High Q-factor plasmonic resonators in continuous graphene excited by insulator-covered silicon gratings

Abstract

We propose a structure to excite plasmons in large-area continuous graphene films with insulator-covered sub-wavelength silicon gratings (ICSWSG). By numerical simulations we have demonstrated that, after adding a low-permittivity insulator underneath graphene, the graphene/gratings hybrid structure has a high Q-factor (∼66) and a sharp notch (with the full width at half maximum of ∼122 nm) in the transmission spectra at mid-infrared resonant wavelength. Furthermore, the plasmonic properties, e.g. the resonant wavelength, magnitude and Q-factor, can be tuned over a wide range via structure modulation and/or gating of graphene. The transmission dip is achieved over a wide angle range. Finally we demonstrate that such highly confined graphene plasmons could also be excited in graphene sandwiched between silicon gratings and a SiO₂ substrate.

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1. Introduction

Graphene emerging as a novel two-dimensional (2D) material has attracted significant attention due to its unique electronic and optical properties, which has inspired a plethora of fascinating applications in photonics and optoelectronics.^1–5 Graphene has been found to support plasmons (collective oscillations of charged carriers) for a wide wavelength range from mid-infrared to terahertz with interesting properties such as sub-wavelength confinement and prominent enhancement of electromagnetic field near graphene surface.^6,7 The confinement of plasmons in graphene is stronger than that on metallic surface due to the 2D nature of graphene and extremely short plasmonic wavelength compared to the excitation wavelength, which can create strong light–matter interactions and can be potentially used to build optical detectors, modulators and nonlinear optical devices with high efficiency.^8–11 Moreover, it was shown that the plasmonic properties can be dynamically tuned by doping or gating graphene.^12,13 Furthermore, the high carrier mobility in graphene at room temperature and at high carrier concentrations leads to an effective propagation of plasmonic waves in graphene with a spatial scale of several times of the wavelength of graphene plasmons at mid-infrared frequencies.^10,14,15 Such large propagation range of graphene plasmons (albeit at different frequencies) are substantially more favorable than those of conventional surface plasmons. For example, the plasmonic propagation lengths are only 0.1 times of the wavelength of surface plasmons at the Ag/Si interface.¹⁴ Due to the high mobility, the tuning response occurs in a duration shorter than a nanosecond.¹ Therefore graphene has been recognized as a versatile and promising plasmonic material.

For exciting plasmons in graphene, a key challenge is to efficiently couple to the plasmonic wave, as its wavevector is much larger than that of free-space waves.^15,16 Experimentally, excitations of plasmons in graphene have been realized using periodically patterned graphene structures, e.g., one-dimensional (1D) nanoribbons¹³ or micro-ribbons⁶ and 2D nanodisks¹² or micro-disks.¹⁷ Graphene/insulator stacking structures have been investigated to enhance the tunability of the plasmonic resonance magnitude.¹⁸ These designs usually suffer a relatively low quality factor (Q-factor) (defined as the ratio of resonant wavelength to the full width at half maximum) which possibly restricts the practical applications, e.g. in sensing. On the other hand, although extremely high carrier mobility, e.g. 230 000 cm² (V⁻¹ s⁻¹), has been demonstrated in high-quality exfoliated graphene samples,¹⁹ the lithography process necessary for fabricating graphene nanostructure or microstructure arrays may severely deteriorate the mobility, thus leading to a big loss and much lower Q-factors.^12,20 It will be valuable to have optimized Q-factors, especially in large-area continuous films.

Plasmonic excitations in graphene with sub-wavelength dielectric gratings to compensate wavevector have been proposed to generate a resonance with a Q-factor of ∼40.^15,16 In these structures, the dispersion of graphene plasmons splits into bands due to the different dispersions of plasmons on different regions of gratings, which allows the excitation of plasmons in graphene by external incident light.¹⁶ Utilizing these structures, plasmonic excitations may be realized without the need of engineering graphene, which may benefit to maintain the excellent electronic property in graphene.²¹ Moreover, by tuning the period of gratings, the structure can work in mid-infrared, far-infrared or terahertz wavelengths.¹⁵ For example, plasmons in a continuous monolayer graphene have been detected in mid-infrared regions with the assistance of sub-wavelength silicon gratings.²¹ However, the challenges could remain considering the proposed process of experimental preparations and microstructure influences. When compared to flat substrates, the rough gratings may increase the interface scattering and deteriorate the mobility in graphene,^12,22–24 thus leading to bigger losses and lower Q-factors in the practical devices.

In this work, a structure with insulator-covered sub-wavelength silicon gratings (ICSWSG) is proposed to excite plasmons in a continuous graphene film. The structure experiences a high Q-factor after a low-permittivity insulator is added underneath graphene. Finite element electromagnetic simulations reveal the strong electric field confinement around the graphene layer at the resonant wavelengths. We demonstrate that the plasmonic properties can be modulated by tuning the insulator layer thickness, grating period, Fermi energy level, carrier mobility and the number of graphene layers. Moreover, the strong resonance has been observed over a wide incident angle of the light. Similar plasmonic resonances and field confinements can also be realized in a graphene layer sandwiched between silicon gratings and a SiO₂ substrate. The excellent features of our proposed structures would make high-performance graphene-based plasmonic sensors possible.

2. Structure and methods

The structure of ICSWSG is schematically illustrated in Fig. 1a and the 2D simulation configuration is depicted in Fig. 1b. The surface of a silicon wafer was patterned into a periodic array of gratings with period p, width w (w = 0.5p) and thickness T₁. The slits between silicon gratings were filled with organic solution of an insulator such as NFC (NFC is a derivative of polyhydroxystyrene that is conventionally used as a planarizing underlayer in lithographic processes.^18,22 It can be diluted in propylene glycol monomethyl ether acetate, and spin-coated onto the surface. The dilution and spin speed can be adjusted to control the desired thickness and uniformity of the buffer layer.²²). Another thin layer of NFC with a thickness of T₂ was spin-coated on the top of silicon gratings and was used as buffer layer, with an attempt to construct a relatively gentle contact for graphene. Finally, a graphene film was transferred onto the top of the buffer layer. To excite the resonance, a mid-infrared wave was incident onto the device from the top with transverse magnetic (TM) polarization (the magnetic field parallel to the silicon grating stripe) and transmittance was recorded to exhibit the electromagnetic response of the hybrid structure. Once the plasmonic resonance is excited, the electrical field is confined around the graphene layer as depicted in the inset of Fig. 1a.

Fig. 1 (a) Schematic view of insulator-covered sub-wavelength silicon gratings-assisted graphene plasmons. The gratings patterned on silicon wafer surface have period p, width w (w = 0.5p) and thickness of T₁. The slits between silicon gratings are filled with an insulator (e.g. NFC), and another thin insulating layer with thickness of T₂ is coated on the top of graphene films. The electrical field distributions in the yz-plane at the resonant wavelength are depicted in the inset at lower right corner. (b) 2D configuration of graphene on NFC-covered silicon gratings for simulation.

For a continuous monolayer graphene, the dispersion relationship of plasmonic wave is given by^14,25

where, k_p is the wavevector of plasmons in graphene, k₀ is the free-space wavevector, ε_r1 and ε_r2 are dielectric constants of the materials above and under the graphene, ε₀ is the permittivity of vacuum, c is the speed of light, and σ is the conductivity of graphene.

The conductivity of graphene is modeled using Drude model with D (Drude weight) and Γ (scattering width) as two fitting parameters,²⁶

where ω is the incident light frequency; D = e²E_F/ħ² and Γ = τ⁻¹ = eν_F²/μE_F, where e is the elementary charge, ħ is the reduced Planck's constant, E_F is the Fermi energy level, μ is the carrier mobility, ν_F ≈ 2.1^1/2 × 10⁶ m s⁻¹ is the Fermi velocity and τ is the intrinsic relaxation time (e.g., τ = 3.8 × 10⁻¹³ s for E_F = 0.8 eV and μ = 10 000 cm² (V⁻¹ s⁻¹)). Here, as the photon energy in the simulated spectral range is always less than 2E_F, interband transitions in graphene are forbidden by the Pauli exclusion principle.^25–27 Thus the effect of the interband transition has been neglected in the simulations.²⁵

Combining eqn (1) and (2), the wavevector of graphene plasmonic wave can be expressed as

When graphene is placed on a uniform dielectric medium, its plasmonic modes can't be excited directly by mid-infrared light, since the wavevector of graphene plasmonic waves is far larger than that of light in vacuum, as shown in Fig. 2a. However, once the difference is overcomed, the plasmonic wave can be excited in graphene and the electric field is highly confined due to the large differences in wavevector.^13,15

Fig. 2 (a) Dispersion curves of graphene plasmons (red lines) on uniform dielectric medium (ε_r1 = ε_r2 = 1) and light line (black lines) in air. (b) Real part of the conductivity of graphene as a function of wavelength. Here, graphene Fermi energy level E_F = 0.6 eV and carrier mobility μ = 10 000 cm² (V⁻¹ s⁻¹) were used.

Herein, the ICSWSG is used to compensate the wavevector mismatches caused by the difference in the dispersion of graphene plasmons on different regions of ICSWSG,¹⁶ which enables the efficient coupling of the incident electromagnetic field and the plasmonic modes in graphene. Introducing a low-permittivity polymer buffer layer between silicon gratings and graphene films may allow a relatively gentle contact for graphene and decrease the resonant wavelength λ₀ (eqn (6)), where Q-factors are further improved as decreased value of Re(σ) (real part of the graphene conductivity) in small wavelength range corresponds to low losses (Fig. 2b). Furthermore, it has been claimed that adding a polymer buffer layer underneath graphene may help to minimize the mobility degradation due to the suppression of extrinsic surface phonons and reduction of the impurity concentration.¹⁸

For a grating period p, the resonant wavelength λ₀ is determined by phase match equation¹⁵

where θ is the incident angle, η is a dimensionless constant which is related to the dielectric constant and the thickness of buffer layer and can be deduced from our simulation results.

For a normal incidence wave, θ = 0, eqn (4) is simplified as

From eqn (5), it can be seen that the plasmonic resonant wavelength λ_p = 2π/Re(k_p) is related to grating period p and η as λ_p = ηp.

Combining eqn (3) and (5), the resonant wavelength λ₀ is given by

Since the optical energy dissipates due to the ohmic loss while the plasmonic wave propagates in the continuous graphene layer, a notch can be observed around the resonant wavelength in the transmission spectrum.¹⁵ The simulations were performed in frequency domain using Comsol Multiphysics (COMSOL 4.3a), which implements the finite element method (FEM) to solve Maxwell's equations and is a widely accepted method for modeling optics.^28,29 In the simulations, we set the perfectly matched layer (PML) in the vertical direction to achieve absorbing boundary conditions, while in the horizontal directions we used periodic boundary conditions for simulating an infinite silicon grating array (Fig. 1b). The graphene film was modeled as a thin layer with a thickness of 0.5 nm, as in ref. 11 and 15 and dielectric constants of silicon, SiO₂ and NFC were taken from ref. 18, 22 and 30. The meshing was done with the program built-in algorithm, which creates a tetrahedral mesh. The mesh maximum element size (MES), which limits the maximum size of the edges of the tetrahedrons, was set to be 0.1 nm in the domain representing the graphene, 1 nm for NFC and 6 nm for all the elements in the air, silicon and SiO₂ subdomains. Direct PARDISO solver was used to solve the problem.

3. Results and discussion

Fig. 3 shows the simulated transmission spectra for a monolayer graphene on silicon gratings with or without a 10 nm-thick polymer buffer layer underneath graphene, respectively. Strong resonance with a transmission dip was seen at 8.08 μm or 11.19 μm, for the case with or without buffer layer, respectively. The full width at half maximum (FWHM) of the resonance decreases from 248.87 nm for graphene on silicon gratings to 121.80 nm after a polymer buffer layer is added, leading to an improvement of 47.55% in the Q-factor (from 44.96 to 66.34). The increase in the Q-factor at smaller resonant wavelength is a result of decreased real part of the graphene conductivity (Fig. 2b), corresponding to lower losses.²⁵ This merit is desired in applications such as sensing as figure of merit (FOM) is proportional to Q-factor. The side-view profile of the electric field in one grating period for graphene on the buffer layer (inset of Fig. 3a) confirms that the electric field is tightly confined around the graphene layer. In addition, the electric field has a 2π phase shift with the sign of the electric field flipping at the edge of the silicon slits. Specially, the confinement of electric field is strong at the corner of silicon gratings, further benefiting the electric field confinement. It is worth noting that the electric field for graphene on silicon gratings (inset of Fig. 3b) is also confined within the graphene layer. Here, the higher-order modes have been neglected at the smaller resonant wavelength due to the shallow notch in the transmission spectra.

Fig. 3 Simulated normal-incidence transmission spectra for graphene on silicon gratings (a) with and (b) without a 10 nm-thick buffer layer beneath when E_F = 0.6 eV, μ = 10000 cm² (V⁻¹ s⁻¹), p = 200 nm and T₁ = 500 nm. The insets show the side-view electrical field distribution in one grating period at the corresponding resonant wavelength of (a) 8.08 μm and (b) 11.19 μm, respectively.

The Q-factor of the plasmonic spectra is determined by the optical loss in graphene and can be calculated from relaxation time τ of charge carriers in graphene at resonance wavelength λ₀. Theoretically, the Q-factor is expressed as²⁵

where Re(k_p) and Im(k_p) are the real and imaginary part of the wavevector of the plasmonic wave in graphene. For a specific resonant wavelength λ₀, the only way to increase the Q-factor is improving the quality of graphene, i.e., by increasing τ or μ (μ = eν_F²τ/E_F). The simulated transmission spectra with various carrier mobilities in graphene are shown in Fig. 4a. It can be clearly seen that the FWHM decreases and Q-factor increases linearly (inset of Fig. 4a) with increasing the carrier mobility while the resonant wavelength (λ₀ = 8.08 μm) maintains unchanged. The curve of Re(σ) versus mobility μ at resonant wavelength λ₀ = 8.08 μm (inset of Fig. 4a) suggests that Re(σ) is inversely proportional to μ, explaining the lower loss, smaller FWHM and higher Q-factor for a graphene with higher mobility at a fixed resonant wavelength. Recent developments in the large-area synthesis and transfer techniques of high-quality graphene films grown on metal substrates make the fabrication of devices with improved performance possible.^18,31,32

Fig. 4 (a) Simulated normal-incidence transmission spectra with various carrier mobilities of graphene when E_F = 0.6 eV, p = 200 nm, T₁ = 500 nm and T₂ = 10 nm. The real part of graphene conductivity and Q-factor with varying carrier mobilities at resonant wavelength λ₀ = 8.08 μm are shown in the inset. The dots are simulated data and the lines are calculated from eqn (2) or (7). (b) Transmission spectra with buffer layer thickness of 5, 10, 20, 30 or 50 nm, respectively when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm and T₁ = 500 nm.

In the proposed structure, another factor affecting FWHM and Q-factor is the thickness of buffer layer, which influences the effective dielectric constants of ε_r2. Fig. 4b shows the simulated transmission spectra with different thicknesses of buffer layers. It can be seen that the resonant wavelength blue-shifts as increasing the thickness of buffer layer due to the additional decrease in the effective permittivity ε_r2. Thus FWHM decreases and Q-factor increases due to the low loss at smaller resonant wavelength. However, if the thickness of buffer layer is too large, the transmission notch is too shallow to ensure enough detection (it is 100 nm in our case); 10 nm was used in the following discussions.

Furthermore, our simulations (Fig. 5) show that the deep transmission dip can be realized over a wide angle range. Such a result is explained by the existence of flat graphene plasmon bands above the light line at mid-infrared regions, which is attributed to the deep sub-wavelength nature of graphene plasmons and effects of Bragg scattering at the Brillouin zone center.¹⁶

Fig. 5 The simulated angular dispersions of the transmittance for TM configurations when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm.

The Q-factor can be tuned by the Fermi energy level E_F in graphene relative to the Dirac points via gate voltage or electrostatic doping and period p of silicon gratings. From the simulation results shown in Fig. 6a, it can be seen that the transmission spectra can be effectively tuned with varying Fermi energy level E_F of graphene. The resonant wavelength and Q-factor with respect to the Fermi energy level E_F agree well with eqn (6) or (7) (η = 1.50), as shown in Fig. 6b. Recent studies suggested that, adding a buffer layer before transferring additional graphene layers could help to distribute carriers into multiple graphene layers and make the structure have a broader tunability.¹⁸ Fig. 6c shows the transmission spectra in the multilayer graphene/insulator structures. It can be seen that the resonant properties can be tuned in a broader range via changing the number of multilayer structures. It is worth noticing that the contribution of the buffer layer to the total conductivity has been ignored since the buffer layer is thin (10 nm) and non-conducting.¹⁸ In the calculations of multilayer graphene, we considered each graphene layer has the same Fermi energy level, mobility and relaxation time. The total conductivity still has the Drude form, σ_total = iD_total/π(ω + iΓ), where the sum of the Drude weights for N layer graphene D_total = N^1/2e²E_F/ħ.^18,26 The resonant wavelength and Q-factor with respect to the number of graphene layers agree well with theoretical values (substituting N^1/2E_F for E_F in eqn (6) or (7)), as shown in Fig. 6d. Thus, multilayer graphene films (e.g. by sequentially transferring monolayer) could be used to further improve the tunability of such devices.

Fig. 6 (a) Simulated normal-incidence transmission spectra with different Fermi energy level E_F in graphene when μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm. (b) Scaling rule of the resonant wavelength λ₀ and Q-factor with respect to E_F. The dots are simulated results and the lines are calculated from eqn (6) or (7). (c) Transmission spectra with different number of graphene/insulator multilayer structure when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm. (d) Scaling rule of the resonant wavelength λ₀ and Q-factor versus the number of multilayer structure. The dots are simulated results and the lines are calculated from eqn (6) or (7) when substituting N^1/2E_F for E_F. (e) Transmission spectra with different period p of silicon gratings when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), w = 0.5p, T₁ = 500 nm and T₂ = 10 nm. (f) Scaling rule of the resonant wavelength λ₀ and Q-factor with respect to p. The dots are simulated results and the lines are calculated from eqn (6) or (7).

The effects of the period of silicon gratings were studied by fixing the ratio of grating width w and period p (w/p) to be 1/2. It can be seen from Fig. 6e that the transmission spectra are largely tuned with varying periods. The resonant wavelength and Q-factor with respect to the period agree well with eqn (6) or (7), as shown in Fig. 6f. Specially, when the period of silicon gratings is reduced to 50 nm, the Q-factor can be as high as 155. For large period, the notches at the higher frequencies are caused by higher order modes.

Finally, the dependence of the resonant wavelength to the refractive index (RI) of dielectric environment above graphene (n₁ = ε_r1^1/2) has been considered for possible applications of the graphene/ICSWSG hybrid structure as sensors since graphene has strong bio-compatibility and adsorption to biomolecules due to the π-stacking interactions and the high surface to volume ratio of graphene.^31,33–37 Fig. 7 shows the transmission spectra with a 20 nm-thick sensing medium on graphene films and corresponding sensitivity calculated (defined as the ratio of the shift of resonant wavelength δλ₀ to the change of RI of the sensing medium δn₁, δλ₀/δn₁), with or without buffer layer. The sensitivity improves 45.13% and figure of merit (FOM, defined as the ratio of sensitivity to FWHM) increases ∼190% (from ∼3.84 to ∼11.38) after a thin buffer layer is present underneath the graphene. The increase in the sensitivity and in the FOM is due to the decrease in the effective permittivity ε_r2 and minimization of the loss at smaller resonant wavelength.²⁵ Furthermore, the sensitivity is related to the thickness of sensing medium since the characteristic decay length of graphene plasmons is as high as ∼100 nm.²⁵ Fig. 8a shows the transmission spectra with sensing medium RI n₁ = 1.31 and thickness of 1, 2, 5, 10, 20, 50, 100 and 200 nm above graphene films, respectively when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm. It can be seen that the resonant wavelength red-shifts with increasing film thickness, and saturation of the shift is observed when the thickness exceeds 100 nm (Fig. 8b), where the sensing is close to the bulk RI sensitivity. For bulk medium, the RI sensitivity can be as high as 1923 nm per RIU, as can be deduced using eqn (6),

Fig. 7 Simulated normal-incidence transmission spectra (a) with and (c) without a 10 nm-thick polymer buffer layer beneath when changing the RI n₁ of 20 nm-thick sensing medium from 1 to 1.5, respectively when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm and T₁ = 500 nm. The resonant wavelength λ₀ versus sensing medium RI curve and the corresponding sensitivity (b) with and (d) without buffer layer underneath. The solid dots are simulated results and the lines are linear fittings to the data.

Fig. 8 Simulated normal-incidence transmission spectra with sensing medium RI n₁ = 1.31 and thickness of 1, 2, 5, 10, 20, 50, 100 and 200 nm when (a) E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm or (c) E_F = 0.2 eV, μ = 20 000 cm² (V⁻¹ s⁻¹), p = 200 nm, T₁ = 500 nm and T₂ = 10 nm, respectively. The resonant wavelength λ₀ with respect to the thickness of sensing medium (b) in (a), giving a bulk sensitivity of 1923 nm per RIU or (d) in (c), giving a bulk sensitivity of 3328 nm per RIU, respectively.

From eqn (8), we can see that the bulk RI sensitivity is related to period, permittivity of material beneath graphene and Fermi energy of graphene. By decreasing the Fermi energy of graphene to 0.2 eV, the bulk sensitivity can be up to 3328 nm per RIU (Fig. 8c and d).

To further demonstrate the flexibility of the dielectric environment surrounding graphene in the hybrid structure, we show that setting sub-wavelength silicon gratings above graphene films can also be used for compensating wavevector differences and exciting graphene plasmons (Fig. 9). Similarly, adding a buffer layer underneath (and/or above) graphene is beneficial to decrease FWHM and to increase Q-factor in the transmission spectra around the resonant wavelength. From the simulated transmission spectra and the side-view electric field profiles, it can be seen that the transmission spectra vary similarly to those for placing sub-wavelength silicon gratings beneath. Moreover, the fundamental mode and second-mode are detected simultaneously for the structure either with or without a buffer layer beneath graphene. When adding buffer layers both on the top and beneath graphene films, the resonant wavelength blue-shifts and FWHM decreases due to the further decrease in the effective permittivity ε_r1 above graphene, and the second mode is too shallow to be detected. The structure provides an alternative to excite plasmons in continuous graphene films.

Fig. 9 Simulated normal-incidence transmission spectra for sub-wavelength silicon gratings on the top of graphene (a) with and (b) without a 10 nm-thick polymer buffer layer beneath when E_F = 0.6 eV, μ = 10 000 cm² (V⁻¹ s⁻¹), p = 200 nm and T₁ = 500 nm. The insets show the side-view electrical field distribution of the fundamental mode and second-order mode in one grating period at the corresponding resonant wavelength, respectively. (c) Transmission spectra for sub-wavelength silicon gratings on the top with 10 nm-thick polymer buffer layer both above and beneath graphene films and corresponding electrical field distribution of the fundamental mode.

4. Conclusion

In conclusion, we have demonstrated that ICSWSG can be used to excite highly confined plasmonic modes in large-area continuous graphene films. By numerical simulations, we found that graphene/silicon gratings hybrid structure exhibits an improvement of 47.55% in the Q-factor and a decrease of 50.91% in the FWHM after a low-permittivity insulator beneath graphene was added. The plasmonic properties including the resonant wavelength and magnitude were tuned via modulating structure and/or gating of graphene. When the hybrid platform was employed in sensing, the sensitivity improved 45.13% and FOM increased ∼190% after a thin buffer layer was present underneath the graphene. In addition, we demonstrated that the highly confined plasmonic modes in graphene could be achieved by embedding graphene between silicon gratings and a SiO₂ substrate. The excellent features of the proposed structures may have implications on the development of high-performance and active plasmonic devices for sensing.

Acknowledgements

Y. Zhao, G. Chen, Z. Tao and Y. Zhu appreciate the financial support from China Government 1000 Plan Talent Program, China MOE NCET Program and Natural Science Foundation of China (51322204).

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