利用对称性计算曲线积分与曲面积分

在计算对称区间上的定积分和对称区域上的重积分时,适当利用积分区域和被积函数的对称性可起到简化计算的作用.同样,在曲线积分和曲面积分的计算中,也可利用对称性简化计算.     

Properties of Zero Dispersion Wavelengths in Silica Strands and Photonic Crystal Fibres

To design and calculate the zero-dispersion wavelength is one of the important aspects for highly nonlinear photonic crystal fibres. By using the air filling fraction f defined as f = （ 6d） / （ 2π∧ ） here for the cladding effective index, and the step effective index model, the relationship between the properties of chromatic dispersion and the two different structures has been analysed. It is pointed that the variation of the zero dispersion wavelength is insensitive to the core diameter change in one range of core diameter D, while keeping the air filling fraction f constant. In the other range of core diameter D, the photonic crystal fibres have the best nearly-zero ultraflattened dispersion. These properties are significant to the design of chromatic dispersion and zero dispersion wavelength in photonic crystal fibres.     

外力作用下熊猫型保偏光纤应力双折射分析

根据光弹性理论，列出熊猫型保偏光纤内的应力方程。由于保偏光纤具有轴对称性，故可以在分析过程中略去应力的轴向分量。利用傅里叶级数展开法分析了仅存在固有热应力时熊猫型保偏光纤内的应力分布，并进一步分析了外力作用下熊猫型保偏光纤的应力分布及应力双折射随应力分布所发生的变化。利用MATLAB进行了数值模拟，给出应力双折射量B随外力的变化曲线，并讨论了随应力区参数的增大，双折射量B先减小后增大的性质。