Photonic bands of a two-dimensional triangular lattice are studied for parallelopiped dielectric rods standing on the all lattice points in air and parallelopiped holes in dielectric bulk. Absolute photonic band gap is found to exist in the case of parallelopiped dielectric rods, but no photonic band gap is found for the case of parallelopiped holes. Since the electromagnetic wave is not allowed to propagate in any direction inside the photonic band gap, the photonic band gap could be used for the control of spontaneous emission. For the 2-D lattice with holes in dielectric bulk the lateral inhibition of spontaneous emission is expected to increase vertical coupling of emitted photons. Especially for the vertical-cavity structure the inhibition angle of spontaneous emission is deduced on the basis of bands calculation.
Based on the comparison of various reported structures, two dielectric circular rods per one triangular unit cell is preferable for experimental realization at optical-wavelength region because of the relatively large diameter/hight ratio of the dielectric rod.
