## 2 Materials and Methods
### Spectral Acquisition  
A THz time-domain spectrometer (Teraview, UK) was applied for spectral acquisition. The central wavelength of the femtosecond laser pulse was 1030 nm, the pulse width was 90 fs, the spectral range was 0.06-4 THz, the spectral resolution was 1.7 GHz, and the scanning precision was 50-150 um. In order to avoid the effect of moisture in air on the test results, the sample bin was filled with nitrogen and the humidity inside the system was less than 2.5%. Additionally, the laboratory temperature was 294 K, and the humidity was below 20%. Meanwhile, the THz time-domain spectra of polyethylene were taken as references. The spectra of references and PGR samples were scanned repeatedly 900 times, and the mean spectra were taken as the acquired data to reduce the effects of random noise. The mean time-domain spectra were transformed into the frequency-domain spectra by Fast Fourier Transform (FFT). On the basis of the Fresnel formula, the absorption coefficient \(\alpha(\omega)\) and refractive index \(n(\omega)\) of the measured sample could be extracted. First, the transmittance \(T(\omega)\) of the sample was expressed as:  
\[T(\omega)=\frac{E_{sample}(\omega)}{E_{ref}(\omega)}=\frac{4n(\omega)}{\left[n (\omega)+1\right]^{2}}\cdot E_{0}(\omega)\cdot\exp[j(\frac{\omega n(\omega)- \omega}{c}-\frac{k(\omega)\omega}{c})d] \tag{1}\]  
\[E_{ref}(\omega)=E_{0}(\omega)\exp(-j\omega t+j\frac{\omega}{c}g) \tag{2}\]  
\[E_{sample}(\omega)= \frac{1}{n(\omega)+1}\cdot\frac{2n(\omega)}{n(\omega)+1}\cdot E_ {0}(\omega)\cdot\exp(-\frac{k(\omega)\omega}{c}d)\cdot \tag{3}\] \[\exp[-j\omega t+i\frac{\omega}{c}(g-d)+j\frac{n(\omega)\omega}{c }d]\]  
where \(\omega=2\pi f\) and \(f\) was the frequency. \(d\) was the thickness of the sample. \(g\) was the distance that THz pulse traveled in free space. \(c\) was the speed of light. \(j\) was the imaginary part. \(E_{0}(\omega)\) was the emitted frequency-domain spectrum. The reference spectrum \(E_{ref}(\omega)\) was the transmitted frequency-domain waveform received by the detector after passing through the polyethylene. The sample spectrum \(E_{sample}(\omega)\) was the frequency-domain waveform received by the detector after passing through the sample. \(1/(n(\omega)+1)\) was the transmission coefficient of the THz pulse that entered the sample. \(2n(\omega)/(n(\omega)+1)\) was the transmission coefficient of the terahertz pulse that exited from the sample.  
The absorption coefficient \(\alpha(\omega)\) and refractive index \(n(\omega)\) of the sample were calculated as:  
\[\alpha(\omega)=\frac{2k(\omega)\omega}{c} \tag{4}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**NO.** & **Plant Growth Regulators** & **Molecular Formula** & **Molecular Mass** & **Melting Point** & **Water Solubility** \\ \hline
1 & 2,4-Dichlorophenoxyoxyacetic acid & C\({}_{8}\)H\({}_{4}\)C\({}_{12}\)O\({}_{3}\) & 221.04 & 137–141 \({}^{\circ}\)C & 0.890 g/L \\
2 & Forchlorfneuron & C\({}_{12}\)H\({}_{0}\)C\({}_{13}\)O & 247.68 & 170–172 \({}^{\circ}\)C & 0.039 g/L \\
5 & Indole-3-acetic acid & C\({}_{10}\)H\({}_{9}\)NO\({}_{2}\) & 175.18 & 165–169 \({}^{\circ}\)C & 1.500 g/L \\ \hline \end{tabular}
\end{table}
Table 1: Chemical and physicochemical properties of the PGRs.  
\[n(\omega)=\frac{\varphi(\omega)c}{\omega d}+1 \tag{5}\]  
The macroscopic optical properties of the measured sample could be expressed by the complex refractive index \(\widetilde{n}(\omega)=n(\omega)-jk(\omega)\). \(n(\omega)\) was the actual refractive index of the sample, which described the dispersion of the sample. \(k(\omega)\) was the extinction coefficient, which described the absorption characteristics of the sample. \(\varphi(\omega)\) was the phase difference between the spectrum of the sample and the reference.