Figure 1D shows the simulation absorption spectra of the designed CMMC and other two structures only with CM or MC. As shown in Figure 1D, the CMMC exhibits two obvious resonant absorption peaks, f ₁ is located at 0.96 THz with absorption of 71.8%, and the resonant peak appears at 1.65 THz f ₂ with absorption of 92.4%.

In order to reveal the physical mechanism of the resonance, the electric field distribution of the proposed CMMC, and other two structures only with CM or MC are investigated. Figures 2A,B show the electric field distribution of CMMC at the resonant frequency of 0.96 and 1.65 THz. As shown in Figure 2A, most of the field intensity is concentrated in the microfluidic channel formed by the integration of CM on the top and MC at the bottom, which will be filled with analytes during sensing detection. It is obvious that the microfluidic channel increases the overlap of space and improves the light-matter interaction between the analytes and the incident THz wave.

From Figure 2B , the intensity of the electric field at 1.65 THz is focused on the surface of the CMMC and the resonance is a surface mode. The electric field intensity distribution of the CM at 1.64 THz is shown in Figure 2C, the field intensity is mostly located on the surface, which is also surface mode. According to Figure 2D,E , the electric field intensity distributions of MC at 0.99 and 1.83 THz are confined on the surface and the gap between adjacent elliptic cylinders along x direction. Although the electric field at 1.83 THz is also concentrated on the surface and the gap between adjacent elliptical cylinders, which is similar to that of 0.99 THz, but the electric field on the surface is not uniformly distributed, which is a surface mode. By comparing the electric field distribution of the three different structures, it is found that the resonant absorption peak at 0.96 THz is related to the coupling of the modes, which increases the interaction between the incident THz wave and the analytes in the microfluidic channel.

To study the sensing characteristics of the CMMC, we investigate the absorption spectra of CMMC with different refractive index of analytes n. The height of the microfluidic channel is fixed as 15 µm and the filling thickness of the analytes is t = 45 µm. The range of refractive index from 1.0 to 2.0 covers most bio and chemo specimens, such as DNA, RNA, and amino acids proteins [33, 34].

As shown in Figure 3A, it is obvious that the resonant absorption peak at 0.96 THz (f ₁) is more sensitive to the change of refractive index than that at 1.64 THz (f ₂). In order to gain a further understanding of the different sensitivity of the two peaks to the change of refractive index, we investigate the resonance mechanism in-depth. As shown in Figure 2A,B , most of the field intensity is concentrated in the microfluidic channel which will be filled with analytes with different refractive index during sensing detection and the concentrated electric field resulting from the mode coupling of the CM and MC will improve the light-matter interaction between the analytes and the THz wave. In contrast, the electric field at 1.65 THz is concentrated on the surface, the resonance is an obvious surface mode. Therefore, the resonance peak is not sensitive to changes of the refractive index of the analyte which is located in the microfluidic channel. As shown in Figure 3A, the resonant absorption frequency decreases when the refractive index of the analytes in the microfluidic channel increase. Obvious red shift of f ₁ is observed, and the total shift is 254 GHz, which indicates that any change in the liquid permittivity will cause the parallel shift of resonance frequency.

In our case, considering the height of the microfluidic channel (t = 15 µm) is far less than the repeat period (p _x = 180 μm, p _y = 110 µm), the gap plasmon model can be used for explaining the physical mechanism [35–37]. In such a model, the resonance at 0.96 THz is caused by the Fabry-Perot resonances in the CNTs/analytes/Si cavity [36]. 2 π ω n λ + φ = k π (1) where w is the coverage width of the CM (w = p _x —2R _x1), n is the effective index of the gap plasmon, λ is the resonance wavelength, φ is reflection phase, and k is the order of resonance. In addition, according to the distribution of electric field in Figures 2A,D, the resonance at 0.96 THz is caused not only by the Fabry-Perot resonances in the CNTs/analytes/Si cavity, but also by the Si elliptic cylinder.

It is observed clearly that the resonant frequency decreases as the refractive index of the analytes in the microfluidic channel increases, and f ₁ is more sensitive to the change of the refractive index. As shown in Figure 3B, the frequency decreases linearly with refractive index increasing, there is a good linear relationships between the position of f ₁ and the refractive indices of analytes with the regression coefficients of 0.99 (the blue fitting line). The frequency sensitivity S ₁ of the proposed CMMC integrated CNTs film metasurface and the microfluidic channel is defined by frequency shift per refractive index unit, which can be calculated as: S 1 = Δ f Δ n (2) where, S ₁ is frequency sensitivity, whose unit is GHz/RIU (RIU = Refractive Index Unit), ∆n is the change of the refractive index; ∆f is the change of resonant frequency with different n. According to Eq. 2 and Figure 3B, the frequency sensitivity S ₁ of the CMMC which equaled to the slope of the blue line in Figure 3B, reached 254 GHz/RIU.

In addition, as the refractive index of the analytes increase, the amplitude of f ₁ also decreases. The intensity of the resonance decreases linearly with refractive index increasing, a good linear relationship between the intensity of resonant peak and the refractive indiex of analytes with the regression coefficients of 0.99 is observed from orange fitting line of Figure 3B. Therefore, apart from the sensitivity defined by the frequency shift, the variation of intensity ∆I can also be used for refractive index sensing. The intensity sensitivity S ₂ of the proposed CMMC is defined dip the variation of intensity ∆I per refractive index unit, which could be characterized as: S 2 = Δ I Δ n (3) where, the unit of S ₂ is/RIU, ∆I is the variation of the intensity of resonance absorption peak with different n. The intensity sensitivity S ₂ of CMMC, (i.e. the slope of the orange fitting lines in Figure 3B), reached 314/RIU. That means that both the variation of frequency shift ∆f and intensity ∆I can be used for refractive index sensing. Figure 3C shows the influence of thickness of the analytes on the absorption spectrum, assuming the RI of the analytes is 1.5. As the thickness of the analytes t increases from 5 to 65 μm, both the frequency and intensity of f ₁ decrease, which indicates that the CMMC is also sensitive to the thickness of the analytes. Due to the increase of the filling thickness, the analytes is gradually closer to the region with the largest field intensity, and the interaction between the THz wave and analytes is further enhanced, leading to a more obvious frequency shift, which indicates that the filling thickness of the analytes has an effect on the sensing performance of the CMMC.

In order to guide the structural design of the CMMC, the absorption characteristics with different structural parameters are investigated. Figure 4A shows the influence of the period in the x-direction p _x on the absorption. As p _x increases, f ₂ shows an obvious red shift, while f ₁ has a relatively weak red shift. On the contrary, as shown in Figure 4B, with the period in the y-direction p _y increasing, the resonance frequency of f ₁ blue shifts while the amplitude gradually decreases. However, the resonance frequency of f ₂ is almost unchanged, but the amplitude is significantly reduced. It is obvious that the variations of the period in x-direction or the y-direction have different effects on the two resonance peaks, implying that the resonance mechanisms of the two peaks are different, which is consistent with the analysis of the electric field distribution in Figures 2A,B.

Due to the importance of CM in the proposed CMMC, we studied the effect of the structural parameters of CM on the absorption characteristics. As shown in Figure 5A, as the major axis radius of the elliptical pore on the CNTs film R _x1 increases from 10 to 80 μm, the amplitude of f ₁ gradually increases, which is resulted from the enlarged aperture and enhanced resonance. With R _x1 increasing from 10 to 40 μm, the resonance frequency of f ₁ decreases. However, the resonance frequency of f ₁ increases when R _x1 increases from 50 to 80 µm. The difference of the shift law might be contribute to the fact that the minor axis radius of the elliptical pore R _y1 is fixed as 50 µm in this case, when R _x1 is less than 50 µm (i.e. R _x1 < R _y1), it means that the major axis of the elliptical pore is along the y direction; when R _x1 is greater than 50 µm (i.e. R _x1 > R _y1), the major axis is along the x direction. Therefore, the asymmetry of the elliptical structure in the x and y directions results in the difference of shift law of the resonance frequency. Figure 5B shows the effect of the change of R _y1 on the absorption when R _x1 is fixed at 70 µm (R _x1 > R _y1). With the increase of R _y1, f ₁ has a slight red shift and the absorption intensity increases significantly. Owing to R _x1 > R _y1, the major axis of the ellipse is in the x direction, and there is no critical point in the variation law of frequency. In this case, the increase of R _y1 has a significant effect on the absorption intensity, indicating that the absorption intensity strongly depends on R _y1.

The absorption spectra with different thickness of the CNTs film is shown in Figure 5C. As z ₁ increases, the intensity of f ₁ decreases linearly, but the position of the resonance peak is almost unchanged, which means that the shape and size of the periodic elliptical pore of the CNTs film metasurface affect the position of the peak, and the thickness of the CNTs film only affects the absorption intensity.

The height of the microfluidic channel of the CMMC t ₀ is an important parameter for sensing application, the influence of the height of the microfluidic channel on the absorption spectrum is investigated. As shown in Figure 5D, as t ₀ increasing from 10 to 20 μm, f ₁ has a slight blue shift, but the amplitude is almost unchanged. Therefore, the integrated CMMC with different height of microfluidic channel can be designed for refractive index sensing according to practical application.

We also investigate the influence of the structural parameters of the microfluidic channel on the absorption. As shown in Figure 6A, with the major axis radius of the Si elliptic cylinder R _x increasing from 60 to 70 μm, both the amplitude and the resonance frequency of f ₁ decrease. However, according to Figure 6B, compared with R _x , as the minor axis radius of the Si elliptic cylinder R _y increases from 45 to 55 μm, the changes of the amplitude and the frequency of f ₁ are not obvious, which results from the electric field distribution of f ₁. As shown in Figure 2A, most of the electric field of f ₁ is along x direction and the intensity is concentrated in the microfluidic channel formed by CM on the top and MC at the bottom. As a result, the amplitude and the frequency of f ₁ are not strongly dependent on R _y . Figure 6C shows the absorption spectra with different height of the elliptic cylinder z ₂. In particular, as z ₂ increases from 10 to 70 μm, the resonance frequency of f ₁ decreases significantly, the resonant peak has a significant red shift, which imply that the position of f ₁ can be controlled by the height of the elliptic cylinder, which provides an idea for sensing and detection in a wider range. Doping concentration is an important parameter affecting the dielectric properties of silicon. Therefore, we investigated the influence of doping concentration on the absorption properties of the proposed CMMC. In Figure 6D, as the doping concentration increases, the resonance absorption is significantly enhanced. As discussed above, it is worth noting that the change of structural parameters of silicon microfluidic channel has little effect on f ₂, which further indicates that f ₂ is a surface mode mainly determined by CM. The results is agree with the electric field distribution in Figures 2B,C.