## 2 Results and Discussions
Therefore, the fitted curve of the resonant frequency (red line) was plotted along with the extracted resonant frequency (black square dots). The resonant frequency of the metamaterials increased while the PSs in the solution were being attached to the gap area but was saturated at a specific frequency as there is no change in the effective dielectric constant of the gap area after a certain level of accumulation of the PS in the gap area over time, as indicated from our simulatio  
Figure 2: (**a**) Experimentally obtained THz transmission amplitude (normalized) of the surface-functionalized fluidic metamaterials after circulation of the specimen with (red solid line) and without (black solid line) the PS in the water. (inset) Dark-field microscope image of metamaterials with PS captured in the gap area. (**b**) Simulated THz transmission amplitude of the metamaterials with a 20 \(\upmu\)m thick water layer for \(N_{PS}\) = 0, 30, 90. (**c**) The resonant frequency of the metamaterials as a function of \(N_{PS}\). To investigate the effect of the PS solution density on the saturation behavior of the resonance, we performed the same in situ THz spectroscopy again but for various PS solution densities (2 \(\times\) 10\({}^{8}\), 1 \(\times\) 10\({}^{9}\), 3 \(\times\) 10\({}^{9}\), 6 \(\times\) 10\({}^{9}\) mL\({}^{-1}\)). In Figure 4, the saturation time (\(T_{sat}\)) of the resonant frequency shift and the saturated resonant frequency (\(\Delta f_{max}\)) were plotted as a function of the PS solution density. Here, \(T_{sat}\) corresponds to the time when the resonant frequency shift reaches the half of the maximum frequency shift. \(\Delta f\)-time curves for different solution densities were best fitted with the sigmodal function of \(\Delta f=\Delta f_{max}(1-1/\left(1+(t/T_{sat})^{p}\right))\), where \(p\) is the exponent. The saturation time of 16.6 min was obtained with the PS solution density of 2 \(\times\) 10\({}^{8}\) mL\({}^{-1}\), which decreased to 18.5 s with the PS solution density of 6 \(\times\) 10\({}^{9}\) mL\({}^{-1}\). We note that FTIR and Raman spectroscopy have been often employed to detect microplastics in water [8, 9, 10]. However, a liquid sample containing microplastics must go through a pre-treatment step called density separation. The density separation extracts microplastics from the sample liquid by either letting microplastics float or sink in solutions with higher or lower densities than the microplastics [8, 9, 10]. This process makes the detection techniques employing FTIR and Raman spectroscopy a time-consuming job, which often takes 5 h to up to 1 day [8]. On the other hand, we could detect microplastics in water with in situ THz spectroscopy by using surface-functionalized fluidic metamaterials. The saturated resonant frequency shift increased further from 15 to 24 GHz as we increased the PS solution density from 2 \(\times\) 10\({}^{8}\) to 6 \(\times\) 10\({}^{9}\) mL\({}^{-1}\) even though it was expected that the number of the accumulated PS in the gap area would be similar for different PS solution densities. This could be explained by the fact that the effective dielectric constant of the surrounding PS solution also decreases as the PS solution density increases, owing to the low dielectric constant of the PS compared to the water, leading to a further increase in the saturated resonant frequency shift. It is noteworthy that we reported the relationship between the dielectric constant of overlaid liquid and the resonant frequency shift in our previous study [31]. For instance, we estimated the effective dielectric constant for the 6 \(\times\) 10\({}^{9}\) mL\({}^{-1}\) case from the saturated frequency shift and found that the dielectric constant decreased by \(-\)1.0 when compared to the water case. Figure 3: (a) A color-scale plot of the normalized transmission amplitude as a function of circulation time of the PS solution. (b) The extracted (black dots) resonant frequency as a function of the circulation time. Red line indicates the fitted curve to the experimental data.