Photonic band gaps of two-dimensional trigonal photonic crystals fabricated by four umbrellalike beam interference technique

The photonic band gap (PBG) properties of a class of two-dimensional (2-D) trigonal structures fabricated by holographic lithography are investigated. The effect of intensity threshold on the filling ratio, the shape of "atoms", and then the photonic gap is comprehensively studied. Our results show that the PBG of 2-D titania arrays open only for TE polarization, and directional PBG can be obtained for TE and TM polarization simultaneously. And the symmetry reduction of "atom" introduced by holographic lithography technique can yield an absolute PBG for the dielectric "atoms" in air.