## 2 Materials and Methods  
### Features of the Polarizability of a Single MoS\({}_{2}\) Disk with a Defect  
We chose a building block of a metasurface in the form of a disk fabricated from anisotropic MoS\({}_{2}\) material [10] with layers arranged parallel to the disk's base. The radius and height of the disk are \(R_{2}=H=418\) nm, and the disk has a round penetrating hole with radius \(R_{1}\) shifted from the disk's center along the x axis on the distance \(\Delta_{x}=159\) nm. Here and below, we consider that single building blocks, as well as the entire metasurface composed of them, are placed in air. Numerical calculation of the scattering spectra of NPs was carried out using COMSOL Multiphysics 5.4. Multipole decomposition was calculated on the basis of our own algorithms realized in the same software. As a result, under normal irradiation of such a disk by waves \(E_{x}(k_{z})\) in Figure 1a and \(E_{y}(k_{z})\) in Figure 1b, the scattering cross section has a smooth dependence without any features in the wavelength range 1480-1700 nm. However, there is an excitation of minor components of the electric dipole ED\({}_{z}\) in Figure 1a and magnetic dipole MD\({}_{z}\) in Figure 1b oriented perpendicular to the disk's base. In addition, under lateral irradiation of the same disk by waves \(E_{z}(k_{x})\) in Figure 1c and \(E_{y}(k_{x})\) in Figure 1d, we find several features at once in its scattering spectrum. To analyze the spectra of the scattering cross section, we use the multipole decomposition in the form:  
Figure 1: Spectra of the scattering cross sections, normalized to the area of disk’s base \(S=\pi R_{2}^{2}\), with corresponding multipole decomposition calculated for the MoS\({}_{2}\) disk (the radius and height \(R_{2}=H=418\) nm) with the through hole shifted from the disk’s center on the distance \(\Delta_{x}=159\) nm with radius \(R_{1}=133\) nm (**a**,**b**) normally and (**c**,**d**) laterally irradiated by linearly polarized plane wave with polarization along (**a**) \(x\), (**b**,**d**) \(y\), and (**c**) \(z\) axis. (Scat) and (Sum) correspond to the scattering cross section of MoS\({}_{2}\) disk calculated numerically and according to Equation (1), respectively. Orientation of the MoS\({}_{2}\) layers is parallel to the \(xy\) plane. \[\sigma_{\text{scat}} \cong \frac{k^{4}}{6\pi\epsilon_{0}^{2}|\textbf{E}|^{2}}|\textbf{p}|^{2}+ \frac{k^{4}\epsilon_{d}\mu_{0}}{6\pi\epsilon_{0}|\textbf{E}|^{2}}|\textbf{m}|^{2} \tag{1}\] \[+ \frac{k^{6}\epsilon_{d}}{720\pi\epsilon_{0}^{2}|\textbf{E}|^{2}} \sum_{\alpha\beta}\lvert Q_{\alpha\beta}\rvert^{2}+\frac{k^{6}\epsilon_{d}^{2 }\mu_{0}}{80\pi\epsilon_{0}|\textbf{E}|^{2}}\sum_{\alpha\beta}\lvert M_{\alpha \beta}\rvert^{2}\] \[+ \frac{k^{8}\epsilon_{d}^{2}}{1890\pi\epsilon_{0}^{2}|\textbf{E}|^ {2}}\sum_{\alpha\beta\gamma}\lvert Q_{\alpha\beta\gamma}\rvert^{2}+\frac{k^{8 }\epsilon_{d}^{2}\mu_{0}}{1890\pi\epsilon_{0}|\textbf{E}|^{2}}\sum_{\alpha \beta\gamma}\lvert MO_{\alpha\beta\gamma}\rvert^{2},\]  
where \(k\) is the vacuum wave number; \(\epsilon_{0}\) and \(\epsilon_{d}\) are the vacuum dielectric and relative dielectric constants of surrounding medium, respectively; \(\mu_{0}\) is the vacuum permeability; **E** is the vector of electric amplitude of the incident plane waves; **p** and **m** are the vectors of electric and magnetic dipole moments of the scatterer, respectively; and \(\hat{Q}\), \(\hat{M}\), and \(\hat{O}\) are the tensors of electric and magnetic quadrupole moments, and electric octupole moment, respectively; \(\alpha,\beta,\gamma=x,y,z\). Corresponding expressions for the multipole moments defined by the density of the displacement current can be found elsewhere [25]. In this article we consider that all multipole moments of individual nanoparticles are located at their center of mass. This also concerns the calculation of the dipole polarizabilities presented further.