Photonic crystals are optical systems whose dielectric permittivity and magnetic permeability vary periodically in space. Thus, they may present gaps in the frequency spectrum. Bloch functions represent propagating modes that are eigenvectors of the translation operators of the crystalline lattice. They are periodic functions of the wave vector and their Fourier coefficients yield the Wannier functions. The Wannier functions of one-dimensional centrosymmetric crystals have been studied in detail. This proposal aims the investigation of such functions in non-centrosymmetric crystals. The main challenge is to develop new methods to optimize the Wannier functions. Numerical calculations will be performed for photonic crystals made of dielectric materials and metamaterials, either at normal or oblique incidence. The optimized Wannier functions will be used to calculate the localized modes induced by defects.
News published in Agência FAPESP Newsletter about the scholarship: