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The photonic band structures in certain two- and three-dimensional periodicnetworks made of one-dimensional waveguides are studied by using theFloquet-Bloch theorem. We find that photonic band gaps exist only in thosestructures where the fundamental loop exhibits anti-resonant transmission. Thisis also true for quasi-periodic networks in two and three dimensions, where thephotonic band structures are calculated from the spectra of total transmissionarising from a source inside the samples. In all the cases we have studied, itis also found that the gap positions in a network are dictated by thefrequencies at which the anti-resonance occurs.Comment: 7 pages, 10 figures and 1 table. Published in Phys. Rev. B, 70,  125104 (2004

Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions