标题： 基于伽辽金方法的局部函数方法，应用一组正弦函数来模拟光子晶体光纤 显示英文标题

标题： Localized Function Method Based on the Galerkin Method Applying a Set of Sine Functions to Model Photonic Crystal Fibres

摘要： 基于伽辽金方法，应用一组正弦函数来近似沿光子晶体光纤传播的局域模式的未知模式场，提出了一种局部函数方法的发展和应用。 在对称孔结构相对于坐标系轴（位于孔中心）的情况下，例如圆形、椭圆形等，也提出了一种显著减少积分数量的方法。 该方法不需要折射率的展开，从而可以避免展开的不准确性。 在孔为圆形的情况下，所有积分都可以解析求解。 显示英文摘要

摘要： A development and an application of the localized function method based on the Galerkin method applying a set of Sine functions to approximate the unknown mode fields of the localized modes propagating along the photonic crystal fibres is proposed. A way for considerably reducing the number of integrals in the case of symmetrical holes shapes with respect to the axes of coordinate systems located at the centers of the holes, circular, elliptical etc., is also presented. The method does not require an expansion of the refractive index and thus inaccuracies of the expansion can be avoided. In the case of a circular form of the holes all integrals are solved analytically.