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优化设计的LMA-PCF横截面如图 1所示。用石英(SiO2)作为基底材料,包层区域为正六边形周期性分布的小空气孔,最外层圆环表示PCF完美匹配层(perfectly matched layers, PML)吸收边界条件,近芯区域分别引入9个大空气孔和9个小空气孔,构成正九边形周期性结构。其中, R1为PCF的直径,R2为完美隔离层外径,Λ为空气孔间距,d为包层周期性排列空气孔直径,d1和d2分别为芯区大空气孔和小空气孔直径,空气折射率为1,基底材料SiO2折射率为1.45[14]
限制损耗是PCF优化设计的一个关键参量,当激光器选取PCF作为其传输光纤时,PCF限制损耗的大小直接影响激光器的输出功率,PCF基模限制损耗的表达式为[15]:
$ L = \frac{{20}}{{{\rm{In}}10}}\frac{{2\pi }}{\lambda }{\rm{Im}}\left( {{n_{{\rm{eff}}}}} \right)\left( {{\rm{dB}} \cdot {{\rm{m}}^{ - 1}}} \right) $
(1) 式中,Im(neff)是基模有效模式折射率的虚部[16]。从(1)式可得出,PCF的限制损耗与有效模式折射率虚部具有线性关系。作为本文中的研究重点,PCF的模场面积能够表示光波的集中密度,且与光纤的非线性系数等密切相关,PCF的非线性系数可以表示为[17]:
$ g\left( \lambda \right) = \frac{{2{\rm{ \mathit{ π} }}{n_2}}}{{\lambda {A_{{\rm{eff}}}}}} $
(2) 式中,材料的非线性系数[18]为n2=3.0×10-20m2·W-1。有效模场面积Aeff可表示为[19]:
$ {A_{{\text{eff}}}} = \frac{{{{\left( {\iint {{{\left| E \right|}^2}}{\text{d}}x{\text{d}}y} \right)}^2}}}{{\iint {{{\left| E \right|}^4}}{\text{d}}x{\text{d}}y}} $
(3) 式中,E为PCF的横向电场分量[20],它与PCF的光输入波长和结构参量等有关。由(3)式可以看出,扩大PCF截面的横向电场分量可以获得LMA-PCF。
大模场低损耗光子晶体光纤的研究与设计
Research and design of large-mode area low loss photonic crystal fiber
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摘要: 为了改善高功率光纤激光器的非线性效应,提出并设计了一种新型的无源、单模、低损耗、大模场的光子晶体光纤结构。利用时域有限差分法并结合完美匹配层边界条件,分析了光子晶体光纤有效模场面积的影响因素,得到光子晶体光纤性能随波长及几何结构的变化规律,从而得到实现更大模场面积的结构参量。结果表明,保证单模传输的情况下,在1.064μm波长处,优化设计的大模场光子晶体光纤有效模场面积可达3118.4μm2,对应的非线性系数可低至5.68×10-5 m-1·W-1,限制损耗可降低到4.55×10-7 dB·m-1。该光纤具备低损耗、低非线性和大模场面积等特性,在实现光子晶体光纤激光器高功率、高光束品质激光输出方面具有重要应用。Abstract: A design of large-mode area photonic crystal fiber (LMA-PCF) was proposed to improve the non-linear effect of high-power fiber laser, which has the properties as large effective mode area, single mode, passive component, and low loss. The perfect matched layer was set as the boundary condition, and the effect of wavelength and structure on the effective mode area of PCF were analyzed by the finite difference time domain method. Further, a program of LMA-PCF was proposed. The results indicate that the transmission of single mode is obtained. At the wavelength of 1.064μm, the effective mode area is able to reach 3118.4μm2, and the non-linear coefficient is only 5.68×10-5 m-1·W-1. Besides, the confinement loss can be reduced to 4.55×10-7 dB·m-1. Therefore, the high-power and high-beam of laser output is realized.
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