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Tunable mode-selective characteristics of a mode-filter petal-fiber with liquid rods

Dai Zhen-Fei Jiang Wen-Fan Wang Ling Chen Ming-Yang Gao Yong-Feng Ren Nai-Fei

Dai Zhen-Fei, Jiang Wen-Fan, Wang Ling, Chen Ming-Yang, Gao Yong-Feng, Ren Nai-Fei. Tunable mode-selective characteristics of a mode-filter petal-fiber with liquid rods. Acta Phys. Sin., 2019, 68(8): 084206. doi: 10.7498/aps.68.20181890
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Tunable mode-selective characteristics of a mode-filter petal-fiber with liquid rods

Dai Zhen-Fei, Jiang Wen-Fan, Wang Ling, Chen Ming-Yang, Gao Yong-Feng, Ren Nai-Fei
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  • In this paper, a novel tunable mode-filter optical fiber consisting of a high-index core and petal-shaped cladding surrounded by a high-index outer ring is proposed. The cladding of the fiber is formed with periodically arranged liquid rods that support cladding modes with effective indexes. These cladding modes form a two-super-mode group. The mode-selection is realized by the coupling between the core mode and the super-mode group. With the petal-shaped cladding, cladding mode can be transmitted at high loss. With the liquid rods, the index-band of super-mode group can be adjusted by external temperature field, thereby achieving the purpose of tunable mode-selective. The super-mode group formed by the LP11 mode of the liquid rods effectively increases its operating bandwidth and temperature tuning range. The numerical simulation results show that the mode-filter fiber with a length of only 71.4 mm can achieve a particular mode loss more than 20 dB, while other modes’ losses are below 1 dB. This special fiber can be used as a mode-filter in the few-mode fiber transmission system to reduce mode crosstalk of converters, multiplexer/demultiplexer, optical switch and optical routing.
      PACS:
      42.79.Ci(Filters, zone plates, and polarizers)
      42.79.Sz(Optical communication systems, multiplexers, and demultiplexers)
      42.81.–i
      42.81.Qb(Fiber waveguides, couplers, and arrays)
      Corresponding author: Chen Ming-Yang, miniyoung@163.com
    • Funds: Project supported by the Key Research and Development Projects (Industry Foresight and Common Key Technologies) of Zhenjiang, China (Grant No. GY2015033) and the Zhenjiang Key Laboratory of Advanced Sensing Materials and Devices, Jiangsu University, China (Grant No. SS2018001).

    单模光纤的信息容量通过时分复用、波分复用、偏振复用等技术获得了极大的提高, 已经接近于极限. 近年来, 采用多芯光纤[1]、少模光纤[2], 以不同的模式传输不同的信息的方法, 即所谓的模分复用技术[3], 可以成倍地提高光纤的传输容量[4]. 而波分复用中密集波分复用已成为长途光信号传输的关键技术[5]. 波长可调的滤波器, 利用连续改变谐振腔腔长的方法实现波长的选择和分配成为了重要配置[6]. 同样, 在模分复用系统中也应该存在可调模式的滤模器作为重要配置.

    滤模器主要工作方式有: 模式转换滤除和直接滤除. 模式转换主要是利用波导结构使模式之间进行转换[7-9], 但是结构相对复杂并且模式间依然存在串扰. 直接滤模的方法近几年有着更多的关注和研究. 利用低阶模的弯曲损耗较小, 而高阶模的弯曲损耗较大的特点, 通过弯曲的方法, 可以使光纤中的某个或某些高阶模产生大的损耗, 从而实现滤模. 但如果想要滤除基模或低阶模而保留高阶模, 则难以用这种方法实现. 基于以上原因利用多芯光纤[10,11]、双光纤耦合[12-14]和带隙光纤[15]来实现不同模式的滤除, 成了滤模的重要结构. 近年来, 基于上述结构又有了新的发展. 基于单模光纤与少模光纤耦合, 级联组成的双芯级联光纤可以实现多模式分离[16], 但需要传输的高阶模损耗过大. 新型多芯光子灯笼可实现多种模式分离与复用[17-19], 但模场形变严重. 基于以上问题, 利用带隙光纤(photonic bandgap fibers, PBF)进行滤模成了新的结构选择, 但普通带隙一般较窄, 导致其对高阶模的束缚能力较弱, 因而高阶模的泄漏损耗也往往很大[15]. 2016年Chen 和Chiang[20]提出新型固体带隙光纤滤膜结构, 可以有效滤除基模保留高阶模, 但滤模损耗不够大并且无法在线调控更改滤模对象.

    近年来, 基于液体填充的微结构光纤(microstructures optical fiber, MOF)获得了广泛的关注[21], 通过改变外界物理场, 如温度、电场、磁场[22]等方法, 可以对填充液体的导光特性(如折射率等)进行控制, 从而实现可调谐的光纤光子器件, 其应用包括传感、光开关、光路由等. 2016年液芯高折射光纤光栅的提出[23], 实现了利用液芯调控实现在线热编程, 但是液芯传输损耗过大.

    本文提出一种基于PBF结构的可调滤模器, 改变包层结构, 增大了滤模效率, 并通过在微结构介质柱中填充液体, 利用温度作为外界物理场, 使液体折射率发生改变, 从而实现对光纤中传导模式的选择.

    图1为提出的花瓣形带隙结构光纤. 其中, 纤芯折射率高于其周围的背景材料折射率. 周围为微结构包层, 其中周期性地排列着三层介质柱, 柱中填充液体材料, 其折射率高于纤芯折射率. 液体柱之间模式的耦合形成超模群. 微结构包层外侧为外包层, 其折射率高于液体介质柱中模式的有效折射率, 从而破坏超模群的传输, 形成强泄漏模式. 若纤芯中特定模式的有效折射率与超模群相近, 则其将与超模群发生耦合, 进而形成强的泄漏损耗, 从而实现滤模的目的[24-26]. 通过调节液体的折射率, 可改变超模群的有效折射率区间, 从而达到选择性滤模的目的[27].

    图 1  花瓣形MOF结构
    Fig. 1.  Petal-shape structure of MOF.

    图1中结构参数选择如下: 纤芯折射率${n_{{\rm{core}}}}{\rm{ = }}$${\rm{1.464}}$, 纤芯直径${d_{{\rm{core}}}}{\rm{ = 14 \; {\text{μ}} m}}$, 纤芯周围的背景材料折射率${n_{{\rm{clad}}}}{\rm{ = 1}}{\rm{.45}}$, 处于1450—1650 nm波长时, 其可以支持LP01, LP11, LP21, LP02四种模式的传输. 液体柱的周期$\varLambda = 7.75\;{\rm{ {\text{μ}}m}}$, 直径${d_{{\rm{liquid}}}}=$${\rm{ 4}}{\rm{.65\; {\text{μ}} m}}$, 其折射率初始值设为${n_{{\rm{liquid}}}} = 1.4927,$$\delta = {\rm{7}}{\rm{.75\; {\text{μ}} m}}$. 为增强液体模式的泄漏损耗, 外包层应尽量与液体柱接近. 为此, 这里将包围最外层液体柱的背景材料层的宽度设置为$\left(\delta - {d_{{\rm{liquid}}}}\right)/2$, 即有${d_{{\rm{petal}}}}{\rm{ = }}\delta $, 形成类似于花瓣形结构. 设入射波长$\lambda = 1550\;{\rm{ nm}}$. 外包层折射率设为${n_{{\rm{outer}}}} = 1.4{\rm{9}}$, 以保证其折射率高于液体柱中模式的有效折射率.

    这里主要通过耦合来实现模式的滤除, 下面简单阐述下耦合的原理.

    两根平行光纤中平行传播a模式和b模式[28]. 定义振幅的${\left| {A\left( z \right)} \right|^2}$, ${\left| {B\left( z \right)} \right|^2}$和a, b两种模式能量值相同. 根据能量守恒定律:

    $\frac{{\rm{d}}}{{{\rm{d}}z}}\left( {{{\left| A \right|}^2} + {{\left| B \right|}^2}} \right) = 0, $

    (1)

    边界条件:

    $b\left( 0 \right) = {B_0},\quad a\left( 0 \right) = 0, $

    (2)

    证明[29]耦合系数KabKba关系:

    ${K_{{\rm{ab}}}} = - K_{{\rm{ba}}}.$

    (3)

    根据本征模式公式和(1)—(3)式可得:

    $\begin{split}A\left( z \right) = \;& {B_0}\frac{{2{K_{{\rm{ab}}}}}}{{{{\left( {4{K^2} + {\varDelta ^2}} \right)}^{1/2}}}}{{\rm{e}}^{ - {\rm i}\varDelta z/2}} \\ &\times\sin\left[ {0.5{{\left( {4{K^2} + {\varDelta ^2}} \right)}^{1/2}}z} \right],\end{split}$

    (4)

    $\begin{split} B\left( z \right) = \; &{B_0}{{\rm{e}}^{ - {\rm{i}}\varDelta z/2}}\Bigg\{ {\cos \left[0.5{{\left( {4{K^2} + {\varDelta ^2}} \right)}^{1/2}}z\right]} \Bigg. \\& \left. { - {\rm{i}}\frac{{2{K_{{\rm{ab}}}}}}{{{{\left( {4{K^2} \!\!+\!\! {\varDelta ^2}} \right)}^{1/2}}}}\sin \left[ {0.5{{\left( {4{K^2} \!\!+\!\! {\varDelta ^2}} \right)}^{1/2}}z} \right]} \right\}, \end{split}$

    (5)

    ${K^2} = {\left| {{K_{{\rm{ab}}}}} \right|^2}$在相位匹配条件$\varDelta = 0$时, 模式a, b完整能量交换发生在${\text{π}}/(2K)$周期.

    (4)式、(5)式简化为

    $\begin{split} a\left( {z,t} \right) &\;=\; {B_0}\dfrac{{{K_{{\rm{ab}}}}}}{K}{{\rm{e}}^{{\rm{i}}\left( {{\omega _{\rm{a}}}t - \beta \alpha } \right)}}\sin \left({Kz} \right), \\b\left( {z,t} \right)&\;=\; {B_0}{{\rm{e}}^{{\rm{i}}\left( {{\omega _{\rm{b}}}t - \beta \alpha {\rm{z}}} \right)}}\cos \left( {Kz} \right).\end{split}$

    (6)

    相位不匹配时, 模式功率交换忽略不计, 相位匹配时, 进一步考虑模式之间功率交换比率. 实际应用中, 模式折射率接近或相等, 产生模式匹配, 耦合发生.

    这里采用有限元法分析光纤的模式传输特性. 图2 给出了纤芯模式的有效折射率和微结构包层的超模群区间. 超模群区间为超模群中最低阶模式的有效折射率的和最高阶模式的有效折射率形成的区间. 由于单个液体柱本身可支持LP01, LP11模的传输, 其超模群也因此分为两个区间, 折射率较高的区间是液体柱中为LP01模时, 耦合形成的超模群区间. 而折射率较低的区间是柱中为LP11模时, 耦合形成的超模群区间. 在所示波长区间, LP11模所形成的超模群区间内, 模式数量超过50个模式. 因而, 若纤芯中某个模式的有效折射率落入此区间, 则其将与某个或多个超模发生耦合, 从而发生模式泄漏. 由图2可知, 根据前述结构参数, 在1535—1605 nm波长处, 纤芯的LP01模处于LP11超模群区间时, 将与包层超模发生耦合.

    图 2  ${n_{{\rm{core}}}} = 1.464$时, 图1中MOF的纤芯4种模式和2个包层超模群区间的色散特性
    Fig. 2.  Dispersion characteristics of the two cladding super-mode band and the four core modes for the MOF shown in Fig.1, when ${n_{{\rm{core}}}} = 1.464$.

    图3为入射波长$\lambda = 1550\;{\rm{ nm}}$时, 纤芯中LP01, LP11, LP21和LP02模的模场分布图. 由图3可见, 此时, 纤芯LP01模与LP11超模群发生耦合. 利用LP11模的模场在包层扩展更显著的特点, 超模群与纤芯LP01模的耦合更加强烈, 从而增大其泄漏损耗. 由于有效折射率与超模群折射率不匹配, 其他纤芯模式仍保持在纤芯中传输, 其模场分布形式与常规PBF相似. 计算得到四个模式的泄漏损耗分别为488.9, 0.015, 0.00743 dB/m和0.0168 dB/m, 可见, 此结构可有效滤除LP01模.

    图 3  波长$\lambda = 1550\;{\rm{ nm}}$时, 纤芯模式的模场分布图 (a) LP01模; (b) LP11模; (c) LP11模; (d) LP02
    Fig. 3.  Field distributions of the core-mode at the wavelength $\lambda = 1550\;{\rm{ nm}}$: (a) The LP01 mode; (b) the LP11 mode; (c) the LP21 mode; (d) the LP02 mode.

    这里通过改变液体折射率的方法, 来实现滤除纤芯其他模式. 设液体为甲苯, 光纤基质材料为二氧化硅. 利用室温(20 ℃)情况下的塞耳迈耶尔方程[30,31], 得到甲苯折射率(nt)和二氧化硅折射率(ns):

    ${n_{\rm{t}}} = 1.474775{\rm{ }} + \frac{{0.0699031{\rm{ }}{\lambda ^2} + 2.1776{\rm{ }} \times {{10}^{ - 4}}}}{{{\lambda ^4}}}, $

    (7)

    $\begin{split} {n_{\rm{s}}} =\;&1 + \frac{{0.6961663{\lambda ^2}}}{{{\lambda ^2} - {{(0.0684043)}^2}}} + \frac{{0.4079426{\lambda ^2}}}{{{\lambda ^2} - {{(0.1162414)}^2}}}\\& + \frac{{0.8974794{\lambda ^2}}}{{{\lambda ^2} - {{(9.896161)}^2}}},\end{split} $

    (8)

    在宽波段1450—1650 nm时, 可以得出甲苯折射率变化在0.003以内, 二氧化硅折射率变化在0.0002以内. 相比于二氧化硅, 甲苯的折射率随波长变化更为显著. 为了得到外界温度场变化条件下的光纤模式传输特性, 我们需要了解两种材料的折射率与温度的变化关系, 由文献[32]可得:

    甲苯折射率与温度关系

    $ {n_{\rm{t}}} = \left[ {{{\left. {{n_{\rm{t}}}} \right|}_{T = 20{\text{℃}}}} + \frac{{{\rm{d}}{n_{\rm{t}}}}}{{{\rm{d}}T}} \times \left( {T - 20} \right)} \right], $

    (9)

    甲苯热光系数

    ${\rm{d}}{n_{\rm{t}}}/{\rm{d}}T = - 5.273 \times {10^{{\rm{ - }}4}}, $

    (10)

    二氧化硅折射率与温度关系

    ${n_{\rm{s}}} = {\left. {{n_{\rm{s}}}} \right|_{T = 20{\text{℃}}}} + \frac{{{\rm{d}}{n_{\rm{s}}}}}{{{\rm{d}}T}} \times \left( {T - 20} \right), $

    (11)

    二氧化硅热光系数

    ${\rm{d}}{n_{\rm{s}}}/{\rm{d}}T \approx - 4 \times {10^{ - 6}}. $

    (12)

    由(9)—(12)式可知, 温度对二氧化硅折射率的热光系数要比甲苯的低两个数量级. 利用上述方程, 得到两种材料的折射率随温度变化. 在20—65 ℃范围内, 溶液折射率可以实现从1.505线性减小到1.4805. 因而, 改变温度即可以在纤芯模式有效折射率基本不变的情况下, 使包层超模群区间移动, 进而实现对不同模式的滤除.

    图4可见, 液体柱折射率改变后, 其超模群区间也发生改变, 选择不同的液体折射率, 即可使不同的纤芯模式落入超模群区间. 图4所对应的折射率区间为甲苯在20—65 ℃范围内的折射率变化范围, 因此调整温度即可实现对不同模式的滤除.

    图 4  波长1550 nm时, 超模群区间随液体介质柱折射率(温度)变化曲线
    Fig. 4.  Variation of super-mode band with liquid-rod index change at the wavelength 1550 nm.

    考虑到液体吸收的影响, 通过通光率公式[33]

    $\alpha = 10\lg \left( {1 - T} \right),$

    (13)

    可以计算出液体介质柱的吸收损耗. 图5分别给出入射波长$\lambda = 1550 {\rm{ nm}}$时, 考虑和不考虑液体吸收损耗时纤芯LP01模式和LP11的损耗曲线. 可见液体吸收损耗对高损耗的模式影响较小, 而对低损耗的模式影响较大. 为此, 在后面的模式损耗分析中, 均包含液体吸收损耗.

    图 5  考虑和不考虑液体吸收损耗两种情况下的纤芯LP01模和LP11模损耗曲线
    Fig. 5.  Variation of the core-mode LP01 mode and LP11 mode loss with and without liquid absorption loss.

    以上已经阐述了滤模光纤的结构和选择性滤模的原理, 下面我们分析其传输性能. 根据图4结果, 可以得到纤芯四种模式单独处于超模群区间时, 液体柱折射率范围. 其对应的损耗曲线如图6所示. 当LP01, LP11模分别处于超模群区间时, 其损耗可达300 dB/m以上, 而其他模式损耗低于1 dB/m, 因而可实现有效滤模. 而LP21和LP02模虽然在分别处于超模群区间时, 损耗更大, 可达380 dB/m以上, 但是由于两种模式的有效折射率比较接近, 因而在滤除一个模式的同时, 也会使另一模式发生一定的损耗. 例如, 当液体折射率为1.4860—1.4864时, LP02模损耗小于14 dB/m, 而当液体折射率为1.4810—1.4816时, LP21模损耗小于9 dB/m. 根据图4图6, 我们可以得出四种模式抑制区间的温度改变量都在4 K左右, 滤模器的工作温度范围比较大, 因而有较大的容差, 利于实际操作.

    图 6  纤芯四种模式单独处于超模群区间时损耗曲线 (a) LP01模; (b) LP11模; (c) LP21模; (d) LP02
    Fig. 6.  The loss of single core-mode on the super-mode band: (a) The LP01 mode; (b) the LP11 mode; (c) the LP21 mode; (d) the LP02 mode.

    为了得到工作带宽, 我们分别选取液体折射率为1.4927, 1.4892, 1.486和1.4812从而分别滤除LP01模、LP11模、LP21模和LP02模. 这里液体折射率的选择兼顾了抑制模式的损耗须足够大、其他模式损耗又比较低的要求. 四种纤芯模式的损耗曲线如图7所示. 为了实现有效滤模, 要求抑制模式的损耗应不小于20 dB, 而其他模式的损耗均小于1 dB. 可以得出, 在工作波长为1540—1555 nm时, 抑制模式的损耗都可以达到280 dB/m以上, 同时其他模式的损耗都低于14 dB/m. 因此, 滤模光纤的长度可以做到仅为71.4 mm, 便于制备和集成.

    图 7  不同液体折射率时, 四种纤芯模式的损耗曲线 (a) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4937}}$; (b) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4892}}$; (c) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.486}}$; (d)${n_{{\rm{liquid}}}}$ = 1.4812
    Fig. 7.  The loss of four core-mode with various liquid index: (a) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4937}}$; (b) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4892}}$; (c) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.486}}$; (d) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4812}}$.

    级联所提出的结构, 就可实现3种模式滤除, 保留单一需要传输的模式.

    本文提出花瓣形包层结构, 以增大纤芯模式损耗, 减小光纤长度. 为此, 我们对比了介质柱折射率${n_{{\rm{rod}}}} = 1.4937$时, Chen和Chiang[20]提出的圆形外包层结构光纤与本文提出的花瓣结构光纤的损耗情况. 为了便于对比, 除外包层形状外, 其他结构参数均相同. 图8(a)为圆形外包层结构的LP01模场分布, 图8(b)为花瓣结构光纤的LP01模场分布.

    图 8  不同结构光纤的LP01模的模场分布 (a)圆形结构; (b)花瓣结构
    Fig. 8.  Field distributions of LP01 mode with various circle structures: (a) Circle structure; ( b) petal-shape structure.

    四种模式损耗的对比如图9所示. 从图9(a)中可以看出, 花瓣结构的损耗明显更大. 特别地, 其LP01模的损耗在波长为1550 nm时比圆形结构大100倍, 达到了488 dB/m. 在1550 nm波长处, LP01模的损耗最大, 而LP21模的损耗最小, 对于花瓣结构和圆形结构光纤, 两者的损耗比分别为65066∶1, 60003∶1. 可见, 采用花瓣结构可以在保证抑制模式和其他模式保持足够大的损耗差情况下, 有效减小光纤的长度, 有利于液体介质的填充和温度控制.

    图 9  两种MOF的模式损耗对比 (a) LP01模和LP11模损耗曲线; (b) LP21模和LP02模曲线
    Fig. 9.  Loss of two MOF: (a) Loss band of the LP01 mode and LP11 mode; (b) loss band of the LP21 mode and LP02 mode.

    本文以液体柱的LP11模所形成的超模群作为耦合区间. 下面分析其与LP01模所形成超模群区间的不同之处.

    图4所示, LP11模所形成的超模群区间更宽, 同时其超模的斜率曲线更小. 以纤芯LP01模传输为例, 使其分别处于两种超模群区间, 对比损耗. LP01超模群区间设置${n_{{\rm{liquid}}}} = 1.472$, LP11超模群区间设置${n_{{\rm{liquid}}}} = 1.492$, Loss-band为当取光纤长度为71.4 mm时, 抑制模式损耗达到20 dB时所对应的工作区间. 如图10所示, 相比于介质柱LP01模所形成的超模群区间, 介质柱LP11模所形成的超模群区间可以在更宽的温度和波长范围内实现对纤芯LP01模式的滤除. 其主要原因是, LP11模的能量耦合进包层中更多, 因而更容易与相邻介质柱的模式发生耦合.

    图 10  纤芯 LP01模式在双超模群时的两种超模群区间LP01模损耗 (a)波长为1550 nm, 温度改变量相同; (b)温度相同, 波长改变
    Fig. 10.  Dependence of the loss of the core LP01 mode locating in different two super-mode region: (a) With same temperature variation at wavelength 1550 nm; (b) with various wavelength at the same temperature.

    我们提出一种新型的可调滤模MOF, 利用纤芯模式与微结构包层模式之间的耦合实现选择性滤模, 采用花瓣形包层, 使包层中传输的模式更易产生高的泄漏损耗. 以液体填充包层介质柱, 使包层形成的超模群有效折射率区间可以通过改变环境温度来调节. 利用液体柱的LP11模所形成的超模群有效增大了其工作带宽和温度调节范围. 提出的光纤可以在少模光纤传输系统中作为滤模器, 以解决模式转换器、复用器/解复用器以及光开关和光路由等的模式串扰问题, 并可实现在线可调滤除模式, 进而实现特定模式信号的下载与上传.

    [1]

    Turukhin A, Sinkin O V, Batshon H G, Zhang H, Sun Y, Mazurczyk M, Davidson C R, Cai J X, Bolshtyansky M A, Foursa D G, Pilipetskii A 2016 Proceedings of Optical Fiber Communications Conference and Exhibition (OFC 2016) Anaheim, California, USA. March 20−24, 2016

    [2]

    Hong X, Zeng X, Li Y, Mo Q, Tian Y, Li W, Liu Z, Wu J 2016 Appl. Opt. 55 9360Google Scholar

    [3]

    姚殊畅, 张敏明, 唐明, 沈平, 刘德明 2013 物理学报 62 144215Google Scholar

    Yao X C, Zhang M M, Tang M, Sheng P, Liu D M 2013 Acta Phys. Sin. 62 144215Google Scholar

    [4]

    Koebele C, Salsi M, Sperti D, Tran P, Brindel P, Mardoyan H, Bigo S, Boutin A, Verluise F, Sillard P, Astruc M, Provost L, Cerou F, Charlet G 2011 Opt. Express 19 16593Google Scholar

    [5]

    Sarmiento S, Altabas J A, Izquierdo D, Garces I, Spadaro S, Lazaro J A 2017 J. Opt. Commun. Netw. 9 1116Google Scholar

    [6]

    Ramachandran S, Fini J M, Mermelstein M, Nicholson J W, Ghalmi S, Yan M F 2008 Laser Photon. Rev. 2 429Google Scholar

    [7]

    Driscoll J B, Grote R R, Souhan B, Dadap J I, Lu M, Osgood R M 2013 Opt. Lett. 38 1854Google Scholar

    [8]

    Nobutomo H, Kuimasa S, Taiji S, Takashi M, Kyozo T, Masanori K, Fumihiko 2013 Opt. Express 21 25752Google Scholar

    [9]

    Riesen N, Love J D 2012 Appl. Opt. 51 2778Google Scholar

    [10]

    Saitoh F, Saitoh K, Koshiba M 2010 Opt. Express 18 4709Google Scholar

    [11]

    Yu C P, Liou J H, Chiu Y J, Taga 2011 Opt. Express 19 12673Google Scholar

    [12]

    Tsekrekos C P, Syvridis, 2012 IEEE Photonic Tech. L. 24 1638Google Scholar

    [13]

    Chang S H, Chung H S, Ryf R, Fontaine N K, Han C, Park K J, Kim K, Lee J C, Lee J H, Kim B Y, Kim Y K 2015 Opt. Express 23 7164Google Scholar

    [14]

    Chang S H, Moon S R, Chen H, Fontaine N K, Park K J, Kim K, Lee J K 2017 Opt. Express 25 5734Google Scholar

    [15]

    Pureur V, Knight J C, Kuhlmey B T 2010 Opt. Express 18 8906Google Scholar

    [16]

    Park K J, Song K Y, Kim Y K, Lee J H, Kim B Y 2016 Opt. Express 24 3543Google Scholar

    [17]

    Yerolatsitis S, Harrington K, Thomson R R, Birks T A 2017 Optical Fiber Communications Conference and Exhibition (Ofc 2017) Los Angeles, California, USA. March 19−23

    [18]

    Velazquez-Benitez A M, Alvarado J C, Lopez-Galmiche G, Antonio-Lopez J E, Hernandez-Cordero J, Sanchez-Mondragon J, Sillard P, Okonkwo C M, Amezcua-Correa R 2015 Opt. Lett. 40 1663Google Scholar

    [19]

    Sai X, Li Y, Yang C, Li W, Qiu J, Hong X, Zuo Y, Guo H, Tong W, Wu J 2017 Opt. Lett. 42 4355Google Scholar

    [20]

    Chen M Y, Chiang K S 2016 IEEE J. Sel. Top. Quant. 22 4900307

    [21]

    姚建铨, 王然, 苗银萍, 陆颖, 赵晓蕾, 景磊 2013 中国激光 40 0101002

    Yao J Q, Wang R, Miao Y P, Lu Y, Zhao X L, Jin L 2013 Chinese J. Lasers 40 0101002

    [22]

    吴倩, 郭晓晨, 施伟华 2018 物理学报 67 184212Google Scholar

    Wu Q, Guo X C, Shi W H 2018 Acta Phys. Sin. 67 184212Google Scholar

    [23]

    Qi T, Jung Y, Xiao L, Wang J, Xiao S, Lu C, Tam H Y, Peacock A C 2016 Opt. Lett. 41 4763Google Scholar

    [24]

    程兰, 罗兴, 韦会峰, 李海清, 彭景刚, 戴能利, 李进延 2014 物理学报 63 074210Google Scholar

    Cheng L, Luo X, Wei H F, Li H Q, Peng J G, Dai N L, Li J Y 2014 Acta Phys. Sin. 63 074210Google Scholar

    [25]

    Stone J M, Pearce G J, Luan F, Birks T A, Knight J C, George A K, Bird D M 2006 Opt. Express 14 6291Google Scholar

    [26]

    Argyros A, Birks T A, Leon-Saval S G, Cordeiro C M B, Russell P S 2005 Opt. Express 13 2503Google Scholar

    [27]

    Park J, Kang D E, Paulson B, Nazari T, Oh K 2014 Opt. Express 22 17320Google Scholar

    [28]

    Dimitropoulos D, Houshmand B, Claps R, Jalali B 2003 Opt. Lett. 28 1954Google Scholar

    [29]

    Poon J, Istrate E, Allard M, Sargent E H 2003 IEEE J. Sel. Top. Quant. 39 778Google Scholar

    [30]

    Samoc A 2003 J. Appl. Phys. 94 6167Google Scholar

    [31]

    Zhang R, Teipel J, Giessen H 2006 Opt. Express 14 6800Google Scholar

    [32]

    Couris S, Renard M, Faucher O, Lavorel B, Chaux R, Koudoumas E, Michaut X 2003 Chem. Phys. Lett. 369 318Google Scholar

    [33]

    Liu Y Q, Guo Z Y, Zhang Y, Chiang K S, Dong X Y 2000 Electron. Lett. 36 56

    期刊类型引用(0)

    其他类型引用(1)

  • 图 1  花瓣形MOF结构

    Figure 1.  Petal-shape structure of MOF.

    图 2  ${n_{{\rm{core}}}} = 1.464$时, 图1中MOF的纤芯4种模式和2个包层超模群区间的色散特性

    Figure 2.  Dispersion characteristics of the two cladding super-mode band and the four core modes for the MOF shown in Fig.1, when ${n_{{\rm{core}}}} = 1.464$.

    图 3  波长$\lambda = 1550\;{\rm{ nm}}$时, 纤芯模式的模场分布图 (a) LP01模; (b) LP11模; (c) LP11模; (d) LP02

    Figure 3.  Field distributions of the core-mode at the wavelength $\lambda = 1550\;{\rm{ nm}}$: (a) The LP01 mode; (b) the LP11 mode; (c) the LP21 mode; (d) the LP02 mode.

    图 4  波长1550 nm时, 超模群区间随液体介质柱折射率(温度)变化曲线

    Figure 4.  Variation of super-mode band with liquid-rod index change at the wavelength 1550 nm.

    图 5  考虑和不考虑液体吸收损耗两种情况下的纤芯LP01模和LP11模损耗曲线

    Figure 5.  Variation of the core-mode LP01 mode and LP11 mode loss with and without liquid absorption loss.

    图 6  纤芯四种模式单独处于超模群区间时损耗曲线 (a) LP01模; (b) LP11模; (c) LP21模; (d) LP02

    Figure 6.  The loss of single core-mode on the super-mode band: (a) The LP01 mode; (b) the LP11 mode; (c) the LP21 mode; (d) the LP02 mode.

    图 7  不同液体折射率时, 四种纤芯模式的损耗曲线 (a) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4937}}$; (b) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4892}}$; (c) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.486}}$; (d)${n_{{\rm{liquid}}}}$ = 1.4812

    Figure 7.  The loss of four core-mode with various liquid index: (a) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4937}}$; (b) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4892}}$; (c) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.486}}$; (d) ${n_{{\rm{liquid}}}} = {\rm{1}}{\rm{.4812}}$.

    图 8  不同结构光纤的LP01模的模场分布 (a)圆形结构; (b)花瓣结构

    Figure 8.  Field distributions of LP01 mode with various circle structures: (a) Circle structure; ( b) petal-shape structure.

    图 9  两种MOF的模式损耗对比 (a) LP01模和LP11模损耗曲线; (b) LP21模和LP02模曲线

    Figure 9.  Loss of two MOF: (a) Loss band of the LP01 mode and LP11 mode; (b) loss band of the LP21 mode and LP02 mode.

    图 10  纤芯 LP01模式在双超模群时的两种超模群区间LP01模损耗 (a)波长为1550 nm, 温度改变量相同; (b)温度相同, 波长改变

    Figure 10.  Dependence of the loss of the core LP01 mode locating in different two super-mode region: (a) With same temperature variation at wavelength 1550 nm; (b) with various wavelength at the same temperature.

  • [1]

    Turukhin A, Sinkin O V, Batshon H G, Zhang H, Sun Y, Mazurczyk M, Davidson C R, Cai J X, Bolshtyansky M A, Foursa D G, Pilipetskii A 2016 Proceedings of Optical Fiber Communications Conference and Exhibition (OFC 2016) Anaheim, California, USA. March 20−24, 2016

    [2]

    Hong X, Zeng X, Li Y, Mo Q, Tian Y, Li W, Liu Z, Wu J 2016 Appl. Opt. 55 9360Google Scholar

    [3]

    姚殊畅, 张敏明, 唐明, 沈平, 刘德明 2013 物理学报 62 144215Google Scholar

    Yao X C, Zhang M M, Tang M, Sheng P, Liu D M 2013 Acta Phys. Sin. 62 144215Google Scholar

    [4]

    Koebele C, Salsi M, Sperti D, Tran P, Brindel P, Mardoyan H, Bigo S, Boutin A, Verluise F, Sillard P, Astruc M, Provost L, Cerou F, Charlet G 2011 Opt. Express 19 16593Google Scholar

    [5]

    Sarmiento S, Altabas J A, Izquierdo D, Garces I, Spadaro S, Lazaro J A 2017 J. Opt. Commun. Netw. 9 1116Google Scholar

    [6]

    Ramachandran S, Fini J M, Mermelstein M, Nicholson J W, Ghalmi S, Yan M F 2008 Laser Photon. Rev. 2 429Google Scholar

    [7]

    Driscoll J B, Grote R R, Souhan B, Dadap J I, Lu M, Osgood R M 2013 Opt. Lett. 38 1854Google Scholar

    [8]

    Nobutomo H, Kuimasa S, Taiji S, Takashi M, Kyozo T, Masanori K, Fumihiko 2013 Opt. Express 21 25752Google Scholar

    [9]

    Riesen N, Love J D 2012 Appl. Opt. 51 2778Google Scholar

    [10]

    Saitoh F, Saitoh K, Koshiba M 2010 Opt. Express 18 4709Google Scholar

    [11]

    Yu C P, Liou J H, Chiu Y J, Taga 2011 Opt. Express 19 12673Google Scholar

    [12]

    Tsekrekos C P, Syvridis, 2012 IEEE Photonic Tech. L. 24 1638Google Scholar

    [13]

    Chang S H, Chung H S, Ryf R, Fontaine N K, Han C, Park K J, Kim K, Lee J C, Lee J H, Kim B Y, Kim Y K 2015 Opt. Express 23 7164Google Scholar

    [14]

    Chang S H, Moon S R, Chen H, Fontaine N K, Park K J, Kim K, Lee J K 2017 Opt. Express 25 5734Google Scholar

    [15]

    Pureur V, Knight J C, Kuhlmey B T 2010 Opt. Express 18 8906Google Scholar

    [16]

    Park K J, Song K Y, Kim Y K, Lee J H, Kim B Y 2016 Opt. Express 24 3543Google Scholar

    [17]

    Yerolatsitis S, Harrington K, Thomson R R, Birks T A 2017 Optical Fiber Communications Conference and Exhibition (Ofc 2017) Los Angeles, California, USA. March 19−23

    [18]

    Velazquez-Benitez A M, Alvarado J C, Lopez-Galmiche G, Antonio-Lopez J E, Hernandez-Cordero J, Sanchez-Mondragon J, Sillard P, Okonkwo C M, Amezcua-Correa R 2015 Opt. Lett. 40 1663Google Scholar

    [19]

    Sai X, Li Y, Yang C, Li W, Qiu J, Hong X, Zuo Y, Guo H, Tong W, Wu J 2017 Opt. Lett. 42 4355Google Scholar

    [20]

    Chen M Y, Chiang K S 2016 IEEE J. Sel. Top. Quant. 22 4900307

    [21]

    姚建铨, 王然, 苗银萍, 陆颖, 赵晓蕾, 景磊 2013 中国激光 40 0101002

    Yao J Q, Wang R, Miao Y P, Lu Y, Zhao X L, Jin L 2013 Chinese J. Lasers 40 0101002

    [22]

    吴倩, 郭晓晨, 施伟华 2018 物理学报 67 184212Google Scholar

    Wu Q, Guo X C, Shi W H 2018 Acta Phys. Sin. 67 184212Google Scholar

    [23]

    Qi T, Jung Y, Xiao L, Wang J, Xiao S, Lu C, Tam H Y, Peacock A C 2016 Opt. Lett. 41 4763Google Scholar

    [24]

    程兰, 罗兴, 韦会峰, 李海清, 彭景刚, 戴能利, 李进延 2014 物理学报 63 074210Google Scholar

    Cheng L, Luo X, Wei H F, Li H Q, Peng J G, Dai N L, Li J Y 2014 Acta Phys. Sin. 63 074210Google Scholar

    [25]

    Stone J M, Pearce G J, Luan F, Birks T A, Knight J C, George A K, Bird D M 2006 Opt. Express 14 6291Google Scholar

    [26]

    Argyros A, Birks T A, Leon-Saval S G, Cordeiro C M B, Russell P S 2005 Opt. Express 13 2503Google Scholar

    [27]

    Park J, Kang D E, Paulson B, Nazari T, Oh K 2014 Opt. Express 22 17320Google Scholar

    [28]

    Dimitropoulos D, Houshmand B, Claps R, Jalali B 2003 Opt. Lett. 28 1954Google Scholar

    [29]

    Poon J, Istrate E, Allard M, Sargent E H 2003 IEEE J. Sel. Top. Quant. 39 778Google Scholar

    [30]

    Samoc A 2003 J. Appl. Phys. 94 6167Google Scholar

    [31]

    Zhang R, Teipel J, Giessen H 2006 Opt. Express 14 6800Google Scholar

    [32]

    Couris S, Renard M, Faucher O, Lavorel B, Chaux R, Koudoumas E, Michaut X 2003 Chem. Phys. Lett. 369 318Google Scholar

    [33]

    Liu Y Q, Guo Z Y, Zhang Y, Chiang K S, Dong X Y 2000 Electron. Lett. 36 56

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  • Abstract views:  9922
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  • Cited By: 1
Publishing process
  • Received Date:  23 October 2018
  • Accepted Date:  23 January 2019
  • Available Online:  01 April 2019
  • Published Online:  20 April 2019

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