本論文採用數值分析方法Dirichlet-to-Neumannu映射(DtN map)來計算光子晶體的頻帶結構。由Dirichlet-to-Neumann映射的基本原理開始，探討DtN映射法在常見二維光子晶體結構：正方晶格、三角晶格、超晶格結構與蜂巢狀晶格中的應用。我們引入色散性介質，以DtN映射法模擬正方晶格頻帶結構，調配其參數使晶體具有雙負折射性質。在晶柱介質為Drude色散模型，背景介質為Lorentz色散模型的情況下，晶柱介質的電漿頻率( )為2.0，背景介質的無阻尼震盪頻率( )為0.38且填充率( )為0.56時，其雙負折射效應最為明顯。

This thesis introduce a numerical analysis method,the Dirichlet-to-Neumann map(DtN map), to calculate the band structure of photonic crystals. From the basic principle of Dirichlet-to-Neumann map, we investgate the applications on general two-dimensional photonic crystal structures: such as square lattice, triangular lattice, super lattice and honey-comb lattice. We introduce dispersion material to simulate band structure of square lattice by DtN map, change the parameter that makes doule negative refractive medium. In Drude model cylinder and Lorentz model background crystal structure, the cylinder plasma frequency 2.0 and background non-damping resonant frequency 0.38 with filling rate 0.56 makes better double negative refractive medium.

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