提出了基于二阶透明边界条件(2nd TBC)的二维矢量伽辽金有限元法(FEM),并用其对任意横截面形状和折射率分布的光纤进行了模式分析。二阶透明边界条件与一阶透明边界条件(1st TBC)相比,提高了光纤模式限制损耗(CL)的精度,与多极法(MM)计算结果的相对误差在10%以内。对单模光子晶体光纤(PCF)温度特性进行了数值模拟,得出光子晶体光纤有效折射率neff,有效半径Reff和限制损耗随温度变化的近似公式,研究表明当折射率温度系数ξ在所研究的波长和温度范围内变化不剧烈时neff随温度升高线性增加,增加量与波长λ,光子晶体光纤空气孔直径d和孔距Λ无关; 温度变化对光子晶体光纤色散特性无影响; Reff随温度升高线性减小,减小量与ξ,温度增量ΔT,Λ2,λ2成正比,与d成反比; 限制损耗随温度升高线性减小,减少量与ξ,ΔT,限制损耗成正比,在大d/Λ,长波长处限制损耗随温度变化较快。

The two-dimensional (2D) Galerkin vectorial finite-element method (FEM) with 2nd transparent boundary conditions (2nd TBC) is reported and the modes of fibers with arbitrary cross-section shape and arbitrary refractive indices distribution are analyzed. By 2nd TBC the confinement loss (CL) of modes of photonic crystal fibers (PCF) is solved more accurately than by 1st TBC. The relative error between results of FEM with 2nd TBC and multipode method (MM) is no more than 10%. After the temperature properties of a single mode PCF is numerically simulated, the approximate formulas for the change of effective refractive index neff, effective radius Reff and CL of PCF with temperature are constructed. When the temperature coefficient of refractive index ξ varies slowly within the range of wavelength and temperature, as temperature inceases, neff inceeases linearly and the increment has nothing to do with wavelength λ, diameter of air hole d and distance between two nearest holes Λ; Reff decreases linearly and the decrement is in proportion to ξ, temperature increment ΔT, Λ2 and λ2, and inverse proportion to d; CL decreases linearly and the decrement is in proportion to ξ, ΔT, and CL, CL varies more rapidly with larger d/Λ at a longer wavelength. The dispersive properties of PCF are not affected by temperature change.