• To solve the diffraction problem of the periodical sequence of bi-isotropic and material layers and investigate properties of the scattered and transformed fields.
• To apply the antenna theory and the FDTD technique to calculate the frequency selective surfaces that including the chiral elements. To make a prototype and provide experimental measurements.
• To investigate the process of three-dimensional Gaussian beam scattering on a bounded periodical sequence of bi-isotropic and isotropic layers.
• To investigate the periodicity defect influence on electromagnetic properties of bounded periodical structures with chiral layers.
• To investigate the reflection and transmission of light from quasiperiodic substitutional (Fibonacci, Thue-Morse, Rudin-Shapiro, and double-periodic) and model fractal structures (Cantor sets and Koch fractals).
• To apply the Mode Basis Method (Evolutionary Approach to Electromagnetics) to investigate in time domain the electromagnetic properties of a waveguide filled bi-isotropic medium.

       One-dimensional periodic structures have found particularly wide application as frequency selective surfaces and lasers. They are the basis of distributed Bragg reflection lasers. In the last time a lot of investigations are pointed on the periodical structures that include layers which are made from natural (cholesteric liquid crystal) or artificial material with the spatial dispersion (bi-anisotropic, reciprocal (chiral) and nonreciprocal bi-isotropic media). Such structures realize the polarization transforming of the waves in additional to their spatial and frequency selections.

       The problem of reflection and transmission of a wave beam from single isotropic and anisotropic layers, metal-dielectric heterogeneities and their periodical sequences has been the subject of numerous research papers. Several beam-wave phenomena such as lateral shift, focal shift, angular shift, beam splitting that are not found in the reflection of plane wave are the major features for investigation. Some papers are devoted to investigate the wave beam scattering on the structures with the spatial dispersion that include single layers of the natural and artificial reciprocal (chiral) and nonreciprocal bi-isotropic, bi-anisotropic medium, gyrotropic crystals, etc. Most of these studies were based on a two-dimensional beam-wave structure. The reason for this choice was perhaps the confidence that essential insights would not be lost while mathematical complexities could be reduced. However, that this confidence may not be warranted, in particular, the two-dimensional model is not to take into consideration the polarization effects and not able to predict the change in ellipticity of the scattered beam and it is required the three-dimensional beam representation.
       Introducing a quarter-wavelength defect in the middle of a periodic one-dimensional sample produces a photonic mode in the center of the reflection band. Such a defect is used to produce high-Q laser cavities in vertical cavity surface-emitting lasers and may be the basis of large-area coherent laser emission in thin films. For chiral structures a defect can be created by modifying the refractive index, thickness, rotating helical axis of existing layers or inserting additional layer into the sequence. Defect modes in chiral structures have received much attention and may be used for realizing low threshold lasers, narrow bandpass circular-polarization filters. The other aspect is the possibility of the periodicity defect appearing in the structure when it has been made. Therefore investigations of the sequence with defect are important to provide the quality assurance of the bandpass filters manufacturing and allow determining both the disturbance type and the position of defect element in the structure.
       The approach is named as Mode Basis Method (MBM) or Evolutionary Approach to Electromagnetics (EAE) an account of the evolutionary (i.e. with time derivative) differential equations play topping role in studies of electromagnetic phenomena in the time domain. The MBM was effectively applied to analyze the electromagnetic properties of waveguides and resonators. It is useful to extend the MBM on the chirowaveguide theory.

       The circuit theory and the transfer matrix methods are applied to solve the plane wave diffraction problem for the DBR-like bounded periodic sequence of pairs of bi-isotropic and magnetodielectric layers and analyzing its electromagnetic properties. The frequency and angular dependences of the scattering and transformation coefficient magnitudes are obtained. The dynamic of the quasi-stop bands and the quasi-pass bands is determined on the basis of the structure basic element transfer matrix eigenvalues analysis. The revealed effects of the studied structure allows to design of cascaded high-Q and stop-band frequency filters, wave transformers, angular discriminators and absorbers.

The frequency dependences of the reflection coefficient magnitude for the sequence of isotropic and chiral layers	The distribution of the absolute value of the field of the reflected wave beam in the z=0 plane for the sequence of isotropic and bi-isotropic layers
The reflection coefficient magnitude as a function of the layer permittivity for a fractal Cantor structure of metal strips and magnetodielectric layers	The frequency dependences of the reflection coefficient magnitude for a fractal Cantor structure of metal strips and magnetodielectric layers

       The three-dimensional Gaussian beam scattering for the bounded periodic sequence of pairs of bi-isotropic and magnetodielectric layers is investigated. It is found that after reflection from the structure, the circular Gaussian beam becomes, in general, an elliptical Gaussian beam, in addition to a displacement of the beam axis from the position predicted by ray optics. The lateral shift, ellipticity change, beam splitting is studied.

       The circuit theory and the transfer matrix methods were applied to solving the plane wave diffraction problem for bounded bi-isotropic layers sequence with periodicity defects. The analysis of its electromagnetic properties was carried out.