- Computational Electromagnetics: Various techniques in line with the Method of Analytical Regularization (MAR) and Nystrom method for singular integral equations, to build numerically exact solutions of the Maxwell equations in open domains with finite and infinite boundaries,
- Lasers: MAR-based investigation of the lasing eigenvalue problems (LEP) for the “warm” models of semiconductor lasers with active regions, such as VCSELs equipped with quantum wells and DBRs, ultra-low-threshold microdisks, ABR microcavities, and photonic molecules,
- Lenses: MAR analysis of quasioptic size rod-type antennas and elliptic and truncated-elliptic lenses; beamforming by discrete Luneburg lenses fed by the Complex-Source-Point feeds and printed elements,
- Plasmonics: MAR analysis of optical near and far field enhancement due to the localized surface-plasmon-polariton resonances in stand-alone and coupled noble-metal wires, strips, disks and arrays,
- Open Waveguides: Mathematical foundations of excitation theory; solution existence in the space and Fourier-transform domains; modified radiation condition; complex modes on dielectric fibers and circular cylindrical microstrip and slot lines,
- Optoelectronic Components: MAR-based modeling of dielectric-slab mode scattering from resonance inhomogeneities; whispering-gallery-mode effect in dielectric resonators and narrow-band filters,
- Reflector Antennas: MAR analysis of radome-covered, imperfect, and edge-loaded quasioptical size reflectors fed by the Complex-Source-Point beams; flat earth effect on reflector antenna radiation,
- Printed Antennas: MAR-based study of perfect and imperfect circular-disk antennas printed on flat and spherical substrates; directivity and efficiency of radiation,
- Scattering by Gratings: MAR analysis of wave scattering and absorption by resistive, impedance and material strip gratings,
- Scattering by Cavities: MAR analysis of 2-D cavity-backed apertures; suppressing RCS resonances by material loading; investigation of the low-frequency TE-resonance.
- History of Microwaves: early magnetrons and radars in Ukraine; quasioptics of near-mm and sub-mm waves; spaceborne SLRs.