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, 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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