Progress in research of polymer optical fiber communication and sensing
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摘要: 光纤技术的诞生使得信息传输速度显著提高，目前已经进入了光纤技术应用的全新阶段。在这个阶段中，聚合物光纤作为一种新型光纤备受关注，由于其材料的性质，比硅光纤更加柔软、轻便以及成本更低廉；同时，聚合物光纤的成型和处理方式也比硅光纤更加灵活，可以根据不同的需求和应用进行定制。随着制造和性能的不断改进，聚合物光纤在传输和传感领域都显示出了强大的潜力和多种应用的可能性，如光纤通信、物理研究、健康监测、生物医疗和环境监测等。介绍了聚合物光纤在上述领域的应用，总结了聚合物光纤在光纤通信和传感应用中的前景，最后指出了未来的研究方向。Abstract: The birth of fiber optic technology makes the information transmission speed greatly improved, now we have entered a brand new stage of fiber optic technology application. In this stage, polymer optical fiber as a new type of optical fiber has attracted much attention. Due to the nature of its material, it is softer, lighter and cheaper than silicon fiber. At the same time, polymer fiber is more flexible than silicon fiber in terms of forming and handling, and can be customized for different needs and applications. With continuous improvements in manufacturing and properties, polymer optical fibers show strong potential and multiple applications in both transmission and sensing, such as fiber optic communications, physics research, health monitoring, biomedical and environmental monitoring. The applications of polymer optical fibers in these fields are presented in turn, the prospects of polymer optical fibers in fiber optic communication and sensing applications are summarized, and finally, future research directions are indicated.
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0. 引言
奇异光学是现代光学的重要分支[1-2]。自1973年NYE等人提出波在传输过程中波前存在缺陷[3]，光学中的奇异现象就引起了研究人员的兴趣。1992年，ALLEN及其同事基于拉盖尔-高斯光束提出了光的轨道角动量[4]，引起了研究奇异光学的热潮。在奇异光学中，相位奇异是指标量光场相位为涡旋相位，表现为光场中存在强度为0的点，围绕该点的封闭路径的相位变化是2π的整数倍，该倍数即为拓扑荷。对于相位奇异，其拓扑荷通常为整数，但是也存在为非整数的情况。BERRY从理论上预测了分数涡旋相位的相位阶梯不连续将导致奇异线，并在其传播过程中会产生一系列复杂的演化[5]。LEACH等人在实验中观察到了该现象[6]。GBUR则发现这种复杂的演化与希尔伯特旅馆悖论密切相关[7]。XIONG等人利用连续镜面反射镜实现了对分数涡旋光束的动态调控[8]。
此外，对于矢量光场，存在着偏振奇异现象[9]。对于2维非均匀椭圆偏振光场，偏振奇异是指光场中无法定义其偏振方向的圆偏振点(C-points)或无法定义其偏振旋向的线偏振线(L-lines)。对于C点，其拓扑荷为±1/2。此外，还有光场中均为线偏振，但偏振方向成径向或旋向分布的柱矢量光束(V-points)和高阶偏振奇点。目前，偏振奇异光场可以由基于拉盖尔-高斯光束[10]、贝塞尔-高斯光束[11]、马修-高斯光束[12]、圆艾里光束[13]、分数涡旋光束[14]等新型光场得到。研究人员已经将偏振奇异应用于光学显微操作[15]、光学微加工[16]和光学通信等方面[17]。同时，偏振奇异还带来了很多有趣的物理现象，比如伪拓扑性[18]、奇点结19]、奇点爆炸[20]以及C点偶极子的产生与湮灭等[21]。对于V点，其拓扑荷通常为整数，然而ZHANG等人研究了V点拓扑荷为分数的情形，可以观察到偏振奇异线[22]。此后，他们又创造实现了Julia分数矢量光场，并验证了其伪拓扑性[18]。GU等人从理论和实验两方面研究了弱聚焦分数矢量光束的自旋角动量分离和传输特性[23]。
另一方面，无衍射光束因其独特的传输特性近些年来也越来越受到研究人员的关注，而其中艾里光束更是由于其加速性和自愈性吸引了大量的研究[24]。基于艾里光束，EFREMIDIS等人又提出了圆艾里光束[25]，而后研究人员将其与涡旋相位结合，提出了艾里涡旋光束，并研究了其传播性质[26-28]。虽然C点的拓扑荷为分数，但是其通常基于整数拓扑荷的涡旋光束生成得到，对基于分数涡旋光束的偏振奇异光场虽已提出，但尚未研究其传输特性。本文中拟用携带分数涡旋相位的圆艾里光束来进行偏振奇异光场的传播特性研究。利用两束正交圆偏振的圆艾里光束的叠加，其中一束拓扑荷为0，另一束拓扑荷为分数，可以得到基于分数涡旋光束的偏振奇异光场，并且可以控制偏振奇异光场的拓扑荷并非传统的C点的±1/2，圆艾里光束的自聚焦特性会影响该光场在自由空间传播中的拓扑结构。本文中的研究展示了基于圆艾里光束的分数偏振奇点在传播过程中的拓扑结构演变，为其应用于自由空间光通信做好了理论基础，从而拓宽了圆艾里光束的应用场景。
1. 基于分数圆艾里涡旋光束的偏振奇异光场
为生成得到偏振奇异光场，采用了生成全庞加莱光束的方法[10]，即叠加两束正交偏振的圆偏振光。位于初始平面z=0的叠加光场可以表示为[10]:
\boldsymbol{E}(\boldsymbol{r} ; \gamma)=\cos \gamma \cdot \boldsymbol{e}_1 U_1(\boldsymbol{r})+\sin \gamma \cdot \boldsymbol{e}_{\mathrm{r}} U_2(\boldsymbol{r}) (1) 式中: r为空间向量; γ为控制光束强度的常量参数; el和er分别为左旋和右旋圆偏振基矢量; U1(r)和U2(r)分别为携带或不携带涡旋相位的圆艾里光束。位于初始平面的携带涡旋相位的圆艾里光束，其电场在柱坐标系(r, φ, z)中可表示[26]:
\begin{aligned} U(r, \varphi, z=0)= & A_0 \cdot A\left(\frac{r_0-r}{w_0}\right) \exp \left(a \frac{r_0-r}{w_0}\right) \cdot \\ & {[r \exp (\mathrm{i} \varphi)]^l } \end{aligned} (2) 式中: A0为振幅常量; A(·)为艾里函数; r0为主艾里光环的半径; w0为径向缩放; a为决定传播距离的衰变参数; l为涡旋相位的拓扑荷。对于l=0，即代表圆艾里光束不携带涡旋相位。
为生成分数偏振奇异光场，将U1设置为携带涡旋相位且拓扑荷l为分数数值的圆艾里光束，U2为不携带涡旋相位的圆艾里光束。设定光场U1中l的数值为0.1、0.3、0.5、0.7、0.9和1.0，设定γ=π/4，r0=1 mm，w0=0.08 mm，a=0.1，光场尺寸为4 mm×4 mm。将上述参数结合式(1)和式(2)，即U1为左旋圆偏振、U2为右旋圆偏振时，初始平面光场的偏振态分布如图 1所示。图中偏振椭圆的不同颜色代表了不同的旋向，绿色为右旋偏振，红色为左旋偏振。图 1展示了左旋分量U1中的拓扑荷不同时，光场偏振态分布的演化过程。当l=0.1时，光场偏振态接近于线偏振；随着l数值的不断变大，光场中偏振椭圆的椭圆率也随之变大；当l=1.0时，光场中出现了一个圆偏振点，即C点，此时光场的偏振态分布是一个典型的“柠檬”结构；当l取其它数值时，虽然其偏振态分布与“柠檬”结构相似，但是其光场中并没有圆偏振点，可将其称为“准柠檬”结构。
![图 1 左旋圆偏振分量U1中不同拓扑荷(l≤1.0)时初始平面光场的偏振态分布]()
图 1 左旋圆偏振分量U1中不同拓扑荷(l≤1.0)时初始平面光场的偏振态分布Figure 1. Polarization states of light fields in the initial plane for different values of topological charge (l≤1.0) in left-handed circularly polarized component U1与之类似，将U1设置为右旋圆偏振、U2为左旋圆偏振时，初始平面光场的偏振态分布如图 2所示。此时初始平面的偏振态从接近于线偏振逐渐变化到“星”结构；当l取其它数值时，其偏振态分布可称为“准星”结构。
![图 2 右旋圆偏振分量U1中不同拓扑荷(l≤1.0)时初始平面光场的偏振态分布]()
图 2 右旋圆偏振分量U1中不同拓扑荷(l≤1.0)时初始平面光场的偏振态分布Figure 2. Polarization states of light fields in the initial plane for different values of topological charge (l≤1.0) in right-handed circularly polarized component U1l＞1.0时的情形同样值得关注，以U1为左旋圆偏振为例，当拓扑荷l取值为1.1、1.3、1.5、1.7、1.9和2.0时，初始平面的偏振态分布如图 3所示。结合图 1中l=1.0的情形，图 3展示了光场从“柠檬”到高阶偏振奇异光场的演化过程。
![图 3 左旋圆偏振分量U1中不同拓扑荷(l＞1.0)时初始平面光场的偏振态分布]()
图 3 左旋圆偏振分量U1中不同拓扑荷(l＞1.0)时初始平面光场的偏振态分布Figure 3. Polarization states of light fields in the initial plane for different values of topological charge (l > 1.0) in left-handed circularly polarized component U12. 偏振奇异光场的动态传输
对于圆艾里光束，无论是否携带涡旋相位，其在自由空间传输时的光场都无法用解析式U(r, φ, z)来表示，因此只能用数值模拟的方式来展现其在某特定传输距离z时的光场分布。在此采用角谱的方法来进行计算，即在初始平面通过快速傅里叶变换将其变换到频域，通过乘以传递函数，得到传输距离z处的频谱，再经过快速傅里叶逆变换，得到其在z处空域的光场分布[29]。对于传输距离z，分别选取为100 mm，400 mm，464 mm和500 mm，可以数值模拟U1和U2在各传输距离的光强分布。其中对于U1，分别选取l=0.5和l=1.5为例，如图 4所示。可以看到，无论是否携带涡旋相位，也无论拓扑荷l的数值，随着传播距离z的不断变大，U1和U2主光环的尺寸在不断减小，这印证了圆艾里光束的自聚焦特性。在传输距离z=464 mm时，光场尺寸达到最小值，而后又随着传输距离不断变大，即二者的焦距均为464 mm。
![图 4 不同传输距离z时U1和U2的光场强度分布]()
图 4 不同传输距离z时U1和U2的光场强度分布Figure 4. Intensity distribution of light fields U1 and U2 at different propagation distances z根据图 4中两个正交圆偏振分量的光场分布，可以计算得出在传输距离z处叠加光场的偏振态分布，如图 5所示。需注意的是, 图 5中第1列光场尺寸是3 mm×3 mm，而后3列的光场尺寸为1 mm×1 mm。从图示来看，光场中偏振椭圆的分布规律并不明显，将在下一节中讨论这一问题。
![图 5 不同传输距离z处叠加光场的偏振态]()
图 5 不同传输距离z处叠加光场的偏振态Figure 5. Polarization states of the superposed light fields at different propagation distances z3. 分析与讨论
为研究光场的拓扑结构，斯托克斯相位是一个非常重要的参量[30]。斯托克斯相位场中的相位奇异点对应矢量光场中的偏振奇异点，其表达式为[30]:
S_{12}=S_1+\mathrm{i} S_2 (3) 式中: S1、S2分别为斯托克斯参量; i为虚数单位。斯托克斯相位ϕ=arctan(S2/S1)，对于U1, l=0.5+U2, l=0, 在不同传输距离z处的斯托克斯相位场计算如图 6所示。在初始平面，斯托克斯相位从-π/2变化到π/2;而在其传输过程中，其相位的变化均为从-π到π。在传输过程的初段，可以看到其中心涡旋结构遭到破坏，经过一段距离之后，如z为464 mm和500 mm处，发现相位场中又至少出现了一个相位奇异点，如图中红色圆圈所示。
![图 6 叠加光场U1, l=0.5+U2, l=0在不同传输距离z处的斯托克斯相位场]()
图 6 叠加光场U1, l=0.5+U2, l=0在不同传输距离z处的斯托克斯相位场Figure 6. Stokes phase fields of superposed light fields U1, l=0.5+U2, l=0 at different propagation distances z如果将传输距离z=464 mm和z=500 mm两处的光场尺寸缩放到0.2 mm×0.2 mm，这个局部区域的光场偏振态分布如图 7所示。图中黄线表示S1=0，蓝线表示S2=0，两者交点，即图中实心红圆即为偏振奇异点。也就是说在初始平面不存在偏振奇异点的情况下，经过一定距离的传输，光场中出现了偏振奇异点。
![图 7 U1, l=0.5+U2, l=0中心为0.2 mm×0.2 mm的区域在不同传输距离z的偏振态分布]()
图 7 U1, l=0.5+U2, l=0中心为0.2 mm×0.2 mm的区域在不同传输距离z的偏振态分布Figure 7. Polarization states of the center section 0.2 mm×0.2 mm of U1, l=0.5+ U2, l=0 at different propagation distances z对于U1, l=1.5+U2, l=0的情形，不同传输距离的斯托克斯相位场如图 8所示。由图可以看出，在初始平面，斯托克斯相位场仅包含一个相位奇异点，而在传输距离z=464 mm和z=500 mm处，至少都包含两个相位奇异点。
![图 8 叠加光场U1, l=1.5+U2, l=0在不同传输距离z处的斯托克斯相位场]()
图 8 叠加光场U1, l=1.5+U2, l=0在不同传输距离z处的斯托克斯相位场Figure 8. Stokes phase fields of superposed light fields U1, l=1.5+U2, l=0 at different propagation distances z同样地，可以得出在z=464 mm和z=500 mm处中心0.2 mm×0.2 mm区域的偏振态分布，如图 9所示。结合图 8可以看出，在传输初期拓扑结构遭到破坏的情况下，经过一定的传输距离之后依旧可以重建，并且出现了更多的偏振奇异点。结合图 7可以看出，基于圆艾里光束的分数偏振奇点在空间中传播时拓扑结构的可恢复性，利用这一特性可将该偏振奇点用于自由空间光通信中。
![图 9 U1, l=1.5+U2, l=0中心为0.2 mm×0.2 mm的区域在不同传输距离z的偏振态分布]()
图 9 U1, l=1.5+U2, l=0中心为0.2 mm×0.2 mm的区域在不同传输距离z的偏振态分布Figure 9. Polarization states of the center section 0.2 mm×0.2 mm of U1, l=1.5+ U2, l=0 at different propagation distances z4. 结论
由于圆艾里光束的自聚焦特性，叠加光场在传播过程之初，主瓣半径不断减小直至其焦点；由于分数涡旋光束的传输特性，叠加光场在传输之初存在缺口，然后得以闭合。无论其在初始平面有无C点，当叠加光场传输到焦点时，光场中出现了C点，并在焦点之后的传输过程中将出现更多的C点。与基于整数圆艾里涡旋光束的偏振奇异光场相比[13]，两者均具有奇异拓扑结构的自恢复特性，然而基于分数的涡旋光束会给恢复后的光场中带来更多的C点。该工作从理论和数值模拟研究了对基于分数涡旋光束的偏振奇异光场在自由空间传输时拓扑结构的演变规律，为其应用提供理论基础。
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图 3 a—轮状结构悬浮梯度折射率多孔芯光纤[51] b—方晶格多孔芯微结构光纤[57] c—传统六方晶格包层的多孔芯微结构光纤[58] d—六角多孔包层菱形多孔芯微结构光纤[59] e—椭圆七水平开槽气孔芯微结构光纤[62] f—基于圆形的星形微结构光纤[63] g—矩形气孔悬槽芯微结构光纤[64] h—六边型圆形气孔包层的可变长度矩形槽悬槽芯微结构光纤[65] i—八角型四方形包层开槽芯微结构光纤[66] j—六边型圆形气孔包层的多孔芯微结构光纤[70] k—带有4管嵌套半椭圆包层管的微结构光纤[71]
Figure 3. a—wheel-like structure suspended gradient refractive index porous core fiber[51] b—square lattice porous core microstructured fiber[57] c—conventional hexagonal lattice cladding porous core microstructured fiber[58] d—hexagonal porous cladding rhombic porous core microstructured fiber[59] e—elliptical seven-level horizontally slotted porous core microstructured fiber[62] f—circular-based star microstructured fiber[63] g—rectangular porous overhanging slot core microstructured fiber[64] h—hexagonal circular porous cladding variable length rectangular slot overhanging slot core microstructured fiber[65] i—octagonal tetragonal cladding slotted core microstructured fiber[66] j—porous core microstructured fiber with hexagonal circular aperture cladding[70] k—microstructured fiber with 4-tube nested semi-elliptical cladding tubes[71]
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图 4 a—脉搏监测传感器的配置和监测结果[77] b—传感器于胸部定位和心率呼吸率仿真结果[82] c—传感器在手肘关节处的位置和关节角度测量结果[92] d—POF传感器在肘关节处的定位和对弯曲角度的响应曲线[93]
Figure 4. a—configuration of the pulse monitoring sensor and monitoring results[77] b—sensor localization on the chest and heart rate simulation results[82] c—sensor position on the elbow joint and joint angle measurements[92] d—position of the POF sensor on the elbow joint and response curves to bending angles[93]
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图 5 a—SPR传感原理示意图 b—透射光谱
Figure 5. a—schematic diagram of the SPR sensing principle b—transmission spectra
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图 6 a—带有溅射金膜POF的平面[144] b—带有溅射金膜POF的截面示意图[144] c—传感原理示意图[145] d—湿度传感器制造和3-D示意图[147]
Figure 6. a—schematic of planar with sputtered gold film POF[144] b—cross section with sputtered gold film POF[144] c—schematic of the sensing principle[145] d—schematic of the humidity sensor fabrication and 3-D[147]
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表 1 POF的通信性能
Table 1 Performance of the POF for communication
类型 芯材 波长/nm 损耗 带宽 传输速率/(Gbit·s-1) 特点 参考文献 SI PMMA — 160 dB/km 200 MGz·50m — 商业ESKA MH [27] GI PMMA 650 140 dB/km 1.5 GHz·100m — 高温高湿稳定性 [28] GI PMMA 650 — 2.32 GHz·100m 1~2.5 超低弯曲损耗 [29] GI CYTOP 632 — 200 MHz·km — 多模光纤干涉仪 [30] GI BPT to PMMA 650 800 dB/km 4.0 GHz·50m — 高热稳定性 [31] GI adding DBT to PS 670~680 166 dB/km~193 dB/km 4.4 GHz·50m — 高带宽；热稳定性 [32] GI PF 850 — — 120 高速传输 [33] GI halogenated polymers 850 65 dB/km 26.5 GHz·100m 10 低噪声 [34] SI PS 670 — — — 超高带宽数据通信 [35] GI PMMA 850 60 dB/km 500 MHz·km — 高质量的信号RoF传输 [36] SI PMMA 650 — 500 MHz·10m 1~5(10 m) 低误比特率(10-10) [37] GI PMMA 850 1.04 dB/m 26.5 GHz·m — 低噪声；高稳定数据传输 [38] 
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表 2 MPOF通信性能
Table 2 Performance of the MPOF for communication
x光纤 材料型号 芯孔x直径/m 带宽/THz 损耗/cm-1 色散/(ps·THz-1·cm-1) 特点 参考文献 图 3a TOPAS 432 0.71~0.95 0.06 0.14±0.07(0.8 THz~1 THz) 超平坦近零色散，GI悬浮多孔芯 [51] 图 3b ZEONEX 390 0.7~1.15 0.06 0.85±0.12 低EML；宽带低色散变化；功率分数(47%) [57] 图 3c TOPAS 300 0.4~1.7 0.04 0.47±0.05 平坦近零色散 [58] 图 3d ZEONEX 54.1 0.7~1.5 0.0145(0.7 THz) 0.469±0.246(0.8 THz~1.3 THz) 高功率分数(75%)；极低弯曲损耗(3.1×10-20 cm-1) [59] 图 3e TOPAS — 0.85~1.7 0.056 ＜0.5 双折射(9.73×10-2)；机械稳定 [62] 图 3f TOPAS 355 0.5~2.5 0.016 — 超低损耗；大有效面积(1.38×106 μm2) [63] 图 3g TOPAS 400 0.8~1.2 0.016(TE), 0.028(TM) 0.54±0.08(TE), 0.94±0.1(TM) 高双折射(0.09)；低损耗；平坦色散 [64] 图 3h TOPAS 270 0.5~1.6 0.025 0.65±0.05 低EML，高双折射(0.0911) [65] 图 3i TOPAS 290 0.4~2.1 0.007(0.5 THz) 0.3±0.1 超低损耗；大模有效面积(4×10-6 m2) [66] 图 3j ZEONEX — 0.2~1 0.0180~0.0345(0.3 THz~0.5 THz) -0.285±0.02(0.39 THz~0.45 THz) 低EML；平坦近零色散 [70] 图 3k ZEONEX — 0.42~0.60 0.98dB/m(0.5 THz) — 小尺寸；最高PLR [71]
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表 3 不同液体传感器性能比较
Table 3 Performance comparison of different liquid sensors
分析物 频率/THz 有效材料损耗/cm-1 约束损耗 双折射率 有效面积/μm2 相对灵敏度/% 参考文献 水 2.4 0.0061 1.64×10-13 cm-1 — — 97.60 [104] 甲醇 2.0 0.00085 2×10-16 dB/cm 0.00015 1.85×108 99.36 [105] 乙醇 1.7 0.0057 3.85×10-13 cm-1 — 3.12×105 93.80 [106] 苯 1.4 0.0027 8.63×10-16 cm-1 0.007 1.49×105 98.92 [107] HCN 2.0 0.023 1.62×10-9 cm-1 0.009 — 85.80 [108] 血红蛋白 1.5 — 1.135×10-14 cm-1 — 1.66×105 80.56 [109] 福尔马林 1.8 0.0048 2.798×10-11 cm-1 — 9.77×105 77.71 [110] 苯丙胺 1.0 0.02 6.2×10-8dB/m — 1.39×105 89.50 [111] 煤油 1.0 0.0025 2.16×10-8 cm-1 — — 97.6 [112] 神经毒剂 1.8 0.00859 1.71×10-14 cm-1 0.00682 — 94.40 [113] 汽油 2.8 0.0072 8.10×10-9 cm-1 — — 96.87 [114]
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表 4 不同温度光纤传感器性能参数
Table 4 Performance parameters of fiber optic sensors for different temperatures
结构 长度/mm 温度/℃ 灵敏度/(nm·℃-1) 参考文献 PMMA POF — 15~45 0.1275 [115] UCNP-SPOF 25 25~70 — [117] CYTOP POF 10 30~40 0.0143 [118] PMMA-POF — 25~100 1.04 [119] PEDOT：PSS-SPOF 20 21~70 — [121] PDMS-assisted BFS 27 21~25 -1.63 [122] SMF-FPI 100 36.0~36.4 83.13 [123] the SMF end-face coated with PDMS — -30~85 0.698 [124] ZnO@Gr/MMF-TSCF-MMF 10 89~98 0.33268 [125] dual-core toluene and ethanol filled PCF — 0~70 -11.64 [126] -80~0 -7.41 SCF-EU-LPFG 5.5 30~100 0.53 [127] MMF-TDF-MMF 7 100~650 0.088 [128] 650~850 0.150 900~1000 0.285
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