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 modes. In order to access a trapped mode (which is the TE${}_{01\delta }$ mode of the resonator), a round eccentric penetrating hole is made in the disk. In the lattice, the disks are arranged into clusters (unit supercells) consisting of four particles. Different orientations of holes in the supercell correspond to different symmetry groups producing different electromagnetic responses 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, the representation theory, and the microwave circuit theory. Both polarization-sensitive and polarization-insensitive arrangements of particles and conditions for dynamic ferromagnetic and antiferromagnetic orders are derived. Finally, we observe the trapped mode manifestation in the microwave experiment.

A silicon metasurface with a symmetry-protected quasi-dark resonant mode is designed and demonstrated as a refractometric sensor and tunable notch filter in the near-infrared spectrum. The resonant mode is excited by perturbing a periodic array of Si cuboids patterned on a glass substrate. Thanks to the delocalized nature of the resonant mode, intense light-matter interaction with the overlayer material is manifested. Such interaction leads to strong dependence of the resonant wavelength on the overlayer refractive index and high achievable quality factors, including the case of lossy materials. High sensitivity and figure of merit is calculated for operation of the metasurface as a refractometric sensor. In a complementary approach, three types of tunable notch filters are demonstrated, based on the use of thermo-optic, electro-optic polymers, and nematic liquid crystals.

We theoretically investigate and optimize a multilayer planar structure with enhanced magneto-optical (MO) activity. The extraordinary optical transmission observed in a periodically perforated metal plate with subwavelength holes is used to produce a higher MO activity. We consider a three-layer structure that consists of a dielectric layer placed between the perforated metal and the MO layers. In this structure, we obtained the enhancement of Faraday rotation by three times and the Kerr effect by an order as compared to the published results.

A compact optical switch based on a 2D photonic crystal (PhC) and a magneto-optical cavity is suggested and analyzed. The cavity is coupled to two parallel and misaligned PC waveguides and operates with dipole mode. When the cavity is nonmagnetized, the dipole mode excited by a signal in the input waveguide has a node in the output waveguide. Therefore, the input signal is reflected from the cavity. This corresponds to the state off of the switch. Normal to the plane of the PhC magnetization by a dc magnetic field produces a rotation of the dipole pattern in the cavity providing equal amplitudes of the electromagnetic fields in the input and the output waveguides. This corresponds to the state on with high transmission of the input signal. Numerical calculations show that at the 1.55 μm wavelength the device has the insertion loss $-0.42\mathrm{dB}$ in the on state, the isolation $-19\mathrm{dB}$ in the off state and the switch off and on ratio $P_{\text{on}}/P_{\text{off}}$ about 72. The frequency band at the level of $-15\mathrm{dB}$ of the resonance curve in off state is about 160 GHz.