Virtual boundary method for the analysis of elliptically cross-sectional photonic-crystal fibers with elliptical pores
Virtual boundary method for the analysis of elliptically cross-sectional photonic-crystal fibers with elliptical pores
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DOI：
10.1109/jlt.2005.844497
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发表时间：
2005-04
影响因子：
4.7
通讯作者：
N. Florous;M. Koshiba
中科院分区：
文献类型：
--
作者：
N. Florous;M. Koshiba
本文介绍了一种新的半解析方法，用于分析椭圆孔椭圆截面光子晶体光纤的传输特性。这种被称为虚拟边界法（VBM）的方法是基于实际PCF和三层横向非均匀波导之间的等效性。将PCF的复杂折射率曲线写成双傅立叶级数，并在椭圆坐标系下建立了纵向场分量的近似可分波动方程。导出方程的精确解用高阶超越函数表示，如正则和不规则的库仑波函数和马修函数。在表示所有场分量后，在边界上施加边界条件，推导出传播常数的超越方程，并对其进行数值求解。通过将有效指数、模态双折射和电磁场分布等物理量与精确的全矢量有限元模拟结果进行比较，证明了该方法的有效性。该方法正确地证实了PCFs的一些独特特性，例如光在光纤内的强局部化和模态双折射的增强（作为孔排列拓扑的函数）。
This paper introduces a new semianalytical method for the analysis of propagation characteristics of elliptically cross-sectional photonic-crystal fibers (PCFs) with elliptical pores. This method known as a virtual boundary method (VBM) is based on the equivalency between an actual PCF and a three-layered, transversely inhomogeneous waveguide. The complicated refractive-index profile of the PCF is written as a double Fourier series, and an approximate separable wave equation is found in an elliptical coordinate system for the longitudinal field components. The exact solution to the derived equation is expressed in terms of higher order transcendental functions, such as regular and irregular Coulomb-wave functions and Mathieu functions. After having expressed all the field components, boundary conditions are imposed on the boundaries, and then, a transcendental equation for the propagation constant is derived, which is solved numerically. The validity of the method is ensured by comparing various quantities, such as effective indexes, modal birefringences, and electromagnetic field distributions, with those from an accurate full-vector finite-element method (FEM) simulator, showing relatively good agreement between the results. The method correctly confirms some of the unique PCFs' properties, such as strong localization of light within the fiber and enhancement of modal birefringence as a function of the topology of hole arrangement.