2D photonic crystals on the Archimedean lattices (tribute to Johannes Kepler (1571–1630))

Results of our research on 2D Archemedean lattice photonic crystals are presented. This involves the calculations of the band structures, band-gap maps, equifrequency contours and FDTD simulations of electromagnetic propagation through the structures as well as an experimental verification of negative refraction at microwaves. The band-gap dependence on dielectric contrast is established both for dielectric rods in air and air-holes in dielectric materials. A special emphasis is placed on possibilities of negative refraction and left-handedness in these structures. Together with the familiar Archimedean lattices like square, triangular, honeycomb and Kagome’ ones, we consider also, the less known, (32, 4, 3, 4) (ladybug) and (3, 4, 6, 4) (honeycomb-ring) structures.