  We investigate the resonant optical response of single material-anisotropic
nanoparticles (NPs) of molybdenum disulfide (MoS$_2$) and their two-dimensional
arrays (metasurfaces) irradiated by plane waves of the telecomunication optical
range. Nanoparticles in the form of a disk with centered and shifted hole are
considered. Using the recently experimental measured the MoS$_2$ dielectric
permittivity and numerical calculations with analytical multipole analysis, we
show that the material-anisotropy of NPs can lead to specific nonlocal
contributions in their magnetic and electric dipole response and affect the
effective dipole polarizabilities. Applying a special procedure we determine
the period of the MoS$_2$ metasurfaces supporting the quasi-trapped mode (QTM)
resonance around the tellecom wavelength of 1550 nm. It is shown that
regardless extremely weak absorption of the single nanoparticles, the
excitation of the QTM leads to effective narrowband absorption in the
metasurfaces. Influences of the linear polarization direction of normally
incident waves on the QTM implementation and the reflection and transmission
spectra are studied. It is found and demonstrated, for the first time, that a
metasurface, composed of the MoS$_2$ disks with their anisotropy
perpendicularto the metasurface plane, has the properties of a continuous
birefringent medium. Due to these properties, normally incident and
linear-polarized waves can be transformed in the transmitted and reflected
waves with changed polarizations.
