Comparative study of photonic band gaps of germanium-based two-dimensional triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals

Photonic band gaps (PBGs) of germanium-based two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) with the scatterer radius in the range of [0, 0.3a] and within two cases of the construction (germanium cylinders being placed in air, air cylinders being placed in germanium) have been calculated by using the plane wave expansion (PWE) method. Germanium-based 2D triangular-lattice PC and 2D decagonal quasi-periodic PC are more easily to generate PBG than 2D square-lattice PC. 2D decagonal quasi-periodic PC is more easily to generate complete band gap than the other two kinds of PCs. The PBG properties of the three PCs are similar to the properties of silicon-based system as the radius of the scatterer cylinder increases. Nevertheless, the germanium-based system is more likely to generate PBG than silicon-based system. These findings will guide the design of PBG-type microstructure devices.

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