  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.
