In order to get more insight into detection mechanism using THz sensing chip, concentration dependence was examined for one subtype of the viruses. We measured transmission spectra for H9N2 virus in various concentrations via nano-antenna sensing chip (f res = 1.4 THz) as shown in Fig. 3a–d. The various concentrations of virus samples were prepared by diluting virus samples (total protein concentration: 0.28 mg/dl) with buffer liquid (total protein concentration: 0 mg/dl) by 1:1 and 2:1 volume ratio, producing four samples: 0, 1, 0.14, 0.28 mg/ml, respectively. The buffer is prepared without inoculation of any virus, as same as the control sample used in pellet experiment. As the concentration of virus increases, the maximum transmittance value decreases, due to its absorption change as shown in Fig. 3e (magenta). It is noted that the clear linearity can be extracted from the data, allowing a promising quantification tool of such protein samples which is one of the critical issues in protein studies. On the one hand, the resonance frequency is maintained, whereas the maximum value of the transmittance was obviously changed in terms of the concentration. The virus-concentration-dependent refractive index was assumed with an effective medium approximation that treats heterogeneous media as homogeneous. The film-likely coated sample on the metamaterial is assumed as 5 μm thick cladding, same as previous FDTD simulations in Fig. 2b, and the densest concentration of protein among three virus samples is 0.54 mg/ml. According to ref. 22, the density of the influenza virus is calculated as 1.104 g/ml24, the volume fraction in the coated virus sample on the sensing chip can be estimated as about 0.05%. The used volume fraction is too small to evidently affect the whole refractive index of the sample. Therefore, the resonance frequency is not significantly changed in terms of the concentration increase, besides initial change Δf = 0.18 THz was observed from bare antenna to first dropping. The FDTD simulation results (Fig. 3e) also confirm that the transmittance value is mainly changed, whereas the resonance shift is negligible with increasing of κ. To exclude the concentration dependency in classifying and subtyping various viruses, considering the normalization per unit mass of virus is essential.Figure 3Virus quantification by nano-metamaterial based THz detection. (a–d) Normalized THz spectra for various concentrations (0, 1, 0.14, 0.28 mg/ml) of H9N2 virus in the buffer solution. (e) The changes in the maximum values of the normalized transmittances (ΔT, magenta closed circle) and shifted resonance frequency (Δf, green closed triangle) are plotted for H9N2 virus in different concentrations as a function of concentration level. The red bar is error bar of buffer solution measurement. Black line and gray dashed line are linear fitting of the transmittance change and frequency shift data, respectively. (f) FDTD simulation results of transmittances for three different model samples with various composition of dielectric constants (n and κ) are shown.