Large Photonic Band Gaps in Certain Periodic and Quasi-Periodic Networks in two and three dimensions

The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the fundamental loop exhibits anti-resonant transmission. This is also true for quasi-periodic networks in two and three dimensions, where the photonic band structures are calculated from the spectra of total transmission arising from a source inside the samples. In all the cases we have studied, it is also found that the gap positions in a network are dictated by the frequencies at which the anti-resonance occurs.