We formulate a scattering-matrix-based numerical method to calculate the optical transmission properties and quasiguided eigenmodes in a two-dimensionally periodic photonic crystal slab (PCS) of finite thickness. The square symmetry (point group $C_{4v})$ is taken for the illustration of the method, but it is quite general and works for any point group symmetry for one-dimensional (1D) and 2D PCS’s. We show that the appearance of well-pronounced dips in the transmission spectra of a PCS is due to the interaction with resonant waveguide eigenmodes in the slab. The energy position and width of the dips in transmission provide information on the frequency and inverse radiative lifetime of the quasiguided eigenmodes. We calculate the energies, linewidths, and electromagnetic fields of such quasiguided eigenmodes, and analyze their symmetry and optical activity. The electromagnetic field in such modes is resonantly enhanced, which opens possibilities for use in creating resonant enhancement of different nonlinear effects.

Strong coupling between localized particle plasmons and optical waveguide modes leads to drastic modifications of the transmission of metallic nanowire arrays on dielectric waveguide substrates. The coupling results in the formation of a new quasiparticle, a waveguide-plasmon polariton, with a surprisingly large Rabi splitting of 250 meV. Our experimental results agree well with scattering-matrix calculations and a polariton-type model. The effect provides an efficient tool for photonic band gap engineering in metallodielectric photonic crystal slabs. We show evidence of a full one-dimensional photonic band gap in resonant plasmon-waveguide structures.

We calculate the binding energies, wave functions, and diamagnetic coefficients of excitons in perovskite lead iodine based compounds in the form of self-organized semiconductor/insulator superlattices with allowance for the image potential and the superlattice structure of these materials. We demonstrate a good agreement between our theory and the experiment; the fitting of our theory to the experiments makes it possible to evaluate the reduced mass of excitons in these compounds of the order of 0.2${\mathit{m}}_0$.

New effects of polarization multistability and polarization hysteresis in a coherently driven polariton system in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.

We report on results of transmission measurements of metallic nanowire arrays deposited on top of different dielectric substrates. The appearance of grating anomalies, which critically depend on the substrate thickness, provides evidence that the optical response of these planar metallic photonic crystal structures can be strongly modified. While only Rayleigh-type anomalies are observed for thin dielectric substrates, thicker waveguiding substrates can induce strong coupling phenomena. This strong coupling results in the formation of waveguide-plasmon polaritons with a large Rabi splitting up to $250\mathrm{meV}$. We show that the coupling phenomena vary with the nanowire grating period, the angle of incidence, and also the waveguide layer thickness. A scattering-matrix-based numerical method is used to calculate the transmission properties and the near-field spatial distributions of such metallic photonic crystal structures. All experimental results are well confirmed by our theoretical calculations.