Off-plane angle dependence of photonic band gap in atwo-dimensional photonic crystal

We present an analysis of off-plane angle dependence of the photonic band gap in a two-dimensional triangular lattice with circular air rods embedded in a dielectric background. The plane-wave expansion theory is used to calculate band structures within the first Brillouin zone, and an effective refractive index approach is introduced to derive the off-plane angle dependence. The off-plane angle at which the in-plane band gap decreases to half of its gap width has been obtained, which can be increased significantly by increasing the filling fraction of the air rods. For a typical semiconductor material with a refractive index of 3.6 as the background, this angle reaches 26° at a high filling fraction of 0.84 (where the normalized in-plane band gap width is 24%). The corresponding solid angle of 1.75π could cover about 60 of the spontaneous emission from a linear-polarized dipole along the air rods