We have fabricated three-dimensional periodic quasicrystals exhibiting quasiperiodicity of the Penrose structure in the x-y plane and periodic along the z axis using ten-beam visible light holographic lithography. The quasicrystals show photonic band gaps in the visible range. The band gaps are found to follow a simple relation as a function of periodicity and polymeric volume fraction, in accord with the Bragg’s diffraction relation.
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Wang et al. (2006) studied this question.
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