## 2 Results and Discussions  
Fluidic channel devices that incorporate the functionalized metamaterials were fabricated as shown schematically in Figure 1a,b. The key idea is that the gap areas of metamaterials are filled by the target materials while the PS solution is continuously circulated as the gap area are functionalized. We note that plasmonic and metamaterial sensors generally address the density of target material at the sensor surface [16; 23; 37], while it is the volume density that is required for sensing in the aqueous environment. We monitored the change in the resonant frequency of the metamaterials with in situ THz spectroscopy while injecting the PS solution into the fluidic device. The transmission amplitudes of THz metamaterial devices were obtained from a conventional in situ THz time-domain spectroscopy system with an acquisition time of 4 s as described elsewhere [38; 39]. A conventional photolithography method was used to pattern metamaterials on a high-resistivity Si substrate with a thickness of 550 \(\upmu\)m. Cr/Au (2 nm/98 nm) metal layers were deposited to define the arrays of the split-ring resonator (SRR) with a periodicity of 50 \(\upmu\)m. The SRR consists of a rectangle ring with outer dimensions of 36 \(\times\) 36 \(\upmu\)m\({}^{2}\), a gap width of 3 \(\upmu\)m and a gap length of 10 \(\upmu\)m. The linewidth and the thickness of the SRR were chosen to be 4 \(\upmu\)m and 100 nm, respectively. The geometrical parameters of the metamaterial unit cell are shown in Figure 1c. Metamaterials were then functionalized to capture the PS in the water by partially coating an adhesive poly-L-lysine (PLL) layer only in the gap area, while the rest of the area was coated with an anti-adhesive hexamethyldisilazane (HMDS) layer [27]. The full-width at half maximum of the metapattern resonance in water was 130 GHz and we obtained the resonant peak position by using the Gaussian fitting with an uncertainty of around 1 GHz. To circulate the PS solution on the metasurface, we fabricated the polydimethylsiloxane (PDMS) fluidic channel with a height of 20 \(\upmu\)m and a width of 2 mm on the metamaterials. The height of the PDMS channel is determined by the height of the SU-8 mold which was used to fabricate the PDMS channel. The PDMS fluidic channel was bonded to the surrounding substrate area of the metasurface using the plasma surface treatment method [31]. We note that the PS solution was circulated through the fluidic channel using a peristaltic pump with an 80 \(\upmu\)L/min rate. Figure 2a shows the separated THz transmission amplitudes of the surface-functionalized microfluidic metamaterials when the water (black solid line) and PS solution (red solid line) was circulated through the fluidic channel. The inset of Figure 2a shows an optical image of fabricated metamaterials after the circulation of PS solution through the fluidic channel. The polarization direction of the incident THz waves is indicated with a white arrow. It was clearly shown that the PSs were captured only in the functionalized gap areas where the PLL layer was deposited, while HMDS-coated area repelled the PS in the water [27]. We observed a 15.4 GHz blue-shift in the resonant frequency from 717 to 732 GHz with the presence of the PS in the water. We note that the blue-shift occurred as the PS in the water decreased the effective dielectric constant of the target solution due to its low dielectric constant (\(\varepsilon_{PS}=2.56\)) [27] when compared to that of water (\(\varepsilon_{water}=4.8\)) [31]. At the low density regime, the blue-shift induced by the presence of the PS in the water can be quantified by the following relationship: \(\Delta f/f_{0}=-\alpha N_{PS}(\varepsilon_{PS}-\varepsilon_{water})/\varepsilon _{eff}\), where \(\alpha\) is a sensitivity coefficient, \(N_{PS}\) is the average number of PS in the gap areas, and \(\varepsilon_{eff}\) is the effective dielectric constant near the gap area, which is determined by the combined contributions of the dielectric constants of the substrate and the water [23].