利用超格子模型对布拉格光纤的研究

为了研究布拉格光纤的模式特征和传输特性，提出了超格子模型，利用傅里叶级数表示光纤横向折射率分布，利用平面波展开法分析布拉格光纤的能带结构，基于厄米-主斯函数的局域正交函数展开法，从全矢量耦合波动方程出发，得到关于模式传播常量和电场展开系数的本征方程，从而分析布拉格光纤的模式特征。以高折射率芯布拉格光纤为例，实现了该算法，得到基模与二次模的横向电场分布、基模色散曲线和模式双折射。基模的模式双折射可用于衡量算法的精度，结果表明该算法精度较高。超格子模型不仅可以用于研究高折射率芯布拉格光纤，而且同样可以研究低折射率区域导光的布拉格光纤。

Investigation of the Supercell Model for the Bragg Fibers

The supercell model for the Bragg fibers is proposed for investigating the mode characteristics and propagation properties. The transverse refractive index profile is expressed by Fourier series, and the energy band structure is obtained by the plane wave expansion method. The mode propagation constant and the expansion coefficients of the electric field can be obtained from the eigen system which is deduced from the full-vectorial coupling wave equations based on the localized orthogonal Hermite-Gaussian functions. The supercell mode is implemented when the high-index core Bragg fiber is taken into account. Some lower-order modes are analyzed, and the mode birefringence of the fundamental pairs can be used to scale the accuracy of this algorithm. The supercell model is also efficient for the hollow core Bragg fibers.