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Design of a photonic crystal fiber with low confinement loss and high birefringence
  • Abstract

    A photonic crystal fiber (PCF) for long distance communication was proposed in this paper. The circular and elliptical air holes distribute in the cladding, and there are two small elliptical air holes around the core in cross section of the PCF. The characteristics of the PCF were analyzed by using the finite element method (FEM) systematically. The results show that the PCF offers an ultrahigh birefringence of 3.51×10-2 and the confinement loss as low as 1.5×10-9 dB/m with the optimal structure at the wavelength of 1550 nm. Compared with the existing photonic crystal fibers with elliptical air holes, the birefringence has a large increase, and the confinement loss reduces by 5 orders of magnitude. Additionally, we also analyzed the relationship between the dispersion of the PCF and the wavelength, and obtained the Brillouin gain spectrum characteristics. In general, the PCF can be used in long distance communication system.

    Keywords

  • 本文设计的光子晶体光纤与已有光纤最明显的区别是本文光纤横截面内圆形与椭圆形空气孔交错排列。利用有限元方法系统地进行数值分析之后,得出了所设计光纤最优的结构参数,并且分析了其传输特性和布里渊增益谱特性。研究结果表明,在1550 nm处,此光纤在最佳结构下的双折射系数可达3.51×10-2,限制性损耗低至1.5×10-9 dB/m,y偏振轴具有平坦色散,x偏振轴色散值最低可达到-500 ps·km-1·nm-1x偏振轴和y偏振轴的布里渊频移分别为10.15 GHz和10.4 GHz。本文提出的光纤在光纤传感,制作保偏光纤以及长距离光纤通信系统等领域具有一定的应用价值。

    与传统的光纤相比,光子晶体光纤具有许多优异特性,例如大负色散、非线性特性、限制性损耗和高双折射等。同时,双折射特性、限制性损耗以及色散特性是长距离光纤通信系统中三个重要的衡量标准。当光子晶体光纤的两个偏振轴之间的不对称程度越大,其双折射系数越大,传输过程中两个偏振轴之间的模式耦合程度会减小,有助于提升光信号的传输距离。同时,较低的限制性损耗也有助于提升光信号的传输距离。另外,色散会引起光脉冲的展宽,极大地限制了传输信道的容量和光纤的带宽[]。因此,利用大负色散光纤进行色散补偿在高速度长距离光纤通信系统中也十分必要。

    光子晶体光纤(Photonic crystal fiber, PCF)是一种空气孔沿轴向周期性排列的,端面呈二维周期性分布的光子晶体结构[],又称为多孔光纤或微结构光纤,具有许多传统光纤无法实现的性能,近几年在行业内引起了极大的关注[-]

    2011年,Yang等人[]引入椭圆形空气孔,使得光子晶体光纤的双折射达到了0.87×10-2,限制性损耗为0.01 dB/m。2016年,Wu等人[]设计的光子晶体光纤的双折射系数达到2.21×10-2。2017年,Liao等人[]通过在纤芯引入椭圆空气孔得到了高达3.41×10-2的双折射系数和低至-399.98 ps·km-1·nm-1的色散值。2019年,Liu等人[]设计的光子晶体光纤的限制性损耗有了新的突破,达到了10-6 dB/m,其数量级有明显降低。刘旭安等人[]提出了一种基于双空气孔单元四角晶格排列的光子晶体光纤,其双折射为10-2量级,限制性损耗为10-6 dB/m量级。2020年,Agbemabiese等人[]提出一种包层含圆形和椭圆形空气孔的光子晶体光纤,其双折射系数为2.018×10-2,限制性损耗为10-5 dB/m量级。在目前现存的光子晶体光纤的设计中,空气孔的分布较为单一,大大降低其偏振轴之间的不对称性,影响双折射系数的进一步提高以及其他传输特性的优化,因此,已无法满足当今通信系统高速增长的需求。

    Figure 1. Cross section of the designed photonic crystal fiber
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    Cross section of the designed photonic crystal fiber

    Parameter/unit Ʌ/μm b/μm r/μm d/μm
    Value 0.87 0.4 5.046 0.2
    CSV Show Table

    光纤的横截面示意图如图 1所示。椭圆形空气孔与圆形空气孔呈交错排列,孔间距为Λ。图中灰色区域为椭圆形空气孔,短半轴和长半轴分别用ab表示;绿色区域为半径为b的圆形空气孔;围绕纤芯的黄色区域为两个小椭圆空气孔,其短半轴和长半轴分别为a1b,椭圆率用η=a1/b表示;光纤半径为r

    在利用有限元分析法对建立的模型进行计算时,添加了一层厚度为d的完美匹配层(perfectly matched layer,PML)作为边界吸收条件,使计算结果更加精确。经过系统地数据分析,最终确定的部分结构参数如表 1所示。

    本文仿真模拟基于表 1中的光纤结构参数。在本小节中取a1=0.35 μm,η=0.2。图 2为该结构下光纤xy偏振轴的模场分布。从图 2可以看出,x偏振轴和y偏振轴的模场分布分别呈现出椭圆形和矩形形状,其模式电场关于x轴和y轴的分布失去了极轴对称性,导致了该光子晶体光纤高双折射系数的产生,不对称性越高,光纤模式双折射越高。

    Figure 2. The field distribution and energy contour of LP01 at 1550 nm with η=0.2. (a), (b) x-polarization; (c), (d) y-polarization
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    The field distribution and energy contour of LP01 at 1550 nm with η=0.2. (a), (b) x-polarization; (c), (d) y-polarization

    a发生变化时,双折射系数也会随之发生改变,其变化趋势如图 4所示。

    图 3图 4所示,当a小于0.4 μm,波长小于1800 nm时,同波长下x偏振轴有效折射率和双折射系数的差异较小。图 3中子图部分为波长在1600 nm~2000 nm,a在0.2 μm~0.35 μm范围内变化时光纤xy偏振轴有效折射率的标准差,从图中可以看出,在1800 nm后光纤x偏振轴的有效折射率出现了一定程度的变化,而y偏振轴差异较小,因此双折射系数差异增大。而当a=0.4 μm时,光纤双折射系数有明显下降,是因为此时椭圆孔全部呈现圆形,降低了x偏振轴和y偏振轴的非对称性。

    图 5显示了在典型值η=0.2、0.6和0.8时双折射系数随波长的变化情况,其中a1分别对应于0.08 μm,0.24 μm和0.32 μm。此外,在波长为1550 nm处标注了参考文献[, -]中典型PCF的双折射系数值以与本文提出的光纤结构双折射系数值进行对比。如图 5所示,双折射系数随着η的减小而增加,当波长为1550 nm,η=0.2时获得了3.51×10-2的高双折射。同时从图 5中可以看出,与文献[, -]中设计的光子晶体光纤相比,本文所提出的PCF结构在η=0.2时具有最高的双折射系数,这是因为所提出的空气孔交错分布结构大大提高了两偏振轴之间的不对称性,高双折射光子晶体光纤可以有效减少光信号传输过程中两个偏振轴之间的能量耦合,有助于增加光纤通信系统的传输距离[-]

    Figure 5. The birefringence of the PCF with different η as a function of wavelength
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    The birefringence of the PCF with different η as a function of wavelength

    Figure 3. Effective refractive index of the proposed PCF changes with the increase of a
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    Effective refractive index of the proposed PCF changes with the increase of a

    a小于0.4 μm时其值的大小对光纤特性影响较小,而a偏大时,其制造难度较低。计算表明在其他参数保持最优的情况下,a=0.35 μm接近最优值。接下来我们仅优化η,PCF的其他参数如表 1所示。

    x偏振轴和y偏振轴的有效折射率分别定义为$n_{\rm eff}^x$和$n_{\rm eff}^y$,双折射系数可以定义为

    Figure 4. Birefringence of the proposed PCF changes with the increase of a
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    Birefringence of the proposed PCF changes with the increase of a

    有效折射率(neff)是一个定量描述波导中单位长度相位延迟的量,随着波长的增加,光束的场分布逐渐扩展到包层区域,有效折射率随之减小,如图 3所示。

    $$B = \left| {\left. {n_{\rm eff}^x - n_{\rm eff}^y} \right|} \right.。$$

    其中:λ是波长,c是真空中的光速,Re(neff)是模式有效折射率的实部。本文设计的PCF色散在不同η下随波长变化情况如图 6所示。

    在光纤通信系统中,光纤色散会引起传输信号的畸变,使得通信质量下降,限制通信容量和通信距离,在通信系统中加入适当长度具有较低负色散的色散补偿光纤可以改善色散对通信系统的影响;而色散平坦在超连续谱产生中发挥着重要作用,因此在光通信传输中的光纤设计可以综合考虑色散平坦与负色散两种特性。图 6是根据仿真计算结果得到的色散随波长变化的曲线,当η在0.2~0.6范围内变化时,其xy偏振轴的零色散波长大概在600 nm~1100 nm范围内变化。当η=0.2时,x偏振方向的色散值可低至约-500 ps·km-1·nm-1;在y偏振方向也可以提供相对平坦的负色散,同时具有零色散平坦的特性,近零平坦色散有利于实现非线性光学中的相位匹配、孤子脉冲的产生和传输以及超宽且平坦超连续谱的产生[];当η=0.4时,其具有比η=0.2时更低的色散,但是其色散平坦度较差,不具有零色散平坦的特性;当η=0.6时,其色散平坦度也较差。因此,本文设计的PCF在η=0.2时同时有大负色散以及零色散平坦的特性,可用作高速率长距离传输系统中的色散补偿光纤元件,在超连续谱产生方面也具有重要的应用价值。

    Figure 6. Dispersion of the optical fiber as a function of wavelength
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    Dispersion of the optical fiber as a function of wavelength

    PCF的色散包括材料色散和波导色散[]。在有限元计算过程中已经包括了材料色散,因此本文仅计算波导色散,其计算式如下[]

    $${D_{\rm{w}}}(\lambda ) = - \frac{\lambda }{c} \cdot \frac{{{d^2}\operatorname{Re} ({n_{{\rm{\rm eff}}}})}}{{{\rm{d}}{\lambda ^{\rm{2}}}}}, $$

    图 4图 7可知,当η=0.2时,双折射系数最高,负色散较为平坦且限制损耗最小,具有更好的性能。另外,制造难度随着η减小而增加。因此,我们可以确定η=0.2为光纤包层中小椭圆空气孔的最佳结构。

    光纤限制性损耗的大小直接影响传输距离以及中继站间隔距离的远近。从图 7可以看出,当波长一定时,限制性损耗随η的增加而增大。在1550 nm处,η=0.2时,x偏振轴的限制性损耗约为1.5×10-9 dB/m,y偏振轴的限制性损耗约为4×10-9 dB/m。与文献[]相比降低了5个数量级,因此,它具有更优异的传输性能,可以延长通信系统传输距离。

    限制性损耗是由PCF结构引起的,在光信号传输过程中,光并不能完全束缚在纤芯进行传输。因此,限制性损耗可认为是由光的泄漏引起,表示为

    $$L(\lambda ) = \frac{{40\pi }}{{{\rm{ln}}(10)\lambda }} \cdot \operatorname{Im} ({n_{\rm eff}}), $$

    其中$\operatorname{Im} ({n_{\rm eff}})$是有效折射率的虚部[]图 7(a)7(b)分别为xy偏振轴的限制性损耗。

    Figure 7. The confinement loss of the proposed PCF as a function of wavelength. (a) x-polarization; (b) y-polarization
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    The confinement loss of the proposed PCF as a function of wavelength. (a) x-polarization; (b) y-polarization

    图 9为本文设计的光子晶体光纤的布里渊增益谱。从图 9中可以看出,x偏振方向的布里渊频移小于y偏振方向的布里渊频移,其布里渊频移分别为10.15 GHz和10.4 GHz。在实际应用当中,根据布里渊频移可直接算出声速,由声速可以算出弹性常数,由声速的变化可得到关于声速的各向异性、弛豫过程和相变的信息等;由线宽可以研究声衰减过程。另外,在分布式光纤传感系统中,通过测量布里渊频移的变化能实现对光纤所处环境温度与应变的传感[-],本节为所设计的PCF的进一步应用提供了理论基础。

    图 8为LP01模式的声场分布,从图中可以看到声波的能量集中于纤芯分布,由于光场和声场之间有相互作用,从而可以形成布里渊增益谱中的峰。

    基于确定的光纤最佳结构,分析光子晶体光纤的布里渊增益频谱特性。每个声学模式对应一个布里渊峰。布里渊增益与声学模式的关系可定义为[]

    Figure 8. The distribution of acoustic mode LP01 of the PCF
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    The distribution of acoustic mode LP01 of the PCF

    Figure 9. Brillouin gain spectrum of the proposed PCF
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    Brillouin gain spectrum of the proposed PCF

    其中:vvp分别是散射光和入射光的频率;vmωm分别是布里渊散射谱中第m个峰的布里渊频移和线宽;g是第m个布里渊增益谱的峰值。

    $${g_m}(v) = g\frac{{{{({\omega _m}/2)}^2}}}{{{{(v - {v_{\rm p}} + {v_m})}^2} + {{({\omega _m}/2)}^2}}}, $$

    表 2为所提出的PCF与已有设计之间的双折射系数(B),色散(D)和限制损耗(L(λ))的比较。结果表明,本文提出的PCF性能有显著提高,在高速率和长距离传输系统领域中具有潜在的应用。

    References L(λ)/(dB/m) B D/(ps·km-1·nm-1)
    Ref. [] 0.01 0.87×10-2
    Ref. [] 0.365 3.41×10-2 -399.98
    Ref. [] 2.89×10-2 -600
    Ref. [] 2×10-2 -200
    Ref. [] 5×10-4 8×10-3
    Ref. [] 1.17×10-4 2.54×10-2 -722.48
    Ref. [] 10-3 1.98×10-2
    Ref. [] 1.24×10-4 -100
    The designed PCF 1.5×10-9 3.51×10-2 -500
    CSV Show Table
    Figure 10. Birefringence as a function of wavelength with 1%~2% variations of circular air holes diameter(2b)
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    Birefringence as a function of wavelength with 1%~2% variations of circular air holes diameter(2b)

    近年来,在光子晶体光纤制造[]方面,Sol-gel浇铸法已变得越来越流行,它可以灵活地改变包层中空气孔的形状、大小和间距,而不会产生空隙。该方法先将熔融石英浇注到根据包层结构设计的模具中来制造纤维预制件,然后将预制件放入光纤拉伸器中进行拉制[30]。此方法为我们提出的结构的制造带来了解决方案。然而,在拉制过程中圆形气孔直径仍不可避免地会有1%~2%的误差。图 10显示了制造偏差对光纤双折射系数的影响。从图中可以看出,圆形气孔直径的变化对所设计光纤的双折射系数的影响很小,因此降低了对制造精度的要求,大大提高了其可制造性。

    综上所述,本文设计的PCF可以用于高速率长距离传输通信系统领域,并在光纤传感领域具有潜在的应用前景。

    本文设计了一种新型光子晶体光纤结构,包层中大椭圆形和圆形气孔序列交错分布,纤芯周围有两个小椭圆形气孔。通过有限元方法系统地研究了其传输特性。基于详细的数值分析讨论了小椭圆空气孔椭圆率对光纤性能的影响,得到了PCF的最佳参数。本文的结论如下:

    3) 最佳结构下,光子晶体光纤xy偏振方向的布里渊频移分别约为10.15 GHz和10.4 GHz。

    1) 当波长为1550 nm时,基于最佳参数的光纤双折射系数和限制性损耗分别为3.51×10-2和1.5×10-9 dB/m。与现有研究结果相比,所提出的PCF的双折射增加了0.97×10-2,限制性损耗降低了大约5个数量级,大大提高了光信号在通信系统中的传输距离。

    2) η=0.2时,PCF的y偏振轴可以提供较平坦的大负色散,x偏振轴的色散可低至-500 ps·km-1·nm-1,可用于制造色散补偿元件,有效降低脉冲展宽对信道容量及带宽的限制。

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    Periodical cited type(1)

    1. 廖昆,李娇平,王斌,李芳. 一种空气圆孔缺陷的新型光子晶体光纤. 萍乡学院学报. 2024(03): 54-57 .

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  • Author Information

    • Zhao Lijuan, hdzlj@126.com On this SiteOn Google Scholar
      • School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei 071003, China
      • Hebei Key Laboratory of Power Internet of Things Technology, North China Electric Power University, Baoding, Hebei 071003, China
      • Baoding Key Laboratory of Optical Fiber Sensing and Optical Communication Technology, North China Electric Power University, Baoding, Hebei 071003, China
    • Liang Ruoyu On this SiteOn Google Scholar
      • School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei 071003, China
    • Zhao Haiying On this SiteOn Google Scholar
      • School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei 071003, China
    • Corresponding author: Xu Zhiniu, wzcnjxx@sohu.com On this SiteOn Google Scholar

      Xu Zhiniu, E-mail: wzcnjxx@sohu.com

      • School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei 071003, China
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    DOI: 10.12086/oee.2021.200368
    Cite this Article
    Zhao Lijuan, Liang Ruoyu, Zhao Haiying, Xu Zhiniu. Design of a photonic crystal fiber with low confinement loss and high birefringence. Opto-Electronic Engineering 48, 200368 (2021). DOI: 10.12086/oee.2021.200368
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    Article History
    • Received Date October 11, 2020
    • Revised Date February 04, 2021
    • Published Date March 14, 2021
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  • Parameter/unit Ʌ/μm b/μm r/μm d/μm
    Value 0.87 0.4 5.046 0.2
    View in article Downloads
  • References L(λ)/(dB/m) B D/(ps·km-1·nm-1)
    Ref. [6] 0.01 0.87×10-2
    Ref. [8] 0.365 3.41×10-2 -399.98
    Ref. [12] 2.89×10-2 -600
    Ref. [14] 2×10-2 -200
    Ref. [15] 5×10-4 8×10-3
    Ref. [16] 1.17×10-4 2.54×10-2 -722.48
    Ref. [27] 10-3 1.98×10-2
    Ref. [28] 1.24×10-4 -100
    The designed PCF 1.5×10-9 3.51×10-2 -500
    View in article Downloads

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    Corresponding author: Xu Zhiniu, wzcnjxx@sohu.com

    1. On this Site
    2. On Google Scholar
    3. On PubMed
    Design of a photonic crystal fiber with low confinement loss and high birefringence
    • Figure  1

      Cross section of the designed photonic crystal fiber

    • Figure  2

      The field distribution and energy contour of LP01 at 1550 nm with η=0.2. (a), (b) x-polarization; (c), (d) y-polarization

    • Figure  3

      Effective refractive index of the proposed PCF changes with the increase of a

    • Figure  4

      Birefringence of the proposed PCF changes with the increase of a

    • Figure  5

      The birefringence of the PCF with different η as a function of wavelength

    • Figure  6

      Dispersion of the optical fiber as a function of wavelength

    • Figure  7

      The confinement loss of the proposed PCF as a function of wavelength. (a) x-polarization; (b) y-polarization

    • Figure  8

      The distribution of acoustic mode LP01 of the PCF

    • Figure  9

      Brillouin gain spectrum of the proposed PCF

    • Figure  10

      Birefringence as a function of wavelength with 1%~2% variations of circular air holes diameter(2b)

    • Figure  1
    • Figure  2
    • Figure  3
    • Figure  4
    • Figure  5
    • Figure  6
    • Figure  7
    • Figure  8
    • Figure  9
    • Figure  10
    Design of a photonic crystal fiber with low confinement loss and high birefringence
    • Parameter/unit Ʌ/μm b/μm r/μm d/μm
      Value 0.87 0.4 5.046 0.2
    • References L(λ)/(dB/m) B D/(ps·km-1·nm-1)
      Ref. [6] 0.01 0.87×10-2
      Ref. [8] 0.365 3.41×10-2 -399.98
      Ref. [12] 2.89×10-2 -600
      Ref. [14] 2×10-2 -200
      Ref. [15] 5×10-4 8×10-3
      Ref. [16] 1.17×10-4 2.54×10-2 -722.48
      Ref. [27] 10-3 1.98×10-2
      Ref. [28] 1.24×10-4 -100
      The designed PCF 1.5×10-9 3.51×10-2 -500
    • Table  1

      Parameters of the PCF structure and PML

        1/2
    • Table  2

      Comparison with the existing PCFs

        2/2