All-dielectric metasurfaces with high Q-factor Fano resonances enabling multi-scenario sensing

2.1 Design, results and discussion

The schematic diagram of the proposed symmetric tetramer metasurface is depicted in Figure 1(a). The metasurface consists of four identical Si square nanodisks (ε _si = 11.71) placed on a SiO₂ substrate (ε _sio2 = 1.79). The geometric parameters of the unit cell are set as follows, p is the period width along the x and y axes, m is the thickness of the SiO₂ substrate, a and h are the side length and thickness of the four Si square nanodisks, and g is the gap between adjacent square nanodisks. In this design, owing to the strong coupling among adjacent nanodisks supported by a certain dipole, a sharp BIC resonance is excited in the mid-IR range. Fano resonance is a kind of asymmetric lineshape of a spectrum phenomenon, which is attributed to the interference of a continuum (or broad) state and a discrete (or narrow) state [26]. The sharp Fano resonances of the proposed metasurface are desirable in refractive index sensing. To intuitively investigate the resonance mechanism, we calculate the electric and magnetic field distributions of the unit cell at the resonance wavelength of 6.87 μm in Figure 1(b) and (c), respectively. The electric fields of this resonance are mainly located in the gap of the square disks and the corresponding electric field vectors are shown in Figure 1(d). Notably, the direction of the electric field vectors in the adjacent square disks are twisting in the opposite directions and produces four longitudinal magnetic moments (white crosses and dots in Figure 1(d)) oriented along the z-axis inversely located in the center of the square disks. The direction arrows of the magnetic fields with head-to-tail links in two pairs form dual parallel magnetic toroidal dipoles [27, 28]. Figure 1(e) shows a 3D schematic diagram of the supporting dual parallel magnetic toroidal dipoles (MTD) (the green circular column), which are created by the circular displacement currents (the purple circular column) in the x–y plane. As we know, there are two primitive toroidal dipoles [29]: one is the magnetic toroidal dipole (MTD) and the other is the electric toroidal dipole (ETD). The MTD is created by poloidal electric currents flowing on a surface of a torus along its meridians, and it can also be viewed as a set of magnetic dipoles arranged head-to-tail to form a closed loop. And the ETD is composed of a circular closed loop of electric dipoles. The mode inside of the particle clusters is an intracluster toroidal dipole; the mode between the neighboring particles in the clusters is an intercluster toroidal dipole. For this symmetric tetramer structure, Fano resonance is produced and supported by dual magnetic toroidal dipole (MTD) of intracluster.

Figure 1:

Schematic diagram of the proposed symmetric metasurface. (a) 3D schematic diagram of the symmetric metasurface, where p = 6.2, m = 0.36, g = 1.1, a = 1.9, h = 0.3 μm. (b) Electric field profile in x–y mid-plane. (c) Magnetic field profile in x–y plane and magnetic field vector in x–z plane of Fano resonance. (d) Electric field vector profile. (e) 3D schematic diagram of dual toroidal dipoles in the tetramer.

Next, to study the Fano resonance performance with different geometry parameters and further optimize its Q-factor, we explore the effect of the gap g of adjacent square nanodisk on the Fano resonance wavelengths and full width at half-maximum (FWHM) of the transmission spectra of the proposed symmetric tetramer unit cell. As shown in Figure 2(a), the transmission spectra at different gap sizes are presented. It is found that the resonant wavelength has a blue-shift when the gap g increases from 0.98 to 1.22 μm, while has a red-shift when the gap g further increases from 1.22 to 1.46 μm. The extracted Q-factor, FWHM, and resonance wavelength as the criteria for sensor properties are shown in Figure 2(b)–(d), respectively. Clearly, the minimum FWHM of Fano resonance is 4 × 10⁻⁵ μm, and the corresponding high Q-factor reaches up to 1.71 × 10⁵ when g = 1.22 μm, showing great potential in ultrasensitive biosensor applications.

Figure 2:

Simulated transmission spectra of the symmetric metasurface. (a) The transmission spectra. (b), (c) and (d) are FWHM, Q-factor, and resonance wavelength under different gap distance g between adjacent square disks, respectively.

Before the discussion of broadband sensing performance, we study the dependence of the Fano resonance wavelength of the proposed symmetric tetramer metasurface on the scaling factor q for the size length of the Si nanodisks (a′ = a × q) and incident angle θ. Aiming to use the bandwidth efficiently, the Fano resonant wavelength is moved to a specific range via tuning the scaling factor q. As shown in Figure 3(a) and (b), all the transmission spectra under different scaling factors q have very similar Fano resonances and the Fano resonance wavelength increases linearly from 6.67 to 8.63 μm as q increases 0.97–1.24. Therefore, without the need for a complicated structure redesign, we can flexibly tune the Fano resonance wavelength to the certain targeted range only by adjusting scaling factor q for Si nanodisks of the metasurface, which is very convenient for various sensing applications in different wavelength ranges. Next, to use the angle-multiplexed method to read out a series of transmission and absorption signatures of analytes for broadband molecular fingerprint sensing [19], the proposed sensor should be dependent on the incident angle. Figure 3(c) demonstrates that the resonance wavelength of the transmission spectra is sensitive to incident angle θ, which is of great significance for broadband sensing.

Figure 3:

The dependence of the Fano resonance wavelengths on the scaling factor q and incident angle θ. (a) Transmission spectra of the metasurface with different square disk size scaling factor q, where other parameters remain as the original settings. (b) The linear relation between resonant wavelength and q. (c) Transmission spectra with different incident angles.

2.2 Sensing performance on detection of materials with complex refractive index

Metasurface combined with the angle-multiplexed method can act as an efficient platform for broadband molecular fingerprint sensing. In the process of detection, we utilize the linear relationship between high Q-factor Fano resonance wavelength dip of the transmission spectrum as a function of the incident angle (see Figure 3(c)) to retrieve a series of broadband fingerprint spectra. The broadband fingerprint spectra are related to the chemical characteristics of coated analytes. Owing to the high Q-factor resonance, giant absorbance enhancement is achieved. In this section, we use the angle-multiplexed method for the detection of several ultrathin analytes with complex refractive indices, such as protein A/G biomolecules, single-layer graphene, and explosive 2, 4-dinitrotoluene. Considering the linear relationship between the Fano resonance wavelength and size scaling factor q (see Figure 3), we choose size scaling factor q as 0.974, 1.23, and 1.1 for the metasurface design for the detection of protein A/G biomolecules with a high extinction coefficient in 5.25–7.75 μm, single-layer graphene in 7.3–8.8 μm, and explosive in 6–7 μm, respectively.

2.2.1 Detection of biomolecules

Firstly, we demonstrate molecular fingerprint sensing of recombinant protein A/G biomolecules [19]. The real and imaginary parts of the protein A/G permittivity are shown in Figure 4(a). It has two optical loss peaks located at amide I and II around 6.1 and 6.6 μm, respectively. In the simulation, the proposed metasurface is coated with the 8 nm ultra-thin protein biomolecule film under different incident angles ranging from 0 to 13° (the red line). As shown in Figure 4(b) and (c), the envelopes of transmission dips and reflection peaks are corresponding to the vibrational mode of the protein A/G molecules. Then, we extract the envelope of the absorbance spectra peak of biomolecule film on the proposed metasurface and compare it with that on a flat SiO₂ substrate (the blue dashed line) in Figure 4(d). It is found that even the biomolecule film is as thin as 8 nm, the peak absorbance with the proposed metasurface reaches up to 44.8%, which is much larger than near to zero absorbance with a flat SiO₂ substrate. The sensing performance via metasurface shows obvious infrared absorbance enhancement compared to the sensing signatures without metasurface. To quantify absorbance enhancement of the proposed metasurface, we calculate broadband enhancing factors of absorbance β [23] from the absorbance amplitudes A at each incidence angle by the formula: β = 10 l g ( ∫ λ 1 λ 2 A metasurface d λ / ∫ λ 1 λ 2 A substrate d λ ) , where A _metasurface and A _substrate are the wavelength-dependent absorbance of the metasurface and the flat substrate after coating biomolecules, respectively. Figure 4(d) shows that the maximum enhancement factor of protein A/G is 10.12 dB. It is clear that the enhancement envelopes are consistent with the corresponding biomolecule vibrational modes.

Figure 4:

Permittivity of protein A/G and its detection results. (a) Real part and imaginary part of permittivity of protein A/G. (b) and (c) are transmission and reflection spectra under incident light from 0° to 13° with a step size of 0.5°. (d) Absorbance spectra and enhancement factor of proposed metasurface sensor with protein A/G film.

2.2.2 Detection of two-dimensional material

The proposed metasurface not only can be used to detect biomolecules but also can be used to identify 2D materials. As one of the most common 2D materials, graphene has been applied widely in various optical devices [30]. The thickness of graphene monolayer is only 0.34 nm, and its high transmission makes it hard to be identified only by human eyes without any auxiliary equipment such as scanning electron microscopy or Raman spectrometer. Because of the enhanced localized fields, the proposed metasurface can be used to detect coating graphene monolayer. Figure 5(a) shows the permittivity of graphene in the wavelength range of 7.3–8.8 μm. Then, we adjust the scaling factor q as 1.23 of the side length a of the metasurface to match this target wavelength range. The simulated T, R, and A of the metasurface coated with single graphene under different incident angles ranging from 0 to 13° are shown in Figure 5(b)–(d), respectively. The extracted absorbance peak envelope (the red curve of Figure 5(d)) reproduces the graphene extinction coefficient trend in Figure 5(a). Compared to the maximum absorption of 1.93% of graphene on an unpatterned substrate (the blue dashed curve), the proposed metasurface can achieve significant absorbance enhancement from 26.8 to 34.2%, the corresponding enhancement factor from 2.97 to 3.81 dB in 7.3–88 μm. Therefore, the proposed metasurface possesses excellent ultrathin analytes identification performance, which may have potential applications in the detection of diverse 2D materials such as silicone, h-GaN, h-SiC, h-BN, and h-BAs.

Figure 5:

Permittivity of graphene and its detection results. (a) Real part and imaginary part of permittivity of graphene monolayer. (b) and (c) are transmission and reflection spectra under incident light from 0° to 13° with a step size of 0.5°. (d) Absorbance spectra and enhancement factors of proposed metasurface with graphene film.

2.2.3 Detection of 2, 4-DNT

Furthermore, we investigate the broadband fingerprint sensing of trace-amount explosive 2, 4-dinitrotoluene (DNT). 2, 4-DNT is a precursor of the widespread explosive 2, 4, 6-trinitrotoluene (TNT) [31]. The detection of traces of 2, 4-DNT indicates the presence of TNT. Figure 6(a) provides the real and imaginary parts of the 2, 4-DNT permittivity, which has two obvious extinction coefficient peaks around 6.22 and 6.51 μm. To achieve complete spectral coverage, we set the size scaling factor q to 1.1. The simulated T, R, and A of the metasurface deposited with an 8 nm 2, 4-DNT thin layer under different incident angles ranging from 0 to 13° are shown in Figure 6(b)–(d), respectively. It is found that the envelope of absorbance peaks of the metasurface with 2, 4-DNT (red curve in Figure 6(d)) is in good agreement with the imaginary part of permittivity shown in Figure 6(a), and the absorbance enhancement factor of 2, 4-DNT with metasurface can reach as high as 9.78 dB at 6.56 μm.

Figure 6:

Permittivity of 2, 4-DNT and its detection results. (a) Real part and imaginary part of permittivity of 2, 4-DNT (b) and (c) are transmission and reflection spectra under incident light from 0° to 11° with a step size of 0.5°. (d) Absorbance spectra and enhancement factors of proposed metasurface sensor with 2, 4-DNT overlayer.

The above results indicate the proposed metasurface is a promising high-sensitivity sensing platform, which can be used to strengthen the weak fingerprint absorbance of various ultrathin trance amount analytes in a wide range of wavelengths. Besides, the absorbance enhancement factor of the metasurface mainly depends on the refractive index, thickness of analyte, and the near-field distributions, leading to the different values of enhancement factors for different analytes, as shown in Figures 4(d)– 6(d). In addition, the Q-factor of the metasurface can be further improved by tuning the gap between the resonator without complicated structure redesign and sophisticated nanofabrication. Although a narrower FWHM and a higher Q-factor bring better sensitivity and resolution, they may result in broad spectral coverage limitation and sampling inaccuracy problems. Therefore, it needs tradeoff between high absorbance enhancement and broad bandwidth coverage in the metasurface design for broadband fingerprint detection applications.

3.1 Design, results and discussion

To further increase the Q-factor of the resonances and enrich detection signals, we transformed the symmetry-protected BIC [32] tetramer metasurface design into a quasi-BIC state by breaking the symmetry of the unit cell as shown in Figure 7(a). The quasi-BIC can induce resonant interference between a collective subradiant dark mode and the superradiant collective bright mode, and therefore, the asymmetric dielectric tetramer metasurface can support multi-Fano resonances in mid-infrared. To make it insensitive to the polarization of the incident light, we arrange two pairs of nanodisks in the diagonal direction of the unit cell. The transmission spectra as a function of different linearly scaled factor k (k = a ₁/a ₂) ranging from 0.6 to 1 are shown in Figure 7(b) and (c), where the side length of the larger square nanodisk and the smaller nanodisk are set as a ₁ = 1.9 and a ₂ = 1.9/k μm, respectively. Clearly, for k = 1 (symmetric structure), only one Fano resonance (Mode 3) can be observed at 6.87 μm. The symmetry is broken when the scaled factor k ≠ 1, leading to the energy excitation of additional Fano resonance produced by the interference between discrete states supported by metasurface and the continuum free space radiation [33]. Clearly, as shown in Figure 7(b), the transmission spectra show two additional Fano resonances (Mode 1 and Mode 2) when k = 0.6, 07, 0.8, and 0.9. As k increases, the Mode 1 resonance will show a redshift, a narrower FWHM, and a higher Q-factor.

Figure 7:

Schematic configuration and multi-Fano resonance characteristics of the proposed asymmetric metasurface. (a) 3D schematic diagram of the asymmetric metasurface. (b) The transmission spectra under different linearly scaled factor k. (c) The transmission spectra of Mode 1 under different linearly scaled factor k. (d) Q-factors extracted from calculated spectra under different asymmetric parameters of Mode 1.

We further investigate the relationship between the Q-factor of Mode 1 and the asymmetry parameter α of the metasurface, where α = ΔS/S = (a ₂ ² − a ₁ ²)/a ₂ ² = 1 − k ². According to previous research reported by Koshelev et al. [32], the relationship of the radiative Q-factor of quasi-BIC on the asymmetry parameter meets the inverse quadratic law (Q _rad ∝ α ⁻²). As shown in Figure 7(d), the relation between the Q-factor of Mode 1 and the asymmetry parameter is consistent with the inverse quadratic law, which indicates the resonance is excited by quasi-BIC. As α increases from 0.64 to 0.09, the Q-factor will significantly increase from 57.95 to 2985.80, which will be further improved by orders when the asymmetry parameter α is enough low.

Then we study the impacts of the loss tangent and thickness of SiO₂ substrate and the dimension imperfections of Si nanodisks on the resonance properties of the asymmetric tetramer metasurface. Considering the small loss of the SiO₂ substrate [34] in the mid-IR, we simulate the influence of different loss tangents of the SiO₂ substrate (tanδ = 0, 0.0001, 0.001, 0.01) on the metasurface spectra. As shown in Figure 8(a), it is observed that the large tanδ will deteriorate the Q-factor of the spectrum resonances to some extent. However, when tanδ is smaller than 0.001, the influence of SiO₂ attenuation on transmission spectra is much smaller. The impact of substrate thickness on the transmission spectra is simulated and shown in Figure 8(b). Clearly, by reducing the substrate thickness, the FWHM becomes smaller and the Q-factor of resonance becomes higher with SiO₂ tanδ = 0.001. This implies that the loss can be further minimized by decreasing the substrate thickness. Therefore, one good way to circumvent the SiO₂ substrate loss is using enough thin substrates. For example, metasurface with freestanding membrane as the supporting layer could be a possible way to further reduce the loss from the substrate and improve the dielectric symmetry [35, 36]. Furthermore, the effects of sample imperfections on the resonance properties of the transmission spectra are also investigated. For example, we assume that the metasurface has round corner imperfections in the Si nanodisks. As shown in Figure 8(c), the large rounded corner radius r changes (from 0 to 0.2 μm) only induce a slight blue shift of the resonance, while remaining its FWHM almost unchanged. Moreover, the dependence of the transmission spectra on the silicon square size a ₁ ranging from 1.88 to 1.92 is shown in Figure 8(d). Similarly, the small a ₁ variation causes some frequency shifts, but the resonance line width almost remains the same. Therefore, small sample imperfections have a small impact on the sensing properties, showing high facilitation tolerance.

Figure 8:

The influence of material loss and fabricated imperfection on transmission spectra. (a) Transmission spectra for different loss tangents of SiO₂ substrate. (b) Transmission spectra for different SiO₂ substrate thicknesses with tanδ = 0.001. (c) Transmission spectra for different radius r of rounded corners. (d) Transmission spectra for the different silicon square side length a ₁.

To better understand the resonance mechanism, Figure 9(a) shows the distribution of electric and magnetic field amplitude of Mode 1. The two antiphase magnetic dipoles form a head-to-tail arrangement and further produce two MTD resonances oscillating reversely parallel to the surface of the metasurface along the z-direction. The Fano resonances of Mode 2 and Mode 3 have high Q-factors over 10⁴, and their resonance wavelength exhibits a blue shift as asymmetry parameter α increases. As shown in Figure 9(b) and (c), we display the electromagnetic field distributions of these modes. Clearly, Mode 2 is excited by dual inverted MDs diagonally, where two closed loops of the displacement currents appear in two relatively smaller nanodisks of four clusters and produce reversed magnetic field lines. Similarly, Mode 3 is also excited by dual inverted MDs diagonally, where the closed-loop of displacement currents appeared in two relatively larger nanodisks forming two antiphase MDs.

Figure 9:

Electromagnetic field distributions and resonance modes. (a), (b), (c), and (d) are electric field, electric field vector, magnetic field profiles, and 3D schematic diagram of TD of Mode 1. (e), (f), (g), and (h) are electric field, electric field vector, magnetic field profiles, and 3D schematic diagram of TD of Mode 2. (i), (j), (k), and (l) are electric field, electric field vector, magnetic field profiles, and 3D schematic diagram of TD of Mode 3.

Furthermore, to gain insight into the three asymmetrical lineshapes formation of Fano resonances of Modes 1, 2, and 3, we fit transmission spectra with reproduced Fano model by using the classical Fano formula [21] T ( ω ) = T 0 + A 0 [ q + 2 ( ω − ω 0 ) / τ ] 1 + [ 2 ( ω − ω ) / τ ] 2 , where ω ₀ is the resonant frequency, τ is the resonance FWHM, T ₀ is the transmission offset, A ₀ is the continuum-discrete coupling constant, q is the Breit–Wigner–Fano parameter determining asymmetry of the resonance profile. Figure 10 shows that the prediction of three Fano models (red solid curve) under k = 0.9 agrees well with the simulation results (blue dashed curve) around the resonance dips, indicating the Fano resonance essence. With the fitting results, Q-factors of Modes 1, 2, and 3 reach 818.72, 2.23 × 10⁴, and 1.34 × 10⁴, respectively.

Figure 10:

Comparison of the Fano fitting and simulation results. (a), (b), and (c) are Fano fittings of the three modes when k = 0.9. The solid curves are simulation results, and the dashed curves are Fano fitting results.

3.2 Sensing performance on detection of liquid with various refractive index

For the dielectric tetramer metasurface with the asymmetric nanodisks, multi-Fano resonances with high Q-factor are excited, which provide excellent sensing properties to identify liquid with various refractive index n. As an example, here, we simulate the transmission T and evaluate the sensitivity of the asymmetric metasurface (k = 0.9) immersed by 0.6-μm thickness liquid analytes. The T spectra of different refractive indices of analytes such as water with n = 1.333, ethanol (C₂H₅OH) with n = 1.357, pentanol (C₅H₁₁OH) with n = 1.401, carbon tetrachloride (CCl₄) with n = 1.453, and benzene (C₆H₆) with n = 1.485 are depicted as Figure 11(a). It is found that three Fano resonances exhibit a redshift with the increase of the analyte refractive index. Moreover, we use the sensitivity (S = Δλ/Δn), namely spectral shift per refractive index unit, to evaluate the sensing properties of the metasurface. As shown in Figure 11(b), the S of Modes 1, 2, and 3 is 1.28, 1.43, and 1.39 μm/RIU, respectively. In addition, Table 1 compares the performance of our proposed all-dielectric metasurface sensor with the recently reported refractive sensors in the infrared region. It is found that our structure shows obvious superior to previous work in terms of sensitivity, Q-factor, and polarization insensitivity, demonstrating good sensing performance.

Figure 11:

Refractive sensing performance of the asymmetric metasurface. (a) Transmission spectra of the metasurface with different refractive indices of analytes. (b) The resonant frequency shift of three Fano modes with different refractive indices of analytes.

Finally, a possible large-scale metasurface sample fabrication process flow is discussed. The proposed metasurface can be fabricated by using the state-of-the-art nanofabrication techniques like nanoimprint, electron beam lithography (EBL), and deep-ultraviolet (DUV) lithography [35, 36, 41], [42], [43]. For example, a 360-nm-thick SiO₂ layer can be deposited onto a silicon wafer by atomic layer deposition (ALD). Then, a 300 nm-thick Si layer can be deposited on the SiO₂ layer. The patterned photoresist (PR) layer is coasted as etch mask and the unwanted region of the Si layer is removed by dry plasma etching to form the metasurface. Then, a PR coating on both side of the sample is used as a protective layer for the remaining steps. Then, deep reactive ion etching (DRIE) is used to remove the Si wafer until it reached the SiO₂ substrate. Finally, clean the wafer and remove the PR layer with oxygen plasma. It has been demonstrated that the highly efficient and precise lithography can be utilized for the mass production of various dielectric metasurfaces [35].