## 2 Results and Discussions
\(\varepsilon_{eff}\) can be obtained from the relation of \(f_{water}=f_{air}/\left(\varepsilon_{eff}\right)^{1/2}\), where \(f_{water}\) is the resonant frequency of the metamaterials with an overlaid water layer on the substrate and \(f_{air}\) is the resonant frequency of the metamaterials without the substrate (air embedded). We also note that the fluidic channel device without metamaterials pattern was used as a reference to mitigate the transmission loss from the water layer. Figure 1: (a) Schematic of surface-functionalized fluidic THz metamaterials for microplastic detection in the aqueous environment. The gap area is coated by adhesive polymer (pink area), whereas it is coated by HMDS (blue area), which repels the microplastics. (b) Schematic for the experiments in which the fluidic metamaterials device is connected to a peristaltic pump for the fast circulation of the analyte solution. (c) SRR pattern design used in this work. To verify and understand our experimental findings, we performed FDTD simulations using commercial software (CST Studio Suite 2022). The time-domain solver was used to minimize the effect of the internal reflection from the substrate. The geometric parameters and periodic boundary conditions were adopted from the metamaterials used in the experiments. Dielectric constants of 11.8, 4.8, and 2.56, were used for silicon, water, and PS structures, respectively. Two-ports were assigned to the simulation model to generate and receive a linearly polarized incident THz plane wave in the time-domain. We then performed a fast-Fourier transform to obtain the frequency-domain transmission amplitude of the metamaterials. Figure 2b shows the simulated transmission amplitudes of the metamaterials with a 20 \(\upmu\)m thick water layer for \(N_{PS}\) = 0, 30, 90. The resonant frequency of 667 GHz was observed for \(N_{PS}\) = 0 and the blue-shift of the resonant frequency occurred as \(N_{PS}\) increased. A discrepancy between the experimental results and simulations in the resonant frequency of the metamaterials was observed, which can be attributed to the fabrication tolerance in the experiments. We note that \(N_{PS}\) was first gradually increased to \(N_{PS}\) = 30 with a step of three until there was no space to locate additional PS in the gap area, then we increased \(N_{PS}\) with a step of 30 up to \(N_{PS}\) = 120 by adding the additional PS layer that consists of 30 PS right above the existing PS layer. The resonant frequency of the metamaterials as a function of \(N_{PS}\) was investigated in Figure 2c to see how the presence of the PS in the water layer affects the resonant frequency shift behavior. The amount of blue-shift increased as the number of PS layers increased, but was saturated at a specific frequency owing to the confined effective sensing volume of the metamaterials near the gap area; this is consistent with the saturation thickness of 1.5 \(\upmu\)m estimated for the gap-width of 3 \(\upmu\)m [28]. Conversely, in the monolayer case (for \(N_{PS}\) < 30), the sensitivity coefficient \(\alpha\) of 7.1 \(\times\) 10\({}^{-4}\) was obtained, when \(f_{air}\) = 1963 GHz and \(\varepsilon_{eff}\) = 8.66. In order to study the resonant frequency shift behavior of the surface functionalized fluidic metamaterials, we performed in situ THz spectroscopy while we were circulating the PS solution with a density of 2 \(\times\) 10\({}^{8}\) mL\({}^{-1}\) through the fluidic channel. Figure 3a shows THz transmission amplitude as a function of the circulation time of the PS solution. The blue-shift behavior was observed as the PLL layer in the gap area attracted the PS in the solution. In Figure 3b, we extracted the resonant frequency from Figure 3a as a function of circulation time. We note that a fluctuation was observed in the extracted resonant frequency over circulation time that could be attributed to the mechanical motion of the peristaltic pump [40,41].