All-angle left-handed negative refraction in Kagome and honeycomb   lattice photonic crystals
  Possibilities of all-angle left-handed negative refraction in 2D honeycomb and Kagome lattices made of dielectric rods in air are discussed for the refractive indices 3.1 and 3.6. In contrast to triangular lattice photonic crystals made of rods in air, both the honeycomb and Kagome lattices show all-angle left-handed negative refraction in the case of the TM2 band for low normalized frequencies. Certain advantages of the honeycomb and Kagome structures over the triangular lattice are emphasized. This specially concerns the honeycomb lattice with its circle-like equifrequency contours where the effective indices are close to -1 for a wide range of incident angles and frequencies. 
Rados Gajic, Ronald Meisels, Friedemar Kuchar and Kurt Hingerl