All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals

Possibilities of all-angle left-handed negative refraction in 2D honeycomb and Kagom\'e 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 Kagom\'e 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 Kagom\'e structures over the triangular lattice are emphasized. This especially concerns the honeycomb lattice with its circlelike equifrequency contours where the effective indices are close to $\ensuremath{-}1$ for a wide range of incident angles and frequencies.