Passband and defective bands in photonic and quasi-crystals

The origin of the passband in one-dimensional photonic crystals and Fibonacci quasi-crystals is investigated by the transmission spectra and effective medium theory. The interference and coupling effects influence the formation and properties of the passbands, which can be divided into the basic band and subband formed by coupling interference modes and inhomogeneous dielectric constants, respectively. The optimal length can be obtained through a transcendental equation to show the maximum bandgap for a photonic crystal at the balance condition between interference and coupling effects. By changing the sequence of the two dielectric materials to fabricate a photonic crystal heterostructure, composed of the photonic crystal and quasi-crystal, an enlarging photonic bandgap can be obtained, since the width of the dielectric and air bands can be narrowed by decreasing the photon coupling effect, and the subband and defective band can be eliminated. The effective medium theory provides a good understanding about the formation mechanism of passbands in photonic and quasi-crystals.