## 2 Materials and Methods
### Terahertz Spectra Analysis  
The spectra of aqueous solutions in the terahertz frequency domain generally do not contain clearly defined spectral bands; therefore, to obtain interpretable information, the spectra recorded need to undergo mathematical processing. First, on the basis of the transmittance spectra Tr(\(\
u\)) and the refractive index n(\(\
u\)), we calculated the imaginary part of the complex dielectric permittivity function of the substance according to the following equation:  
\[\varepsilon^{\prime\prime}(\
u)=-\frac{\mathrm{n}(\
u)\mathrm{lnTr}(\
u)}{2 \pi\
u\Delta l} \tag{2}\]  
where \(\
u\)--wavenumber in cm\({}^{-1}\), \(\Delta l\)--difference between the interwindow distances of the two cuvettes used (in the present study \(\Delta l=0.0053\) cm). After calculating the function \(\varepsilon^{\prime\prime}\) (\(\
u\)), we implemented its decomposition into band components which are described in the literature and well-interpreted at the molecular level. To date, at least three water absorption bands with known molecular dynamics interpretation have been reliably established in the spectra of aqueous solutions in the terahertz frequency domain: (1) the Debye relaxation band with an absorption maximum of about 0.6 cm\({}^{-1}\)[46]; (2) the intermolecular bending vibrational band with a maximum of absorption in the range 50-100 cm\({}^{-1}\), and (3) the intermolecular stretching vibrational band with an absorption maximum of about 160-210 cm\({}^{-1}\)[47; 48]. In the complex function \(\varepsilon(\
u)\), these three bands are defined as follows:  
\[\varepsilon_{w}^{*}=\frac{\Delta\varepsilon_{1}}{1-i\omega\tau_{1}}+\frac{A_{ 1}}{\omega_{1}^{2}-\omega^{2}-i\omega\gamma_{1}}+\frac{A_{2}}{\omega_{2}^{2}- \omega^{2}-i\omega\gamma_{2}}+\varepsilon_{\infty}+i\frac{\sigma_{0}}{ \varepsilon_{0}\omega} \tag{3}\]  
where \(\omega\)--cyclic frequency associated with wave number \(\
u\) through a relation \(\omega=2\pi\mathrm{cv}\), \(\mathrm{c}\)--the speed of light; \(\Delta\varepsilon\)--contribution of the Debye relaxation of water molecules to the total dielectric response; \(\tau\)--relaxation time; \(\omega_{1}\)--resonant frequency of the intermolecular bending vibration; A\({}_{1}\)--contribution of the intermolecular bending band to the spectrum; \(\gamma_{1}\)--width of this band; \(\omega_{2}\)--resonant frequency of the intermolecular stretching band; A\({}_{2}\)--contribution of the intermolecular stretching band to the spectrum; \(\gamma_{2}\)--width of this band; the last component considers the ionic conductivity of the solutions, where \(\sigma_{0}\) - conductivity at zero frequency, and \(\varepsilon_{0}\)--vacuum permittivity. Selecting the imaginary part of function (3), we obtain \(\varepsilon^{\prime\prime}\) (v) of the following form:  
\[\varepsilon^{\prime\prime}\left(v\right)=\frac{\Delta\varepsilon\omega\tau}{1+ \omega^{2}\tau^{2}}+\frac{\text{A}_{1}\omega\gamma_{1}}{\left(\omega_{1}^{2} \text{--}\omega^{2}\right)^{2}\text{--}\omega^{2}\gamma_{1}^{2}}+\frac{\text{A} _{2}\omega\gamma_{2}}{\left(\omega_{2}^{2}\text{--}\omega^{2}\right)^{2}\text{ --}\omega^{2}\gamma_{2}^{2}}+\frac{\sigma_{0}}{\varepsilon_{0}\omega} \tag{4}\]  
The model dielectric function (3) was used to describe the lactose solution, while we took into account only water bands and completely excluded from the consideration the spectral contribution of lactose itself. This is justified since the coefficient of water absorption in the studied region is 1.5-3 orders of magnitude greater than the absorption of lactose. If we take into account that the lactose content in the solution is 10%, then the contribution of lactose to the absorption does not exceed 0.3%. However, this does not mean that the spectrum of lactose solution is absolutely identical to the spectrum of water, since lactose can affect the characteristics of water itself through its hydration shells [49; 50]. We also note that model (3) is not the only correct one.