We study the bandgap properties of two-dimensional photonic crystals created
by a lattice of rods or holes conformed in a symmetric or asymmetric triangular
structure. Using the plane-wave analysis, we calculate a minimum value of the
refractive index contrast for opening both partial and full two-dimensional
spectral gaps for both TM and TE polarized waves. We also analyze the effect of
ellipticity of rods and holes and their orientation on the threshold value and
the relative size of the bandgap.Comment: 5 pages, 6 figures, App. Phys. B. styl