Periodic structures are well-known for their excellent capabilities pertinent to controlling and modifying the flow of waves/particles, especially in the domains of solid-state physics and photonics. Perhaps the best-known examples of periodic structures modifying the flow of waves/particles are semiconductors, in which the propagation of electrons in the periodic potential (induced by atoms) in semiconductors is greatly modified. These modifications can be quite significant, to the extent that within certain frequency/energy ranges, electrons are prohibited from propagating through the material. Such energy ranges are known as electronic bandgaps (BGs). The concept of the bandgap has proven to be quite important and has lead to a new era in the electronic industry. A similar phenomenon has been observed for other wave/particles such as photons. Structures with periodic variation in their optical properties, called photonic crystals (PtCs), have already shown their excellent capabilities pertinent to controlling the flow of optical waves or their dual particles (i.e., photons) using photonic bandgaps (PtBGs). PtBGs are ranges of frequencies in which optical waves (or photons) cannot propagate. Several new devices have been introduced through the use of PtCs’ unprecedented PtBGs, including PtC fibers, waveguides, and resonators, which have shown superior performances over their conventional counterparts in several aspects.
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