Enlargement of Photonic Band Gaps and Physical Picture of Photonic Band Structures

Light propagation in a one-dimensional photonic crystal (PC), consisting of alternative slabs with refractive indices (layer thicknesses) n₁ (a) and n₂ (b), is investigated. An important optimal parameter matching condition, n₁a approx n_2b, is obtained for the largest photonic band gap (PBG). Moreover, we find that the exact analytical solutions for the electric/magnetic field eigenmodes at the band edges are standing waves with odd or even symmetry about the centre of each layer. The electric/magnetic field eigenfunctions at the top and bottom of the nth band have n and n-1 nodes in one period of PC, respectively. The PBG arises from the symmetric differences of the field eigenfunctions at the band edges.