Xiang-Yao Wu, Bai-Jun Zhang, Jing-Hai Yang, Xiao-Jing Liu, Nuo Ba, Yi-Heng Wu, Qing-Cai Wang, Guang-Huai Wang
In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $\epsilon_{A}$ and $\epsilon_{B}$. By Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refractive index distribution function $n(z)$, we can obtain more width or more narrow band gap structure than conventional photonic crystals.
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http://arxiv.org/abs/1011.0047
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