  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.
