Sufficient condition for producing photonic band gaps in one-dimensional optical waveguide networks

In this paper, we investigate the influences of the mode, number, and sequence of unit cell on the production of photonic band gaps (PBGs) in one-dimensional (1D) optical waveguide networks (OWNs) and find that the sufficient condition for producing PBG is related to the mode and number of unit cell, but the sequence of unit cell does not affect the production of PBGs. Only when a 1D OWN contains enough evanescent-mode unit cells can it produce PBGs. Otherwise, no matter how the sequence of unit cell is, the 1D OWN can not produce any PBG. It may deepen people's knowledge on the mechanism of the production of PBGs in 1D OWNs and may be useful for the designing of PBG materials/devices. On the other hand, according to the classification method of 1D lattices in solid state physics, we classify the unit cells of OWNs as two types: the simple and complex unit cells. This classification method may be useful for investigating OWNs strictly, deeply, and taxonomically. (C) 2015 Optical Society of America