposed plasmonic multilayer system is composed of stacked Al₂O₃ and SiO₂ layers, a thin metal film, and a dielectric prism substrate. The light is incident on the metal film from the glass prism with an angle θ. The metal is set to be gold, whose relative permittivity can be described by the Drude model ,^[24,37] where ω = 2πc/λ is the angular frequency of light, with c being the free-space light speed and λ the incident wavelength in vacuum. For gold, ε_∞ = 1, γ = 2.79 × 10₁₃ rad/s, and ω_p = 1.3 × 10¹⁶ rad/s represent the relative permittivity at the infinite frequency, electron collision frequency, and bulk plasma frequency, respectively.^[37] n₀, n₁, n₂, n₃, n₄, n₅, and n₆ refer to the refractive indices of the glass prism substrate, the gold film, the first SiO₂ layer, the first Al₂O₃ layer, the second SiO₂ layer, the second Al₂O₃ layer, and the environmental surrounding, respectively. d₁, d₂, d₃, d₄, and d₅ denote the thicknesses of the gold film, the first SiO₂ layer, the first Al₂O₃ layer, the second SiO₂ layer, and the second Al₂O₃ layer, respectively. The light is incident with the transverse magnetic (TM) polarization, the spectral response of the multilayer structure can be theoretically calculated from the following equations:^[32] 1 2 3 4 5 where r_i,i+1 is the reflection coefficient of light propagation at the interface between the adjacent layers i and i+1 (i = 0, 1, . . ., N - 1), N is the number of layers in the multilayer structure, and k_z,i denotes the wavevector of the light propagation along the x-axis direction in the optical layer i (i = 0, 1, . . ., N). Using Eqs. (1)–(5), we can theoretically calculate the evolution of reflection spectrum with d₃ in the multilayer structure with θ = 80°, d₁ = 60 nm, d₂ = 2.0 μm, d₄ = 2.0 μm, d₅ = 0 μm, which is shown in Fig. 2(a). Here, the refractive indices are set to be n₀ = 1.516, n₁ = (ε_m)^1/2, n₂ = 1.45, n₃ = 1.76, n₄ = 1.45, n₅ = 1.76, and n₆ = 1. In Fig. 2(b), we can see that there exists an obvious dip in the reflection spectrum when d₃ = 0 μm. To verify the theoretical calculations, we numerically simulate the spectral response and field distributions in the structure by using the finite-difference time-domain (FDTD) method. In this method, the perfectly matched layer (PML) absorbing boundary conditions and Bloch boundary conditions (BBC) are set at the top/bottom and right/left sides of the computational space, respectively.^[38] The FDTD simulations are in excellent agreement with the theoretical results.

Fig. 2.

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	Fig. 2. (color online) (a) Evolution of reflection spectrum with the Al2O3 thickness d3. (b) Reflection spectra of the multilayer structure with d3 = 0 nm and 635 nm. The other parameters are set to be θ = 80°, d1 = 60 nm, d2 = 2.0 μm, d4 = 2.0 μm, d5 = 0 μm, and n6 = 1.

The reflection dip is generated at a wavelength of 893 nm, where the SPR on the metal satisfies the wavevector matching condition with incident light being in the prism, namely, k₀n_spp = k sin θn₀.^[39,40] At this wavelength, the SPR is excited on the metal film as shown in Fig. 3(a). In Fig. 2(a), we can observe that the distinct peaks appear in the broad reflection spectral dip when d₃ approaches to special values. For instance, a narrow reflection peak can be generated at the wavelength of 893 nm (λ = 893 nm) when d₃ = 635 nm as depicted in Fig. 2(b). At this wavelength, the GMR can be generated in the high-refractive index (Al₂O₃) layer, as shown in Fig. 3(b). This optical phenomenon is analogous to the EIT effect in an atomic system.^[41] Here, the SPR can be regarded as the excitation state |1〉, the GMR can be analogy to the excitation state |2〉, the light is incident on the metal film and generates SPR, which can be analogue to the transition process from ground state |0〉 to |1〉. The incident light cannot directly excite the GMR in the Al₂O₃ layer, which denotes that the transition process from |0〉 to |2〉 is not allowed. The GMR is generated via the coupling of SPR evanescent field, corresponding to the transition between |1〉 and |2〉. Thus, the two possible pathways |0〉 → |1〉 and |0〉 → |1〉 → |2〉 →|1〉 will generate the destructive interference, giving rise to the weakness of SPR field and the spectral splitting. The EIT-like effect is derived from the excitation of dark mode (GMR in the Al₂O₃ layer) induced by the coupling of bright modes (SPR on the metal).^[42,43] The coupling becomes weaker with increasing d₂, resulting in the narrower width and lower height of the EIT-like spectral peak.^[11,41] As shown in Fig. 2(a), the induced reflection peak shows a redshift with the increase of d₃ due to the redshift of resonant wavelength for the Al₂O₃ layer.

Fig. 3.

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	Fig. 3. (color online) Electric field distribution of |E| at λ = 893 nm in the multilayer structure (a) without and (b) with the first Al2O3 layer (i.e., d3 = 0 and 635 nm).

Subsequently, we investigate the evolution of reflection spectrum with d₅ in the multilayer structure with θ = 80°, d₁ = 60 nm, d₂ = 2.0 μm, d₃ = 635 nm, and d₄ = 2.0 μm. We can see in Fig. 4(a) that the reflection spectral peak can be further split when d₅ reaches a particular value. Figure 4(b) shows the reflection spectral response in the multilayer structure with d₅ = 277 nm. A sharp spectral dip can be generated in the EIT-like reflection peak at a wavelength of 892.3 nm. By the FDTD method, we numerically simulate the electric field distribution of the multilayer system at the wavelength of 892.3 nm and the results are shown in Fig. 4(c). It is found that the GMR in the second Al₂O₃ layer is excited, and the GMR in the first Al₂O₃ layer disappears. The successive spectral splitting can be attributed to the coupling and interference between the GMR in Al₂O₃ layers and SPR on the metal film. This interesting spectral response can also be explained according to the EIT-like theoretical mechanism. The introduction of the GMR into the second Al₂O₃ layer provides another excitation state |3〉, giving rise to the generation of new coupling (transition) and interference processes. Here, the GMR in the second Al₂O₃ layer can only effectively couple with the GMR in the first Al₂O₃ layer. Thus, the transition from |1〉 to |3〉 is forbidden. The two possible pathways |0〉 → |1〉 → |2〉 and |0〉 → |1〉 → |2〉 → |3〉 → |2〉 will form destructive interference, resulting in the disappearing of electrical field in the first Al₂O₃ layer, which is shown in Fig. 4(c). Meanwhile, the disappearance of the electric field in the first Al₂O₃ layer prevents the transition from |2〉 to |1〉. Thus, the SPR field still exists on the metal film. As shown in Fig. 4(a), the splitting spectral dip has a redshift with the increase of d₅, which is attributed to the redshift of resonant wavelength of GMR in the second Al₂O₃ layer. This spectral splitting response contributes to the narrower SPR resonant spectrum, providing a new pathway toward the realization of high-performance plasmonic sensing.

Fig. 4.

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	Fig. 4. (color online) (a) Evolution of reflection spectrum with the thickness of the second Al2O3 layer d5. (b) Reflection spectrum of the multilayer structure with d5 = 277 nm. (c) Electric field distribution of |E| at reflection dip (λ = 892.3 nm) in panel (b). Here, θ = 80°, d1 = 60 nm, d2 = 2.0 μm, d3 = 635 nm, d4 = 2.0 μm, and n6 = 1.

Next, we study the influence of the thickness of the second SiO₂ layer d₄ on the splitting of reflection spectrum. As shown in Fig. 5, the reflection dip in the center of the spectral peak becomes narrower with increasing d₄. This spectral response results from the gradual weakening of optical coupling between the first and the second Al₂O₃ layers with the increase of d₄.^[11] For example, the spectral full-width at half-maximum (FWHM) of the reflection dip can reach 0.6 nm when d₄ = 2.5 μm, which is about 20 times smaller than the SPR spectral width. In order to explore the sensing features based on this spectral splitting effect, we investigate the spectral response in this multilayer structure with different surrounding refractive indices. The reflection dip shows a redshift with increasing n₆, while the position of the reflection peak does not change. This is due to the fact that the wavelength of GMR in the second Al₂O₃ layer increases with n₆, while the reflection peak is not sensitive to the change of n₆. As shown in Fig. 6(a), the reflection spectrum can approach a maximum value from the minimum value (spectral dip) when n₆ changes from 1 to 1.003. The sensitivity (S = Δλ/Δn) of the refractive index sensing is about 350 nm/RIU. Thus, the figure of merit (FOM = S/FWHM) as a critical sensing factor can reach as high as 583, which is about 5 times larger than that of traditional Kretschmann configuration SPR sensors.^[36] The FOM is also two orders of magnitude larger than that of plasmonic sensing based on the EIT-like effect in planar metamaterials.^[34] To contain the information about the relative intensity change, the FOM^* was proposed by Becker et al. for the measurement of optical sensing features, which is defined as FOM^* = max[dI/Idn]. Here, I and dI denote the reflection intensity and its variation under the condition of the refractive index change dn, respectively.^[44] The results in Fig. 6(b) show that the FOM^* based on the spectral splitting in the multilayer system can approach 1.46 × 10⁴, which is 29 times larger than our result reported previously in plasmonic waveguides.^[9] The splitting spectrum and FOM^* are dependent on the gold layer thickness d₁. More specifically, when d₁ decreases, the reflection dip of the splitting spectrum will become much shallower and the FOM^* will decrease (not shown here). When another Al₂O₃ layer is introduced into the structure, the reflection spectrum can be further split and generate a narrower spectral peak.

Fig. 5.

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	Fig. 5. (color online) Evolution of reflection spectrum with the thickness of the second SiO2 layer d4 when n6 = 1. Here, θ = 80°, d1 = 60nm, d2 = 2.0 μm, d3 = 635 nm, and d5 = 277 nm.

Fig. 6.

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	Fig. 6. (color online) (a) Reflection spectra of the multilayer structure with different n6. (b) Reflection dip positions with different values of surrounding refractive index n6. Inset shows figure of merit (FOM*) of plasmonic sensing. Here, θ = 80°, d1 = 60 nm, d2 = 2.0 μm, d3=635 nm, d4 =2.5 μm, and d5 =277 nm.

We have theoretically and numerically investigated the generation and application of EIT-like spectral splitting effect in a plasmonic multilayer configuration consisting of a thin gold film on a glass prism substrate (Kretschmann configuration) and stacked Al₂O₃/SiO₂ layers. The results show that the SPR-induced spectral dip can be split and generate a narrow EIT-like peak due to the coupling and interference between the SPR on the metal film and the GMR in the Al₂O₃ layer. The theoretical calculations agree well with the numerical simulations. Especially, we find that the EIT-like induced reflection peak can be further split when another Al₂O₃ layer is introduced into the multilayer structure. This successive spectral splitting response can also be explained from the EIT-like coupling mechanism. By means of the spectral splitting, the ultra-narrow reflection dip with a spectral width of 0.6 nm can be achieved, which contributes to the realization of plasmonic sensors with the ultra-high FOM. The FOM can approach to 583, which is about 5 times larger than that of traditional Kretschmann configuration SPR sensors. The plasmonic spectral response in the proposed multilayer system will pave a new way for the light manipulation and the improvement of optical functionalities, especially biochemical and environmental sensing.