28 February 2006 Theoretical analysis of band gap formation in rotationally symmetric 2D photonic quasicrystal using rotational symmetry arguments
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Abstract
The key feature that gives photonic crystals (PhCs) their ability to form a photonic band structure (PBS) is their translational symmetry. Structures that do not have translational symmetries also have a PBS. One explanation as to how these structures generate a PBS involves long-range interactions resulting in fractal dispersion relations (e.g. 1-D quasi-crystals, Fibonacci layers, etc.) However, long-range interactions do not fully explain why 2-D quasi-crystals structures also exhibit a PBS. This paper proposes an explanation for such results: by applying rotation operators from the SO(2) group to 1-D quasi-crystal dispersion relations. This process mimics the way electronic state amplitudes are calculated when such states have an angular dependence. Simulations results are presented in this paper.
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Khaled Mnaymneh, Khaled Mnaymneh, Robert C. Gauthier, Robert C. Gauthier, } "Theoretical analysis of band gap formation in rotationally symmetric 2D photonic quasicrystal using rotational symmetry arguments", Proc. SPIE 6128, Photonic Crystal Materials and Devices IV, 61280E (28 February 2006); doi: 10.1117/12.651532; https://doi.org/10.1117/12.651532
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