  An all-dielectric metasurface featuring resonant conditions of the trapped
mode excitation is considered. It is composed of a lattice of subwavelength
particles which are made of a high-refractive-index dielectric material
structured in the form of disks. Each particle within the lattice behaves as an
individual dielectric resonator supporting a set of electric and magnetic
(Mie-type) modes. In order to access a trapped mode (which is the TE01 mode of
the resonator), a round eccentric penetrating hole is made in the disk. In the
lattice, the disks are arranged into clusters (unit super-cells) consisting of
four particles. Different orientations of holes in the super-cell correspond to
different symmetry groups producing different electromagnetic response of the
overall metasurface when it is irradiated by the linearly polarized waves with
normal incidence. We perform a systematic analysis of the electromagnetic
response of the metasurface as well as conditions of the trapped mode
excitation involving the group-theoretical description, representation theory
and microwave circuit theory. Both polarization-sensitive and
polarization-insensitive arrangements of particles and conditions for dynamic
ferromagnetic and antiferromagnetic order are derived. Finally, we observe the
trapped mode manifestation in the microwave experiment.
