Key research themes
1. How can operator-based effective medium theory overcome the breakdown limitations of Maxwell Garnett approximation in layered composites?
This research area focuses on developing sophisticated homogenization theories that accurately predict effective electromagnetic properties of periodic multilayered composites, particularly addressing the breakdowns of classical Maxwell Garnett approximations near critical angles of incidence. The theme matters because layered metamaterials and nanophotonic devices rely on precise modeling of wave propagation to optimize their performance, which conventional approximations fail to provide under certain conditions.
2. How can asymptotic and partial domain decomposition methods enable effective medium approximations for spectral problems in complex domains containing thin inclusions or tubes?
This research theme investigates analytical and computational techniques for approximating wave propagation and diffusion spectra in highly heterogeneous media containing small inclusions, thin tubes, or slender microstructures. The motivation lies in the fact that direct numerical simulation is computationally expensive due to multi-scale geometrical features; asymptotic expansions and partial domain decomposition methods (MAPDD) offer dimensional reductions and efficient spectral approximations critical for modeling effective macroscopic behavior in composites and porous media.
3. How can extension of classical effective medium theory using electrodynamic models elucidate and optimize optical properties of nanostructured composites and photonic crystals for photonic applications?
The focus here is on applying effective medium approximations and precise electromagnetic simulations to model and optimize the optical responses of nanostructured materials and composites, including photonic crystals loaded with quantum dots and hierarchical mesocrystals. This research theme is critical for designing materials with tailored optical properties such as color conversion in LEDs, enhanced scattering or absorption, and controlled refractive indices, which impact photonics, sensing, and energy technologies.