Abstract
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.
Highlights
In 1887 Rayleigh [1] studied the propagation of electromagnetic (EM) waves in a onedimensional (1D) periodic material and found that there exists a small frequency area in this kind of material, where the propagation of EM waves is inhibited
For a 1D periodic optical waveguide networks (OWNs) composed of equilateral polygon consisting of asymmetrical mixed connection of simple unit cells with equal waveguide length ratio (see Fig. 4(b)), the dispersion relation can be deduced by the steps that are used for deducing Eqs. (3) and (9)
What is the reason of the production of photonic band gaps (PBGs)? In subsection 3.2.2, we have demonstrated that a complex unit cell composed of series connection of different unit cells must be a complex evanescentmode unit cell
Summary
In 1887 Rayleigh [1] studied the propagation of electromagnetic (EM) waves in a onedimensional (1D) periodic material and found that there exists a small frequency area in this kind of material, where the propagation of EM waves is inhibited. It is found that the sufficient condition for producing PBGs in 1D OWNs is related to the mode and number of unit cell but the sequence of unit cell does not affect the production of PBGs, i.e., only when a 1D OWN possesses enough evanescent-mode unit cells, can it produce PBG(s), otherwise, no matter how the unit cells arrange, it can not create any PBG This is the fundamental difference for producing PBGs between OWNs and PCs. This is the fundamental difference for producing PBGs between OWNs and PCs Our discussions on this problem will deepen people’s understanding on PBG materials/structures and may provide theoretical guidance for the designing of PBG materials/devices.
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