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Design of polarization-insensitive 1×2 directional coupler demultiplexer based on sandwiched structure

Wang Jing-Li Chen Zi-Yu Chen He-Ming

Design of polarization-insensitive 1×2 directional coupler demultiplexer based on sandwiched structure

Wang Jing-Li, Chen Zi-Yu, Chen He-Ming
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  • An ultra-compact 1×2 demultiplexer based on directional coupler (DC) waveguide is proposed to separate the 1310 nm wavelength from 1550 nm wavelength, in which a new Si3N4/SiNx/Si3N4 sandwiched structure is used to realize polarization insensitivity. Firstly, the new sandwiched structure is designed to be polarization-independent. The coupling lengths of two orthogonal polarization modes at the same wavelength versus the gap between two parallel SiNx waveguides g1 are calculated with several groups of structure parameters of the demultiplexer. The result shows that the coupling lengths for the two orthogonal polarization modes at the same wavelength can be identical by choosing the proper g1. Then, how to realize the function of wavelength separation is studied. When one wavelength propagates at even multiple of coupling length and the other wavelength propagates at odd multiple of coupling length, and vice versa, the two working wavelengths will output from different output ports, thereby the two wavelengths are successfully separated. Under the premise of satisfying such conditions, a comparison of size and performance among the devices with different groups of structure parameters is given to find the best one. The demultiplexer based on Si3N4/SiO2 platform has a compact structure, easy integration and good tolerance. Three-dimensional(3D) finite-difference time-domain method is used for simulation, and the results show that the length of the DC waveguide is only 23 μm; the insertion loss and crosstalk are as low as 0.1 dB and–26.23 dB respectively; a broad 3-dB bandwidth of 200 nm is achieved. To demonstrate the transmission characteristics of the demultiplexer, the evolution of the excited fundamental mode in the demultiplexer is also given. The novel demultiplexer is polarization-independent and can work at 1310 nm and 1550 nm wavelengths simultaneously. It has a potential application value in future integrated optical circuits.
      Corresponding author: Wang Jing-Li, jlwang@njupt.edu.cn
    [1]

    Walker R G, Urquhart J, Bennion I, Carter A C 1990 IEE P-Optoelectron 137 33

    [2]

    Zhang S, Ji W, Yin R, Li X, Gong Z, Lv L 2018 IEEE Photonics Technol. Lett. 30 107

    [3]

    Shih T T, Wu Y D, Lee J J 2009 IEEE Photonics Technol. Lett. 21 18

    [4]

    Hibino Y 2002 IEEE J. Sel. Top. Quantum Electron. 8 1090

    [5]

    Song J H, Lim J H, Kim R K, ET AL 2005 IEEE Photonics Technol. Lett. 17 2607

    [6]

    Song J H, Kim K Y, Cho J, ET AL 2005 IEEE Photonics Technol. Lett. 17 1668

    [7]

    刘耀东, 李志华, 余金中 2019 物理 48 82

    Liu Y D, Li Z H, Yu J Z 2019 Physics 48 82

    [8]

    Roeloffzen C G H, Hoekman M, Klein E J, ET AL 2018 IEEE J. Sel. Top. Quantum Electron. 24 121

    [9]

    Sacher W D, Huang Y, Liang D, ET AL 2014 Optical Fiber Communications Conference & Exhibition. IEEE, San Francisco, CA, USA, March 9–13, 2014 pTh1A.3

    [10]

    Gupta R K, Chandran S, Krishna B 2018 3 rd International Conference on Microwave and Photonics, Dhanbad, India, February 9–11, 2018 p1

    [11]

    Chen J Y, Shi Y C 2017 J. Lightwave Technol. 35 5260

    [12]

    Xu H N, Shi Y C 2017 IEEE Photonics Technol. Lett. 29 1265

    [13]

    Shi Y C, Anand S, He S L 2008 Asia Optical Fiber Communication & Optoelectronic Exposition & Conference, Shanghai, China, October 30–November 2, 2018 p1

    [14]

    Chen J Y, Liu L, Shi Y C 2017 IEEE Photonics Technol. Lett. 29 1975

    [15]

    Shi Y C, Anand S, He S L 2009 J. Lightwave Technol. 27 1443

    [16]

    Hardy A, Streifer W 1985 J.Lightwave Technol. LT-3 1135

    [17]

    Chen Y, Joines W T 2003 Opt. Commun. 228 319

    [18]

    Fujisawa T, Koshiba M 2006 IEEE Photonics Technol. Lett. 18 1246

    [19]

    Chiang K S, Liu Q 2011 IEEE Photonics Technol. Lett. 23 1277

    [20]

    汪静丽, 陈子玉, 陈鹤鸣 2020 物理学报 69 054206

    Wang J L, Chen Z Y, Chen H M 2020 Acta Phys. Sin. 69 054206

    [21]

    Lee C C, Chen H L, Hsu J C, Tien C L 1999 Appl. Opt. 38 2078

    [22]

    邹祥云, 苑进社, 蒋一祥 2012 物理学报 61 148106

    Zou X Y, Yuan J S, Jiang Y X 2012 Acta Phys. Sin. 61 148106

    [23]

    Wang Q, He S L 2003 J. Opt. A: Pure Appl. Opt. 5 449

  • 图 1  (a) 夹层结构示意图; (b) TE偏振模在夹层波导中的场分布(n0 > n1); (c) TM偏振模在夹层波导中的场分布(n0 > n1)

    Figure 1.  (a) schematic configuration of the sandwiched structure; (b) field distributions for the TE fundamental mode in a sandwiched waveguide (n0 > n1); (c) field distributions for the TM fundamental mode in a sandwiched waveguide(n0 > n1).

    图 2  解复用器结构示意图 (a) 俯视图; (b) DC波导截面示意图

    Figure 2.  Schematic configuration of the demultiplexer structure: (a) Top view; (b) cross section of the DC waveguide.

    图 3  W0 = 0.6 μm, W1 = 0.7 μm, g1 = 0.1 μm时, (a) Lc, (b) ΔLc(λ)随n(SiNx)的变化关系

    Figure 3.  (a) Lc, (b) ΔLc(λ) as a function of n(SiNx) when W0 = 0.6 μm, W1 = 0.7 μm, g1 = 0.1 μm.

    图 4  当 (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm时, Lcg1的变化关系

    Figure 4.  Lc as a function of g1 when (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm.

    图 5  当 (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm时, ΔLc(λ)随g1的变化关系

    Figure 5.  ΔLc(λ) as a function of g1 when (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm.

    图 6  偏振无关1×2 DC解复用器件的光场分布图 (a) 1310 nm, TE波; (b) 1310 nm, TM波; (c) 1550 nm, TE波; (d) 1550 nm,TM波

    Figure 6.  Field distributions of the DC demultiplexer: (a) Quasi-TE mode, at 1310 nm; (b) quasi-TM mode, at 1310 nm; (c) quasi-TE mode, at 1550 nm; (d) quasi-TM mode, at 1550 nm.

    图 7  Port2和Port3两端口归一化输出光功率随波段的变化 (a) 1310 nm波段; (b) 1550 nm波段

    Figure 7.  Output powers (normalized to the input power) from Ports 2 and 3 as the wavelength varies: (a) 1310 nm band; (b) 1550 nm band.

    表 1  DC型偏振无关解复用器的结构参数

    Table 1.  Structural parameters of the polarization-insensitive DC demultiplexer.

    结构参数Pg1/µmLDC/µm
    W0 = 0.4 µm, W1 = 0.6 µm00.0826.5
    W0 = 0.4 µm, W1 = 0.7 µm20.0827
    W0 = 0.4 µm, W1 = 0.8 µm00.0823
    W0 = 0.5 µm, W1 = 0.7 µm20.0726
    W0 = 0.5 µm, W1 = 0.8 µm20.0637
    W0 = 0.5 µm, W1 = 0.9 µm00.0735
    DownLoad: CSV

    表 2  DC型偏振无关解复用器的透过率

    Table 2.  Transmittance of the polarization-insensitive DC demultiplexer.

    结构参数T(1310
    nm, TE)
    T(1310
    nm, TM)
    T(1550
    nm, TE)
    T(1550
    nm, TM)
    W0 = 0.4 µm, W1 = 0.6 µm0.9420.9310.810.8
    W0 = 0.4 µm, W1 = 0.7 µm0.9410.9360.820.814
    W0 = 0.4 µm, W1 = 0.8 µm0.9770.9640.930.84
    W0 = 0.5 µm, W1 = 0.7 µm0.9250.950.840.87
    W0 = 0.5 µm, W1 = 0.8 µm0.960.9640.9070.848
    W0 = 0.5 µm, W1 = 0.9 µm0.980.9670.8530.916
    DownLoad: CSV

    表 3  偏振无关1 × 2 DC解复用器的性能参数

    Table 3.  Performances of the polarization-insensitive DC demultiplexer.

    性能参数IL/dBCT/dB
    1310 nm, TE0.1–20.92
    1310 nm, TM0.16–21.62
    1550 nm, TE0.32–26.23
    1550 nm, TM0.76–24.2
    DownLoad: CSV

    表 4  DC型偏振无关解复用器的性能参数比较

    Table 4.  Comparison of performances of the polarization-insensitive DC demultiplexer.

    器件类型(LDC/面积)/(µm/µm2)$\overline {{\rm{IL}}} $/dB$\overline {{\rm{CT}}} $/dB
    本文230.335–23.24
    文献[14]40 × 25(弯曲波导结构)0.33–22.1
    文献[15]48.20.225–21.25
    DownLoad: CSV
  • [1]

    Walker R G, Urquhart J, Bennion I, Carter A C 1990 IEE P-Optoelectron 137 33

    [2]

    Zhang S, Ji W, Yin R, Li X, Gong Z, Lv L 2018 IEEE Photonics Technol. Lett. 30 107

    [3]

    Shih T T, Wu Y D, Lee J J 2009 IEEE Photonics Technol. Lett. 21 18

    [4]

    Hibino Y 2002 IEEE J. Sel. Top. Quantum Electron. 8 1090

    [5]

    Song J H, Lim J H, Kim R K, ET AL 2005 IEEE Photonics Technol. Lett. 17 2607

    [6]

    Song J H, Kim K Y, Cho J, ET AL 2005 IEEE Photonics Technol. Lett. 17 1668

    [7]

    刘耀东, 李志华, 余金中 2019 物理 48 82

    Liu Y D, Li Z H, Yu J Z 2019 Physics 48 82

    [8]

    Roeloffzen C G H, Hoekman M, Klein E J, ET AL 2018 IEEE J. Sel. Top. Quantum Electron. 24 121

    [9]

    Sacher W D, Huang Y, Liang D, ET AL 2014 Optical Fiber Communications Conference & Exhibition. IEEE, San Francisco, CA, USA, March 9–13, 2014 pTh1A.3

    [10]

    Gupta R K, Chandran S, Krishna B 2018 3 rd International Conference on Microwave and Photonics, Dhanbad, India, February 9–11, 2018 p1

    [11]

    Chen J Y, Shi Y C 2017 J. Lightwave Technol. 35 5260

    [12]

    Xu H N, Shi Y C 2017 IEEE Photonics Technol. Lett. 29 1265

    [13]

    Shi Y C, Anand S, He S L 2008 Asia Optical Fiber Communication & Optoelectronic Exposition & Conference, Shanghai, China, October 30–November 2, 2018 p1

    [14]

    Chen J Y, Liu L, Shi Y C 2017 IEEE Photonics Technol. Lett. 29 1975

    [15]

    Shi Y C, Anand S, He S L 2009 J. Lightwave Technol. 27 1443

    [16]

    Hardy A, Streifer W 1985 J.Lightwave Technol. LT-3 1135

    [17]

    Chen Y, Joines W T 2003 Opt. Commun. 228 319

    [18]

    Fujisawa T, Koshiba M 2006 IEEE Photonics Technol. Lett. 18 1246

    [19]

    Chiang K S, Liu Q 2011 IEEE Photonics Technol. Lett. 23 1277

    [20]

    汪静丽, 陈子玉, 陈鹤鸣 2020 物理学报 69 054206

    Wang J L, Chen Z Y, Chen H M 2020 Acta Phys. Sin. 69 054206

    [21]

    Lee C C, Chen H L, Hsu J C, Tien C L 1999 Appl. Opt. 38 2078

    [22]

    邹祥云, 苑进社, 蒋一祥 2012 物理学报 61 148106

    Zou X Y, Yuan J S, Jiang Y X 2012 Acta Phys. Sin. 61 148106

    [23]

    Wang Q, He S L 2003 J. Opt. A: Pure Appl. Opt. 5 449

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Publishing process
  • Received Date:  13 May 2020
  • Accepted Date:  13 May 2020
  • Available Online:  14 December 2020
  • Published Online:  05 January 2021

Design of polarization-insensitive 1×2 directional coupler demultiplexer based on sandwiched structure

    Corresponding author: Wang Jing-Li, jlwang@njupt.edu.cn
  • 1. College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
  • 2. Bell Honors School, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Abstract: An ultra-compact 1×2 demultiplexer based on directional coupler (DC) waveguide is proposed to separate the 1310 nm wavelength from 1550 nm wavelength, in which a new Si3N4/SiNx/Si3N4 sandwiched structure is used to realize polarization insensitivity. Firstly, the new sandwiched structure is designed to be polarization-independent. The coupling lengths of two orthogonal polarization modes at the same wavelength versus the gap between two parallel SiNx waveguides g1 are calculated with several groups of structure parameters of the demultiplexer. The result shows that the coupling lengths for the two orthogonal polarization modes at the same wavelength can be identical by choosing the proper g1. Then, how to realize the function of wavelength separation is studied. When one wavelength propagates at even multiple of coupling length and the other wavelength propagates at odd multiple of coupling length, and vice versa, the two working wavelengths will output from different output ports, thereby the two wavelengths are successfully separated. Under the premise of satisfying such conditions, a comparison of size and performance among the devices with different groups of structure parameters is given to find the best one. The demultiplexer based on Si3N4/SiO2 platform has a compact structure, easy integration and good tolerance. Three-dimensional(3D) finite-difference time-domain method is used for simulation, and the results show that the length of the DC waveguide is only 23 μm; the insertion loss and crosstalk are as low as 0.1 dB and–26.23 dB respectively; a broad 3-dB bandwidth of 200 nm is achieved. To demonstrate the transmission characteristics of the demultiplexer, the evolution of the excited fundamental mode in the demultiplexer is also given. The novel demultiplexer is polarization-independent and can work at 1310 nm and 1550 nm wavelengths simultaneously. It has a potential application value in future integrated optical circuits.

    • 随着时代的发展, 人们对通信速率及容量的需求越来越高, 波分复用技术作为提高通信容量的典型解决方案得到了广泛研究. 解复用器是波分复用技术中的核心器件, 用于分离多个波长, 最常见的器件结构包括马赫-曾德尔干涉仪(Mach-Zehnder Interferometers, MZI)型[1]、多模干涉(multimode interference, MMI)型[2]、光子晶体 (photonic crystal, PhC)型[3]、阵列波导光栅 (arrayed waveguide grating, AWG)型[4]、定向耦合器(directional coupler, DC)型[5-6]等. 其中, MZI型解复用器尺寸偏大且高损耗; MMI型、PhC型和AWG型解复用器偏振依赖性高且带宽较低; 而DC型解复用器因其结构简单、损耗低及带宽高, 在光子集成方面得到了广泛应用.

      迄今为止, 大多数DC型解复用器是在绝缘体上硅(silicon-on-insulator, SOI)平台实现的, 尺寸及损耗偏大, 影响光子集成度. 例如, 文献[5]提出了一种基于SOI波导的偏振有关单纤三向器, 其中DC波导的长度约等于6.3 mm, 平均串扰约等于–18 dB; 文献[6]提出了一种基于SOI波导的偏振有关单纤三向器, 其中DC波导的长度约等于8.3 mm, 平均串扰约等于–20 dB. 因此一种新的波导材料Si3N4[7-9]应运而生, 成为研究热点. 采用低压化学气相沉积方法在SiO2上生长的Si3N4薄膜具有结构稳定、损耗低、禁带宽度宽等优点, 有利于提高光子集成度. 与SOI平台相比, Si3N4/SiO2平台表现出了损耗低、工艺容差性好及灵活性高等诸多优势.

      此外, 大部分DC型解复用器都是偏振相关[10-12]的, 即仅考虑某一个偏振模, 这大大限制了其应用范围. 实际上, 正是由于横电模(transverse electric mode, TE)和横磁模(transverse magnetic mode, TM)的耦合长度不同, 从而导致了DC型器件无法实现偏振无关. 为解决这一问题, 人们也陆续提出了若干结构用于调节TE和TM偏振模的耦合长度相等. 例如基于滞后效应制备中间有浅槽的非对称波导[13]; 采用弯曲DC波导结构[14]; 以及采用脊形波导结构[15]等. 这些结构虽然实现了器件的偏振无关, 但同时还存在着尺寸较大、带宽较小和损耗较大等缺点.

      本文提出了一种基于Si3N4/SiNx/Si3N4夹层结构的偏振无关1 × 2 DC型解复用器. 通过合理选择夹层结构芯区的折射率及波导间隙, 可以调节同一波长两个正交偏振模的耦合长度相等, 实现偏振无关; 通过合理选择夹层结构波导宽度, 可以使两个波长分别从不同输出波导端口输出, 实现解复用功能. 采用三维有限时域差分法(three-dimensional finite-difference time-domain, 3 D-FDTD)进行建模和分析, 结果表明: 器件尺寸较小, DC波导的长度仅为23 µm, 仅为文献[15]中DC波导长度的一半. 同时性能优越, 损耗低且带宽高, 在未来的集成光路中具有潜在的应用价值.

    2.   工作原理与器件结构设计
    • DC波导由两根相距较近的直波导构成, 根据耦合模理论[16], 当两根波导靠的很近时, 波导之间会发生横向耦合, 在光的传输方向上, 光能量会周期性地在两根波导中进行转移.

      最常见的DC结构由两根结构参数完全相同的平行直波导组成, 它们满足相位匹配条件, 当光从第1根波导输入时, 两根波导中的能量随着传输长度的增加周期性变化. 在特定的长度Lc下, 光能量第1次100%转移至另一根波导中, Lc可表示为

      其中, Lc被称作耦合长度, βeβo分别是偶模和奇模的传播常数.

    • 顾名思义, 夹层结构即是A/B/A结构, 它由3层材料依次沉积而成, 其中A与B材料的折射率不等. 假设n0 > n1, 由于高、低折射率材料间的电场不连续性, TE和TM偏振模将被局域在不同的材料层传输. 夹层结构常用于设计偏振无关器件[17-19], 例如文献[19]将MMI波导结构与夹层结构相结合, 通过调整中间层材料的折射率使得TE和TM偏振模的拍长相等, 从而实现偏振无关功能.

      本文将夹层结构应用于DC波导结构中, 若要实现偏振无关功能, 即要求同一波长的两个正交偏振模的Lc相等. 如果仅对中间层材料的折射率进行调整, 经3 D-FDTD建模仿真表明: TE偏振模的耦合长度总是大于TM偏振模的耦合长度, 无法实现偏振无关. 因此提出了一种新型夹层结构, 如图1(a)所示, nens分别为包层和衬底的折射率, 中间B材料层的折射率为n0, 波导宽度为W1; 两侧A材料层的折射率为n1, 波导宽度为W0, 且W1 > W0. 通过调节W0W1的值, 可以使得DC波导结构中输入波长的TE和TM偏振模的耦合长度相等, 从而实现偏振无关. TE和TM偏振模在夹层波导中的场分布如图1(b)图1(c)所示, TE偏振模局域在中间B材料层传输, TM偏振模则局域在两侧A材料层传输.

      Figure 1.  (a) schematic configuration of the sandwiched structure; (b) field distributions for the TE fundamental mode in a sandwiched waveguide (n0 > n1); (c) field distributions for the TM fundamental mode in a sandwiched waveguide(n0 > n1).

    • 所设计的DC型解复用器结构示意图如图2(a)所示: 器件由DC波导、S波导和输出波导3部分构成, 其中DC波导结构由两根平行直波导A和B组成, 且波导A和B的结构参数完全相同. LDC为DC波导的长度, W0W1分别为不同材料层的波导宽度, g0g1分别为波导A和B的不同材料层之间的波导间隙, S波导的长度和宽度分别为Ls = 12 μm和Ws = 2.5 μm. 所有波导均采用夹层结构, 以DC波导为例, 如图2(b)所示, Si3N4层波导的高度和宽度分别为h1 = 0.25 μm和W0; SiNx层波导的高度和宽度分别为h0 = 0.1 μm和W1; 与之对应的, g0为Si3N4层波导之间的间隙, g1为SiNx层波导之间的间隙. 离子辅助沉积方法可调节中间层SiNx[20-21]的折射率n(SiNx)在1.72—3.43范围内变化, Si3N4的折射率约为2; 另外S波导、输出波导与DC波导具有类似的截面结构, 不再赘述.

      Figure 2.  Schematic configuration of the demultiplexer structure: (a) Top view; (b) cross section of the DC waveguide.

    3.   器件功能实现与性能分析
    • 首先设计夹层结构, 用于实现同一波长的两个正交偏振模的Lc相等, 达到偏振无关的目的. 若要实现器件的偏振无关, 需要满足(2)式.

      其中, Lc(λ, TE)和Lc(λ, TM)分别表示波长为λ时的TE偏振模和TM偏振模的耦合长度.

      图3给出了当W0 = 0.6 μm, W1 = 0.7 μm, g1 = 0.1 μm时, 不同波长、不同偏振模的Lc和ΔLc(λ)(其中ΔLc(λ) = Lc(λ, TE)–Lc(λ, TM))随n(SiNx)的变化关系. 当ΔLc(λ) = 0时, 满足偏振无关条件(2)式, 此时器件可实现偏振无关. 图3(a)中虚线表示模式在传输过程中严重衰减; 实线则表示模式在传输过程中损耗低. 因此, 为保证传输质量, n(SiNx)需满足大于等于2.7. 此外, 随着n(SiNx)的增大, 同一波长所对应的两个正交偏振模的Lc均随之单调增加, 且Lc(λ, TE)的增长幅度大于Lc(λ, TM). 由图3(b)可知, 随着n(SiNx)的增大, 无论是波长1310 nm还是1550 nm, 其ΔLc(λ)均呈现由负到正的变化, 且单调递增. 当|ΔLc(λ)|大时, Lc(λ, TE)与Lc(λ, TM)差值也大, 实现器件的偏振无关比较困难, 因此希望n(SiNx)尽量偏小. 综上, 选取n(SiNx) = 2.7, 图3(a)中用绿色环标注出了此时所有Lc的值, 它们并不完全相等. 这在图3(b)中更加明显, 当n(SiNx) = 2.7时, 两个波长所对应的|ΔLc(λ)|均不等于零.

      Figure 3.  (a) Lc, (b) ΔLc(λ) as a function of n(SiNx) when W0 = 0.6 μm, W1 = 0.7 μm, g1 = 0.1 μm.

      为了实现偏振无关性能, 需要进一步探讨夹层波导的结构参数W0, W1及波导间隙g1对不同波长的两个正交偏振模的Lc的影响. 本文选取了若干组W0W1的值, 且g1的值在0.05—0.2 µm范围内变化, 观察Lcg1的变化关系. 图4给出了不同结构参数时, Lcg1的变化关系, 其中图4(a)(d)对应的结构参数依次为W0 = 0.4 µm, W1 = 0.6 µm; W0 = 0.4 µm, W1 = 0.7 µm; W0 = 0.5 µm, W1 = 0.7 µm; W0 = 0.5 µm, W1 = 0.8 µm. 由图4可知, 随着W0W1值的增大, 两个波长所分别对应的两个正交偏振模的Lc均随之增大; 随着g1的增大, 同一波长所对应的两个正交偏振模的Lc均随之单调增加, 且Lc(λ, TE)的增长幅度大于Lc(λ, TM), 从而使得两者存在交叉点, 交叉点处Lc(λ, TE) = Lc(λ, TM) (图4中的虚线环标示了各个交叉点).

      Figure 4.  Lc as a function of g1 when (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm.

      虽然对于1310 nm和1550 nm两个波长来说, 交叉点所对应的g1并不相同, 但是值得注意的是, ΔLc(1310 nm)随着g1的增大而有明显地增加, 而ΔLc(1550 nm) 随着g1的增大变化幅度较小, 在0附近波动, 如图5所示. 因此, 合理选择g1, 可以使得ΔLc(1310 nm)逐渐趋于0, 而ΔLc(1550 nm)本身就对g1的变化不敏感, 在0附近波动, 最终使得两个波长均满足(3)式,

      Figure 5.  ΔLc(λ) as a function of g1 when (a) W0 = 0.4 µm, W1 = 0.6 µm, (b) W0 = 0.4 µm, W1 = 0.7 µm, (c) W0 = 0.5 µm, W1 = 0.7 µm, (d) W0 = 0.5 µm, W1 = 0.8 µm.

      可以较好地实现器件的偏振无关.

    • 当各个波长的偏振无关功能实现后, 需要在此基础上实现多波长的分离功能. Port2和Port3的归一化输出功率[22,23]可以表示为:

      其中, Pbar是Port2的输出功率, Pcross是Port3的输出功率. 为了实现波长分离功能, 引入一个功率参数P:

      其中, Lc(1310 nm)和Lc(1550 nm)分别表示输入波长为1310 nm和1550 nm时的耦合长度. 当且仅当P值等于0或者2时, 即当两个波长在DC波导中传输时, 其中一个波长发生奇数次耦合, 同时另一个波长发生偶数次耦合, 此时1310 nm和1550 nm两个波长将分别从两个输出端口输出, 实现波长分离.

      因此, 当器件的设计同时满足(3)式和(6)式时, 即可实现偏振无关功能和波长分离功能. 表1给出了几组不同的W0W1, 通过优化仿真, 可以确定同时满足(3)式和(6)式时对应的g1LDC. 由表1可知, 当W0 = 0.4 µm, W1 = 0.8 µm时, 器件的尺寸最小, LDC仅为23 μm. 同时对表1所涉及的DC型偏振无关解复用器的性能指标分别进行了仿真计算, 给出了不同波长的两个正交偏振模的透过率. 如表2所示, 当W0 = 0.4 µm, W1 = 0.8 µm或者W0 = 0.5 µm, W1 = 0.9 μm时, 透过率指标整体最优. 综合表1表2可知, 当DC型解复用器的结构参数为W0 = 0.4 µm, W1 = 0.8 µm, g1 = 0.08 μm时, 器件尺寸小, 性能指标优越.

      结构参数Pg1/µmLDC/µm
      W0 = 0.4 µm, W1 = 0.6 µm00.0826.5
      W0 = 0.4 µm, W1 = 0.7 µm20.0827
      W0 = 0.4 µm, W1 = 0.8 µm00.0823
      W0 = 0.5 µm, W1 = 0.7 µm20.0726
      W0 = 0.5 µm, W1 = 0.8 µm20.0637
      W0 = 0.5 µm, W1 = 0.9 µm00.0735

      Table 1.  Structural parameters of the polarization-insensitive DC demultiplexer.

      结构参数T(1310
      nm, TE)
      T(1310
      nm, TM)
      T(1550
      nm, TE)
      T(1550
      nm, TM)
      W0 = 0.4 µm, W1 = 0.6 µm0.9420.9310.810.8
      W0 = 0.4 µm, W1 = 0.7 µm0.9410.9360.820.814
      W0 = 0.4 µm, W1 = 0.8 µm0.9770.9640.930.84
      W0 = 0.5 µm, W1 = 0.7 µm0.9250.950.840.87
      W0 = 0.5 µm, W1 = 0.8 µm0.960.9640.9070.848
      W0 = 0.5 µm, W1 = 0.9 µm0.980.9670.8530.916

      Table 2.  Transmittance of the polarization-insensitive DC demultiplexer.

      综上, 当参数取LDC = 23 μm, W0 = 0.4 µm, W1 = 0.8 µm, g1 = 0.08 μm, n(SiNx) = 2.7时, 可以实现偏振无关的1 × 2 DC型解复用器. 此时1310 nm和1550 nm 2个波长所对应的2个正交偏振光信号传播的光场分布如图6所示: 1310 nm的两个偏振模传输了Lc(1310 nm)的距离, 经由S波导从输出端口Port3 输出; 1550 nm的两个偏振模传输了2 × Lc(1550 nm)的距离, 经由S波导从输出端口Port2输出. 设计的器件成功分离了1310 nm和1550 nm, 且实现了偏振无关.

      Figure 6.  Field distributions of the DC demultiplexer: (a) Quasi-TE mode, at 1310 nm; (b) quasi-TM mode, at 1310 nm; (c) quasi-TE mode, at 1550 nm; (d) quasi-TM mode, at 1550 nm.

    • 对于解复用器, 最重要的性能是插入损耗(Insertion Loss, IL)和串扰(Crosstalk, CT), 其定义如(7)式和(8)式所示:

      其中, Pin是输入波导中的功率, PdPu分别是目标输出波导和非目标输出波导中的输出功率(例如, 对于1310 nm波长, PdPu分别是Port3和Port2的输出功率). 本文设计的偏振无关1 × 2 DC解复用器的各性能参数如表3所示, IL低至0.1 dB, 输出波导间的CT低至–26.23 dB.

      性能参数IL/dBCT/dB
      1310 nm, TE0.1–20.92
      1310 nm, TM0.16–21.62
      1550 nm, TE0.32–26.23
      1550 nm, TM0.76–24.2

      Table 3.  Performances of the polarization-insensitive DC demultiplexer.

      实际上, 光源并不是单色光, 因而需要考虑光波长变化对器件性能的影响. 对于解复用器而言, 通常用3 dB带宽进行衡量. 图7给出了归一化输出功率随波长的变化关系, 由图7(a)可见, 当入射光的波长变化范围为1140—1430 nm时, Port3的输出光功率仍保持在输入光功率的一半以上, 也即对于1310 nm波段, 3 dB带宽可以达到290 nm. 同理, 由图7(b)可得, 对于1550 nm波段, 3 dB带宽也可以达到200 nm. 本文设计的DC型解复用器表现出了优越的高带宽性能, 远远高于其他文献[11-12, 14-15].

      Figure 7.  Output powers (normalized to the input power) from Ports 2 and 3 as the wavelength varies: (a) 1310 nm band; (b) 1550 nm band.

      此外, 我们还将本文所设计器件与其他DC型偏振无关解复用器的性能参数比较, 如表4所示. 其中$\overline {{\rm{IL}}} $为各波长不同偏振态入射时的IL的平均值, $\overline {{\rm{CT}}} $为各波长不同偏振态入射时的CT的平均值. 通过对比可见: 本文所设计的DC型解复用器不仅实现了偏振无关, 且尺寸最小, 具有结构紧凑、损耗低等优点.

      器件类型(LDC/面积)/(µm/µm2)$\overline {{\rm{IL}}} $/dB$\overline {{\rm{CT}}} $/dB
      本文230.335–23.24
      文献[14]40 × 25(弯曲波导结构)0.33–22.1
      文献[15]48.20.225–21.25

      Table 4.  Comparison of performances of the polarization-insensitive DC demultiplexer.

    4.   结 论
    • 本文设计了一种基于Si3N4/SiNx/Si3N4夹层结构的偏振无关1 × 2 DC解复用器, 用于分离1310 nm和1550 nm两个波长. 首先讨论了如何利用Si3N4/SiNx/Si3N4夹层结构实现偏振无关, 分析了不同结构参数时, Lcg1的变化关系, 最终得出结论: 通过合理选择g1, 可以使得Lc(λ, TE) ≈ Lc(λ, TM), 从而实现器件的偏振无关. 然后对如何实现波长分离功能进行了讨论, 给出了不同结构参数时, 器件的尺寸及透过率指标的对比, 确定了当参数取LDC = 23 μm, W0 = 0.4 µm, W1 = 0.8 µm, g1 = 0.08 μm, n(SiNx) = 2.7时, 两个波长分别从不同输出波导端口输出, 器件同时实现了偏振无关和解复用功能. 最后对器件的性能进行了分析, 基于Si3N4/SiO2平台使器件表现出了高带宽的优越性能, 且有效的减小了器件的尺寸. 该解复用器的DC波导的长度仅为23 µm, 在1310 nm(1550 nm)工作波长下, TE模与TM模的IL分别为0.1 dB(0.32 dB)与0.16 dB(0.76 dB), 输出波导间的CT分别为–20.92 dB(–21.62 dB)与–26.23 dB(–24.2 dB). 器件结构紧凑, 性能优越, 在新型集成光子系统中具有潜在的应用价值.

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