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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。
A two-dimensional vector Galerkin finite element method (FEM) based on second-order transparent boundary conditions (2nd TBC) was proposed and used to analyze the optical fiber with arbitrary cross-sectional shape and refractive index distribution. Compared with the first order transparent boundary condition (1st TBC), the second-order transparent boundary conditions improve the accuracy of the optical mode limiting loss (CL), and the relative error between the second-order transparent boundary conditions and the multi-pole method (MM) is less than 10%. The temperature characteristics of single-mode photonic crystal fiber (PCF) are numerically simulated, and the approximate formulas of effective refractive index neff, effective radius Reff and limiting loss with temperature are obtained. The results show that when the temperature coefficient of refractive index ξ Of the photonic crystal fiber, the neff increases linearly with the increase of the temperature, and the increase is independent of the wavelength λ, the diameter d of the photonic crystal fiber air hole and the pitch Λ. The temperature variation has no effect on the dispersion characteristics of the photonic crystal fiber. Reff The decrease of temperature increases linearly with the increase of ξ and temperature ΔT, Λ2 and λ2, and is inversely proportional to d. The limiting loss decreases linearly with increasing temperature, and the decrease is directly proportional to ξ, ΔT and limiting loss , In large d / Λ, long wavelength limit loss changes rapidly with temperature.