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中文摘要：
为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗（confinement loss）随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.
英文摘要：
A full-vector modal based on a finite element scheme is formulated for the analysis of optical waveguides and photonic crystal fibers. In order to avoid spurious solutions,an edge/nodal hybrid element is applied and, to investigate the behavior of not only bound modes but leaky modes in optical waveguides, an anisotropic perfectly matched layer （PML） is employed as boundary condition at the edges of the computational window. The validity and usefulness of this approach is confirmed when a rib anti-resonant reflecting optical waveguide （ARROW） and photonic crystal fibers （PCFs） are taken into account. Furthermore,numerical results shown that confinement loss in PCFs increase with increasing wavelength and it is sharply reduced by adding more ring of air holes to the cladding region.
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