Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering

Li Tianfu; Ba Dexin; Zhou Dengwang; Ren Yuli; Chen Chao; Zhang Hongying; Dong Yongkang

doi:10.12086/oee.2022.220021

Abstract

Abstract

Forward stimulated Brillouin scattering (F-SBS), a 3-order nonlinear effect in optical fibers, has become the hotspot in recent years, due to its great potential in substance identification, and fiber diameter measurement, etc. Through research and analysis of the progress of F-SBS, the main principle and key techniques are generalized in this paper. Distributed sensing schemes based on local light phase recovery, opto-mechanical time-domain reflectometry, and opto-mechanical time-domain analysis are emphatically introduced here. With the gradual practical application of F-SBS, the demand for distributed measurement of F-SBS with high precision and high spatial resolution becomes more and more significant, which will be the main research direction of F-SBS in optical fibers in the future.

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1. 引　言

本文从F-SBS的发展沿革出发，推导了F-SBS的理论模型，研究其进行传感的具体原理，并综述了F-SBS的测量方案及其衍生的传感技术，详细介绍了分布式F-SBS传感技术及当前先进的光力时域分析技术的具体原理。

F-SBS是一种光纤中发生的三阶非线性过程^[10]。入射光因电致伸缩效应在光纤纤芯处引起密度扰动，进而在光纤横截面内形成横向共振声波，再经弹光效应作用于入射光，发生F-SBS。在此过程中，光纤不仅作为光波导，更作为一种性能优良的声波导。横向声波由纤芯出发，在光纤与外界物质的边界发生反射，往复震荡形成一系列的共振声波模式，这使得共振声波的寿命与外界物质的声波阻抗直接相关，从而可以通过测量声波场实现外界物质声阻抗传感。在此过程中，由于光不直接接触外界物质，光路损耗大大降低；无需引入特殊光纤结构，仅用简单的单模光纤即可实现外界物质识别，系统鲁棒性极大增强；由于直接测量的是外界物质的声特性，更无需对待测液体进行标记，这相较很多物质识别手段更具实用价值^[11]。另外，由于横向声波的共振频率对光纤直径高度敏感，F-SBS也为光纤制造和质量检测行业提供了一种精度媲美扫描电子显微镜、结构上无损、高空间分辨率的分布式光纤直径测量手段^[12]。此外，F-SBS在材料特性研究^[13]、温度应变传感^[14-15]等领域也有长足的进展。

近年，光纤传感技术展现了极大的研究空间和磅礴的生命力。光纤传感技术通过测量光强、波长、频率、相位、偏振态等参量在被测物理量作用下的变化感知外界信息，其兼具灵敏度高、安全性强、便于布设、抗电磁干扰等优势，已经逐渐成为了现代信息创新产业的重要一环。现行的光纤传感技术已经实现了多达上百种物理量的传感测量，大多衍生自温度、应变、折射率等，被运用于结构健康监测、地质探测、超声测量、生物医学等领域^[1-6]。作为一种光学手段，光纤传感技术在以折射率传感和吸收光谱为代表的物质识别领域具有巨大优势^[7-9]。然而，为了获取更强的测量灵敏度，常需要构建特殊的光纤结构增加光场与外界物质的重叠面积，这带来了相当的复杂性和不稳定性。基于前向受激布里渊散射(forward stimulated Brillouin scattering, F-SBS)的光纤声阻抗传感技术另辟蹊径，用声代光作为触角，使用无损单模光纤即可实现外界物质识别，成为了近年研究的热点，有望在未来污染监测、无标微流检测、光纤直径测量，以及生物医学等方面发挥重要作用。

2. 前向受激布里渊散射的基本原理

2.1 F-SBS的发展概述和基本原理

\begin{aligned} ω_{p} & = ω_{s} + Ω_{B} \\ k_{p} & = k_{s} + q \end{aligned} .

F-SBS之所以被称为导波声波布里渊散射，是因为这一散射过程只能出现在波导中，而非自由空间内。不同于B-SBS过程中发生作用的轴向声波，F-SBS过程中的声波是在波导截面内的横向声波(transverse acoustic wave, TAW)。在以光纤为代表的圆柱形波导中，受纤芯与包层的折射率差限制，光波仅在轴向传输；而声波则不然，纤芯和包层的机械性能相近，可以视作整体，当纤芯密度扰动时，声波会向各个方向传输，从而在横截面共振。当强激光注入光纤中，由于电致伸缩作用，光强的大小会影响密度和折射率，从而在光场集中分布处，即纤芯处产生密度波动，进而形成声波震荡。共振声波稳定存在的条件是其共振频率满足波导的本征共振频率，这时，声波在边界反射前后恰能形成驻波。波导的本征共振频率可以通过声波的微分方程求解^[26-27]。在以光纤为代表的圆柱形波导中，位移的径向分量可以用第一类$n$阶贝塞尔函数${{\text{J}}_n}$表示，$n$为波导截面一周声波强度最小值的个数。

标准单模光纤(Standard single-mode fiber, SMF)中的${{\rm{R}}_{0,m}}$模和${{\rm{TR}}_{2,m}}$模的位移场在图3中给出。显然，当位移场与光场重叠面积最大时，光-声(电致伸缩效应)、声-光(弹光效应)之间都有最大的作用效率。因此，SMF中F-SBS的强度随阶数$m$的增加而增加，在${{\rm{R}}_{0,7}}$左右处达到最大，而后逐渐变小，如图4所示。

声光相互作用的研究由来已久。1922年，Brillouin Léon提出了著名的布里渊散射^[16]，描述介质中的声学振动对所传输光的散射效应，并预言散射光频率与入射光不同。1930年，Gross首次在液体中观测到了布里渊散射，并指出布里渊频移与散射角有关^[17]。随着激光技术的不断发展，布里渊散射逐渐作为一种实用的表征和探测手段，在海洋探测^[18]、地质探测^[19]等方面都有了长足的进展。上世纪中叶，低损耗光纤的问世为布里渊散射的研究提供了新的舞台，光纤中的后向受激布里渊散射(backward stimulated Brillouin scattering, B-SBS)研究因其对温度和应变的敏感蓬勃发展，逐渐发展成为了一种高灵敏度的分布式传感手段。基于后向布里渊散射的布里渊光时域分析(Brillouin optical time domain analysis, BOTDA)^[20]、布里渊光相关域分析(Brillouin optical correlation domain analysis, BOCDA)^[21]等技术已经可以实现厘米甚至毫米量级的空间分辨，并可以在数百千米长度的光纤中实现无盲区的分布式温度和应变测量^[22-25]。

式(4)为${{\rm{R}}_{0,m}}$模式的色散关系，其中$\alpha $为横波声速${v_{\rm{T}}}$与纵波声速${v_{\rm{L}}}$之比，${v_{\rm{T}}} $和${v_{\rm{L}}} $在${\text{Si}}{{\text{O}}_{\text{2}}}$中分别为3740 m/s和5996 m/s。$k$为声波数，$r$为光纤包层的直径， ${y_m}$和$ {\omega _m} $分别为式(3)的第$m$个特征解和${{\rm{R}}_{0,m}}$模式的第$m$阶共振频率。共振声波在轴向近乎不传播，但以光速出现。换言之，每个横截面内的共振声波仅与该时刻传输的光强有关，而与相邻截面的声波近乎无关，因此其在轴向的相速度趋近于光速而群速度约为0，其声波数$k$也约为0。在$k = 0$处将式(4)重写为

其中：${\varOmega _{\rm{B}}}$是声波的角频率，$ n $为介质的折射率，${V_{\rm{A}}}$为介质的声速，${\lambda _{\rm{p}}}$为入射光在真空中的波长，$\theta $为散射光的角度。当$ \theta = 180^\circ $，即散射光与入射光方向相反时，散射光相较入射光有最大的频差；然而，当$ \theta = 0^\circ $时，即散射光与入射光同向时，上式的右侧为0，没有实际意义。这似乎也和受激布里渊散射的相位匹配关系显示的结果相一致。在受激布里渊散射的物理过程中，入射光$\left( {{\omega _{\rm{p}}}, {{{\boldsymbol{k}}_{{{{{\rm{p}}}}}}}} } \right)$、斯托克斯光$\left( {{\omega _{\rm{s}}}, {{{\boldsymbol{k}}_{\rm{s}}}} } \right)$以及声波场$\left( {{\varOmega _{\rm{B}}}, {\boldsymbol{q}} } \right)$的频率和波矢必须满足严格的匹配关系，如图1(a)所示，即：

v_{B} = \frac{Ω_{B}}{2 π} = \frac{2 n V_{A}}{λ_{p}} \sin \frac{θ}{2},

Ω_{0, m} = \frac{v_{L} {y_{m}}^{2}}{r^{2}} .

从而得到$ {\varOmega _{0,m}} $为${{\rm{R}}_{0,m}}$模式的本征共振频率。在$k$趋近于0时，存在声波频率${\omega _m} \approx {\varOmega _{0,m}}$让其相速度与光波的群速度一致，于是同向传输的入射光和斯托克斯光可以自动与该声波满足相位匹配条件。忽略波导和材料的色散，计算可以得出共振声波和光波的色散曲线，图2中的交点表示可以有效参与F-SBS过程的声波。

Figure 3. Full-Size Img PowerPoint

Transverse displacement profiles. (a) Radial mode R_0,5; (b) Torsional-radial mode TR_2,5

| \begin{matrix} [(3 - y^{2} / 2) J_{2} (α y)] & [(6 - y^{2} / 2) J_{2} (y) - 3 y J_{3} (y)] \\ [J_{2} (α y) - α y J_{3} (α y)] & [(2 - y^{2} / 2) J_{2} (y) + y J_{3} (y)] \end{matrix} | = 0,

Figure 2. Dispersion relation of R0,m-induced F-SBS. The bule solid lines represented the dispersion curve of acoustic waves, and the red one represented which of light wave. The shade of blue lines means the intensity of F-SBS.

Figure 2. Full-Size Img PowerPoint

Dispersion relation of R_0,m-induced F-SBS. The bule solid lines represented the dispersion curve of acoustic waves, and the red one represented which of light wave. The shade of blue lines means the intensity of F-SBS.

类似地，当n=2时，式(4)描述的声波场呈轴对称，被称为扭转辐射声波模式(torsional-radial mode, ${{\rm{TR}}_{2,m}}$) ^[28]。${{\rm{TR}}_{2,m}}$模式描述的声波场在扭转辐射声波模式驱动的前向布里渊散射称为去极化GAWBS，会对光波产生相位调制和偏振调制。在这种情况下，声波方程和色散关系重写为

Figure 4. Full-Size Img PowerPoint

Spectrum of R_0,m modes induced F-SBS

Ω_{2, m} = \frac{v_{T} {y_{m}}^{2}}{r^{2}} .

Figure 1. Full-Size Img PowerPoint

Phase matching. (a) Backward stimulated Brillouin scattering; (b) Forward stimulated Brillouin scattering

当$n = 0$时，声波呈圆对称，称为辐射声波模式(radial mode, ${{\rm{R}}_{0,m}}$)。${{\rm{R}}_{0,m}}$模式驱动的F-SBS称为极化GAWBS，会对光波产生相位调制。在这种情况下，声波方程等效为

B-SBS过程中，因为泵浦光和斯托克斯光方向相反，频率相近，声波矢近乎平行于x轴(波矢的斜率即波的相速度)，当三者满足相位匹配时，上述过程可以稳定存在。而在F-SBS过程中，泵浦光与斯托克斯光的方向相同，这意味着对应的声波矢斜率与光波矢平行（如图1(b)所示），即声波的相速度应与光速相同。

相较于后向布里渊散射，前向研究起步较晚。自由空间中的布里渊散射中，布里渊频移$ {v_{\rm{B}}} $被描述为

(1 - α^{2}) J_{0} (y) - α^{2} J_{2} (y) = 0,

至此，我们明晰了前向布里渊散射的物理过程。由于电致伸缩效应，光纤中传输的光强变化会导致纤芯处密度发生扰动，在特定频率下，截面内声波在边界反射后恰能与原声波相干增强，从而形成稳定存在的共振声波。根据振动模式不同，共振声波可以分为${{\rm{R}}_{0,m}}$模式和${{\rm{TR}}_{2,m}}$模式。共振声波调制纤芯折射率，影响光波的传输特性。${{\rm{R}}_{0,m}}$模振型呈圆对称，对光纤中传输的光产生相位调制，${{\rm{TR}}_{2,m}}$模振型呈轴对称，不仅改变传输光的相位，也对其偏振态进行调制。另外，当光纤中传输同向的两束差频光时，若其频差满足接近${{\rm{R}}_{0,m}}$或${{\rm{TR}}_{2,m}}$模的共振频率，两束光拍频引起的光强变化同样会导致电致伸缩效应从而激发出共振声波场，并且与后向受激布里渊散射类似，高频光将会向低频光转移能量，该部分将在3.2节详细描述。

ω_{m} = v_{L} \sqrt{k^{2} + \frac{{y_{m}}^{2}}{r^{2}}} .

在上述体系中，似乎很难有声波满足此过程，前向布里渊散射的研究也因此一度停滞。然而，1985年，Shelby等在理论和实验上观测到了由共振声波场引导的导波声波布里渊散射 (guided acoustic-wave Brillouin scattering, GAWBS) ^[10]，即F-SBS。他们将此研究描述成在传统布里渊散射理论中“not predicted (预料之外的)”。这一研究填补了布里渊散射理论的空白，也为后续研究提供了理论依据。

2.2 前向受激布里渊散射的传感原理

其中：${\tau _{{{\rm{int}}} }}$为光纤本征的声子寿命，代表着声波在材料中的自然衰减，$ \Delta {\upsilon _{\rm{s}}} $为本征线宽；式(9)、式(10)中的第二项表示过程中因边界反射带来声波衰减及其对应的频谱展宽。常用物质的声阻抗及标准单模光纤在其中的F-SBS谱宽在表1中给出。值得注意的是，在薄涂覆层的光纤，尤其是聚酰亚胺涂覆的单模光纤中，由于声波会在光纤-涂覆层边界以及涂覆层-外界物质边界处发生多次反射，共振模式的频率和寿命均受涂覆层厚度影响，散射谱宽不能简单地通过式(10)计算^[32-34]。当涂覆层足够厚时(~>50 μm)，例如商用丙烯酸酯涂覆的单模光纤中，由于声波衰减，这种多边界反射的效应可以忽略不计。丙烯酸酯和聚酰亚胺用作涂覆层时对应的谱宽在表内对应位置的括号中标出。

R = \frac{| Z_{Si O_{2}} - Z_{outside} |}{Z_{Si O_{2}} + Z_{outside}},

\frac{1}{τ} = \frac{1}{τ_{i n t}} - \frac{v_{L}}{2 r} \ln (R),

其中：${Z_{{\text{Si}}{{\text{O}}_{\text{2}}}}}$和${Z_{{\text{outside}}}}$分别为二氧化硅和外界材料的声阻抗，被定义为材料密度和声速的乘积。当外界环境声阻抗发生变化时，光纤与之边界的声反射率也随之变化，这将导致共振声波寿命变化。声波的存在会对光纤纤芯的折射率进行周期性调制，从而会作用在光波上形成相位调制。进而，测量光波的相位变化，即可反演出共振声波，从而读取其携带的外界声阻抗信息。这一过程可以直观地通过测量声波寿命完成，也可以转而测量F-SBS散射谱的谱宽。${{\rm{R}}_{0,m}}$模式的声子寿命$\tau $可以表示为

类似地，共振谱宽可以表示为

Figure 5. Full-Size Img PowerPoint

The schematic diagram of acoustic impedance sensing

Δ υ = Δ υ_{s} - \frac{v_{L}}{2 π r} \ln (R),

随着F-SBS变为现实，研究人员开始预期其像B-SBS一样在传感领域发挥重要作用。与B-SBS类似，温度和应变同样会因改变二氧化硅的声学特性而对F-SBS的频移造成影响。1998年，Tanaka等使用光纤中的${{\rm{TR}}_{2,5}}$模式激发前向受激布里渊散射，并研究了其频移与温度的关系^[14]；次年，他们又测得了其与拉伸应变的关系^[15]，二者均与前向布里渊频移呈良好的线性关系，灵敏度分别为10 kHz/℃和0.194 kHz/με。注意，因为温度和应变对共振声波场的声速影响甚微，F-SBS的温度和应变灵敏度远小于B-SBS (后向布里渊频移同时受介质折射率和声速影响，温度和应变灵敏度分别为1.17 MHz/℃和0.0478 MHz/με)^[29-30]，因此在随后很长一段时间内，前向布里渊散射并未在传感领域展现出足够的研究潜力。

根据2.1中的相关讨论可以得知，共振声波模式本质是一种存在于光纤横截面上的声驻波，其产生过程高度依赖于波导边界的声反射，其声寿命对波导边界的反射率高度敏感。声波在光纤表面处的反射率R可以用两边的声阻抗描述：

近几年，基于F-SBS的声阻抗传感技术的提出让F-SBS研究重新焕发了新的研究活力。在Shelby等1985年的实验中^[10]，他们发现覆盖了涂覆层的光纤的前向布里渊散射增益谱较裸纤会发生展宽，并将其解释成应力和双折射的影响，这在后来的研究中被验证是不完全正确的。2011年，Wang等研究了标准高非线性光纤中的前向受激布里渊散射，并将谱宽归因于光纤包层的不均匀性以及声波在包层表面处的损耗^[31]。2016年，Antman等探明了F-SBS与外界物质的作用机理，指出共振声波场的寿命与光纤边界反射率直接相关，并提出使用F-SBS测量共振声波场进行外界物质声阻抗传感^[11]。其具体原理如下：

Acoustic impedance and F-SBS spectrum width of common substances

常见物质的声阻抗和SMF在其中发生F-SBS的谱宽

物质名称	声阻抗/(kg·m⁻²·s⁻¹)	F-SBS谱宽/MHz	数据来源
空气	439.6	0.45	[35]
酒精	0.93×10⁶	2.21	[35]
水	1.483×10⁶	3.57	[36]
NaCl溶液(4%)	1.571×10⁶	3.78	[11]
NaCl溶液(8%)	1.664×10⁶	4.00	[11]
NaCl溶液(12%)	1.763×10⁶	4.24	[11]
聚酰亚胺(用作涂覆层)	3.60×10⁶	8.7(2.83)	[32]
丙烯酸酯(用作涂覆层)	3.39×10⁶	8.16(~8)	[37]
二氧化硅	13.19×10⁶	\	[32]

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3. 前向受激布里渊散射的探测手段

F-SBS的探测方法多样，适用于不同的应用场景。对于${{\rm{R}}_{0,m}}$模式驱动的F-SBS，可以分为两大类，分别为相位解调和能量转移探测。由于$ {\rm{T}}{{\rm{R}}_{2,m}} $模式的调制强度高度依赖于入射光的偏振态，也常在光路中引入扰偏器以实现${{\rm{R}}_{0,m}}$模式的独立测量^[11]。针对不同的待测参量，F-SBS测量所侧重的物理量也各不相同，这导致不同的使用需求下测量手段和所需的相位或能量分辨率也各不相同。对于温度、应变和光纤直径、泊松比等参量，研究人员有时更偏重于F-SBS频移的测量，这要求尽可能提升频谱测量的精细度，精确地测量得到共振峰值，例如提升信噪比(增加激发脉冲的峰值、使用更长的待测光纤)，发展更高效稳定的解调方案，或者在需要扫频的方案中减小扫频步长。而在物质识别及与光纤涂层相关的研究工作中，除了需要对共振频谱的精细测量外，有时声波的时域信号也包含了许多重要信息，这时基于相位解调的方案就体现出了其独特的优势，声波在各边界处的反射可以通过相位解调直观地在时域上被观察到，滤波得到的各频率成分的衰减时间也可以直接用于计算外界物质的声阻抗。此外，反演得出共振频率、共振谱宽同样也可以被用于传感，同时也为研究人员提供了多参量同时解调的可能性。另外，减少激发脉冲对读取过程的串扰也是F-SBS测量方案中的重要部分。

3.1 基于相位解调的探测方案

Figure 6. Full-Size Img PowerPoint

SI used to measure F-SBS

在共振声波场被激发到稳态后截断激发光，共振声波场仍会存续一段时间，不断震荡而后衰减。由于这段时间内没有泵浦光的存在，其余的非线性光学效应都变得极弱甚至消失，而衰减的共振声波场仍会对探测光造成影响。为了规避其他非线性效应的影响，对于共振声波场一般都通过测量衰减声波的方式进行，而这为分布式F-SBS传感技术的出现提供了契机。当使用脉冲光而非连续光读取共振声波场产生的相位调制，由于读取脉冲光对应的飞行时间是已知的，其走过的时间也标志了光纤中的空间位置。引入后向探测光和读取脉冲光作用，控制探测光频率诱导探测光依次与读取脉冲经由相位调制产生的多阶边带发生B-SBS作用，从而分别获得各阶边带在光纤不同位置处的背向布里渊散射光强度，进而能够反演出F-SBS效应产生的分布式相位调制信息，实现分布式F-SBS探测。

\begin{aligned} E (Ω, z, t) = & A (z, t) \exp [j (k z - ω t + φ_{0})] \\ \cdot \exp [j Δ φ (Ω, z) \cos (Ω t)] \\ = & A (z, t) \exp [j (k z - ω t + φ_{0})] \\ \cdot [\sum_{n = - \infty}^{\infty} j^{n} J_{n} (Δ φ (Ω, z)) \exp (j n Ω t)], \end{aligned}

2009年，Kang提出了一种波分泵探的Sagnac干涉解调方案，并在后续研究中得到广泛应用^[39]。依靠此方案，他们在光子晶体光纤中激发并观测到了前向受激布里渊散射，其原理如图7所示。光子晶体光纤中紧密排布的空气孔实现了纤芯处轴向光场的局部约束，同时也将共振声波场限制在这一范围内。实验中采用的光子晶体光纤纤芯直径为1.8 μm，长度约为10 m。因低阶模式下声场与光场几乎重合，相当大的重叠面积导致光声相互作用在低阶共振频率处展现了极高的耦合效率，获得了远高于单模光纤的前向布里渊增益($\gamma _{0,1}^{{\rm{PCF}}} = 1.5 \; {{\text{W}}^{{{ - 1}}}}{{\text{m}}^{{{ - 1}}}} > > \gamma _{0,6}^{{\rm{SMF}}} = 8 \times {10^{ - 3}} \; {{\text{W}}^{{{ - 1}}}}{{\text{m}}^{{{ - 1}}}}$)。实验中使用了脉宽100 ps、峰值功率6 W的脉冲光作为泵浦光，可以激发出10 GHz范围内的全部共振模式。在泵浦光的持续时间内，时域信号将受克尔效应影响产生畸变，这一效应会在泵浦光截断后迅速消失，而共振声波会缓慢衰减。由于泵浦光与探测光使用了不同的波长，从而可以通过滤波将强脉冲泵浦光滤除，仅探测探测光所受的影响。

其中：$k$为真空中的光波数，$L$为发生F-SBS效应的有效光纤长度。由式(14)可以得出，前向布里渊散射造成的相位调制是一个随长度累积的过程，光纤长度越长，累积的相移越大。另一方面，由于$ \Delta \varphi $与电致伸缩效应和弹光效应过程中光场与声场的交叠面积有关，这也意味着不同阶次的共振模式具有不同的F-SBS强度，在光声重叠面积最大时达到最大。在这里定义${g_{0,m}}$为F-SBS过程的增益系数，用以描述F-SBS的强度：

其中：${I_{{\text{CW}}}}$表示环路中顺时针传输的光强，${I_{{\text{CCW}}}}$表示逆时针传输的光强，$\Delta \varphi $表示F-SBS产生的相位变化。塞格纳克干涉仪的两臂光路长度严格相同，输出特性十分稳定，因此被广泛应用于解调F-SBS效应^{[11, 28, 33, 38-41]}。值得注意的是，光纤中存在一系列复杂的非线性效应。当使用高能的泵浦光去激发F-SBS效应时，同时存在的其他非线性效应——诸如克尔效应等，会使信号畸变甚至淹没信号。因此，需要使用激发与探测相分离的方式，通过波分、空分、模分、时分等方式隔离激发光，仅观测探测光被声波场的调制情况。

当$ n = 1 $时，有：

当以功率为P的入射光激发声波场时，在光纤位置$\textit{z}$处造成的折射率扰动可以表示为

I = I_{CW} + I_{CCW} + 2 \sqrt{I_{CW} \cdot I_{CCW}} \cos Δ φ,

Figure 7. Full-Size Img PowerPoint

The experimental set-up of F-SBS measurement based on SI. The excitation and probe light are separated by their different wavelengths^[39]

Q_{PE} = (\frac{a_{1}}{2} + a_{2}) \cdot ⟨ E_{0} {(r)}^{2} ρ_{0} (r) ⟩,

此外，通过不同模式分别进行激发与探测，即模分泵探技术，也是探测F-SBS效应的一种解决方案。2021年，Zadok课题组对保偏光纤中两个偏振模式的F-SBS特性进行了研究^[41]。保偏光纤中存在两个对称分布的应力棒，用于限制光场在x和y两个偏振模态中传输。由于x和y模态在光纤中共用同一声波场，因此可以实现在模内或模间进行激发与探测。采用光纤布拉格光栅(fiber Bragg grating, FBG)进行解调，这是根据信号光各边带在FBG上的反射率不同。结果如图9所示。

此外，2020年，西班牙的Díez等提出了一种使用长周期光栅(long-period grating, LPG)的高效F-SBS解调方法，其原理如图10所示^[45]。这种方法严格意义上不属于相位解调的范畴，但因其直接测量的是折射率扰动，故于本节一起讨论。该方案的待测光纤为刻写了LPG的SMF，当共振声波产生时，纤芯处折射率会持续扰动，这将导致LPG的透射谱中心波长随之抖动，即意味着当探测光入射波长固定在透射谱线性区时，F-SBS引起的折射率震荡会直接导致输出光强随之震荡，从而将F-SBS以一种更本真的方式测得。但是，由于F-SBS的非线性系数极弱，要得到可观的实验现象，至少需要峰值功率在kW级的泵浦脉冲，相较于其他方案(峰值功率W级)，系统复杂度更高，安全性也更难保证。即便如此，该方案实现了长11 cm光纤内F-SBS的激发探测，是目前报道所需的最短距离。

其中：${I^{\left( i \right)}}\left( {\Delta \varphi \left( {\varOmega ,{\textit{z}}} \right)} \right)$表示第$i$阶边带对应的光强。载波、+1和+2阶边带强度分别携带了分布式相位调制的信息，在测定这三者光强在空间的分布情况后，即可反演出分布式的F-SBS谱。为了分别测量这三者的分布式光强，引入后向SBS作为窄带滤波器将其分别滤出。

Figure 12. Distributed F-SBS sensor based on local light phase recovery. (a) Distributed light intensity of 0, +1 and +2-order sidebands; (b) Phase accumulation along the fiber; (c) Distributed phase shift demodulated by differentiation; (d)~(f) Distributed F-SBS spectrums measured when the fiber under test placed in air, ethanol, and water[36]

Figure 12. Full-Size Img PowerPoint

Distributed F-SBS sensor based on local light phase recovery. (a) Distributed light intensity of 0, +1 and +2-order sidebands; (b) Phase accumulation along the fiber; (c) Distributed phase shift demodulated by differentiation; (d)~(f) Distributed F-SBS spectrums measured when the fiber under test placed in air, ethanol, and water^[36]

Δ φ (Ω, L) = k \int_{0}^{L} Δ n (Ω, z) d z ，

g_{0, m} = \frac{ω Q_{ES} Q_{PE}}{2 \bar{ρ} n^{2} c^{2} Γ_{0, m} Ω_{0, m}} .

其中：$ \Delta \varphi \left( {\varOmega ,{\textit{z}}} \right) $表示在位置z处累积的频率为$\varOmega $的相位调制量。由贝塞尔函数特性可知：

Figure 9. F-SBS in polarization maintaining fiber. (a) Experimental set-up; (b) Measured F-SBS spectrums. The red trace is measured when the excitation light propagating in the fast axis, and probe in the slow axis; The black trace is measured in the opposite situation[41]

Figure 9. Full-Size Img PowerPoint

F-SBS in polarization maintaining fiber. (a) Experimental set-up; (b) Measured F-SBS spectrums. The red trace is measured when the excitation light propagating in the fast axis, and probe in the slow axis; The black trace is measured in the opposite situation^[41]

2018年，Thévenaz课题组提出基于本地光相位追溯技术的分布式前向布里渊散射探测技术，根据上述原理在730 m长的标准单模光纤中实现了30 m裸纤的信号还原，并用其测量了酒精和水的声阻抗，实现了根据相位解调的分布式F-SBS传感^[36]。实验中所采用的激发脉冲和读取脉冲分别来自两个不同波长的激光器，激发脉冲长约500 ns，由电光调制器进行正弦调制以实现F-SBS效应的定频激发；控制延时使读取脉冲晚于激发脉冲约10 ns，以读取激发脉冲消失后的衰减声波场，并规避激发脉冲带来的克尔效应影响。其原理如图11所示。

Figure 8. F-SBS in multi-core fiber. (a), (b) Transverse displacement profiles of modes R0,7 and R0,8; (c), (d) F-SBS spectrums measured in the inner core and outer core. The excitation light propagates in the inner core[43]

Figure 8. Full-Size Img PowerPoint

F-SBS in multi-core fiber. (a), (b) Transverse displacement profiles of modes R_0,7 and R_0,8; (c), (d) F-SBS spectrums measured in the inner core and outer core. The excitation light propagates in the inner core^[43]

Δ n (Ω, z) = \frac{Q_{ES} Q_{PE} P (Ω)}{4 \bar{ρ} n^{2} c Γ_{0, m} Ω_{0, m} [i - 2 (Ω - Ω_{0, m}) / Γ_{0, m}]},

\begin{aligned} Δ φ (Ω, z) & = 2 (\frac{J_{1} (Δ φ (Ω, z))}{J_{0} (Δ φ (Ω, z)) + J_{2} (Δ φ (Ω, z))}) \\ = 2 (\frac{\sqrt{I^{(1)} (Δ φ (Ω, z))}}{\sqrt{I^{(0)} (Δ φ (Ω, z))} + \sqrt{I^{(2)} (Δ φ (Ω, z))}}), \end{aligned}

在此过程中，F-SBS被看作相位调制器，以读取脉冲为载波，在中心频率左右各产生多阶边带。边带间隔相等，为F-SBS的共振频率，强度呈贝塞尔函数分布。这一过程可以描述为

其中：$ {Q_{{\text{ES}}}} $表示光波通过电致伸缩效应与${{\rm{R}}_{0,m}}$模式声波的交叠积分，$ {Q_{{\text{PE}}}} $表示声波通过弹光效应作用于光波的交叠积分，$P\left( \varOmega \right)$为激发光中频率为$\varOmega $的功率组分，$n$和$\bar \rho $分别为光纤的有效折射率与平均密度，$c$为真空中光速，${\varGamma _{0,m}}$和${\varOmega _{0,m}}$分别为${{\rm{R}}_{0,m}}$模的共振线宽和共振频率，${\rm{i}}$为虚数单位。${a_1} = - {n^4}\left( {{P_{11}} - {P_{12}}} \right)$，${a_2} = - {n^4}{P_{12}}$，其中${P_{11}}$和${P_{12}}$为电致伸缩张量的元。${E_0}\left( r \right)$和${\rho _0}\left( r \right)$分别为归一化的光场与声场的径向分布，$\left\langle {} \right\rangle $表示在圆面内对其积分。

TAW几乎不在光纤轴向扩散。但是，由于F-SBS过程中的TAW是因激发光的电致伸缩效应产生，其大小与纤芯处光强直接相关，可以认为其相速度与激发光群速度相同。因此，当光纤中存在与之同向传输的探测光时，由于其与声波场的相速度和传输方向都相同，探测光会不断受到因共振声波引起的折射率扰动影响，从而在光声共同传输的范围内累积出相位变化。在这个过程中累积的相位调制量可以表示为

此外，在支持多信道传输的光纤——例如七芯光纤中^[42]，泵探分离可以直接依托于不同信道完成，即空分泵探技术。2017年，Avi Zadok课题组提出了基于七芯光纤的空分泵探F-SBS探测方案，并开展了系列工作^[43-44]。在七芯光纤的包层内存在分立的七根纤芯，每根纤芯间光场相互独立，其间无法进行光场的耦合，但光纤仍为一个机械的整体，一根纤芯处产生的折射率扰动会作用在其他纤芯上，七根纤芯共用同一个声波场。他们分别仿真并实验验证了在主芯激发和在侧芯激发的情况，并分别在不同的纤芯进行探测。研究发现，侧芯激发难以形成稳定有规律的共振声波场；而在主芯激发声波场时，出现的共振声波模式与单模光纤中类似，仍为${{\rm{R}}_{0,m}}$模式和${\rm{T}}{{\rm{R}}_{2,m}}$模式，并且在主芯和侧芯探测时情况有所不同：当探测光在主芯传输时，测得的F-SBS频谱仍与单模光纤中类似；而当探测光在侧芯中传输时，由于不同阶模式的位移场分布不同，声光重叠面积小的模式则近乎消失(如图8(a)所示的R_0,7模式)，声光重叠面积大的模式仍展现了高增益(如图8(b)所示的R_0,8模式)。

Figure 11. Distributed F-SBS sensor based on local light phase recovery. The excitation and probe pulses are not only separated by wavelength, but also by time[36]

Figure 11. Full-Size Img PowerPoint

Distributed F-SBS sensor based on local light phase recovery. The excitation and probe pulses are not only separated by wavelength, but also by time^[36]

干涉仪常被用于相位解调。在最初的方案中，Shelby 等使用马赫-曾德尔干涉仪(Mach-Zehnder interferometer, MZI)解调F-SBS^[10]。值得注意的是，由于相位无法匹配，在单模光纤中，与泵浦光反向传输的探测光不会受到声波场的影响。根据这一特性，塞格纳克干涉仪(Sagnac interferometer, SI)在F-SBS解调中表现出了相当大的优势。典型的SI用以解调F-SBS的原理如图6所示。在耦合器一段注入探测光，探测光会同时在环路的顺时针和逆时针方向传输；而泵浦光则只能沿顺时针一路传输，在且仅在合束与选通间的光纤内激发光与探测光在顺时针方向共同传输，因此，探测光仅在这段光纤顺时针传输时会受到来自共振声波场的相位调制，而逆时针传输的探测光则不受影响。这样，耦合器B端输出的光强可以表示为

为了验证该方案的测量能力，Thévenaz课题组对一根730 m长的单模光纤进行了测量。为了区分测量结果，在500 m处剥除了30 m光纤的涂覆层，从而构建出一段增益更高的待测区域。由于声波场几乎被激发至稳态，F-SBS谱宽几乎不受读取脉冲长度影响，读取脉冲长度的选择仅限于B-SBS过程的声子寿命与信噪比。实验中采用了30 ns长的读取脉冲，对应空间分辨率约为3 m，结果如图12所示。然而，从累积相位转化为分布式相位涉及微分过程，这要求数据信噪比极高，因而在实际处理过程中采用分段差分的方式，这导致空间分辨率劣化至15 m以上。

\begin{array}{r} Q_{ES} = (a_{1} + 4 a_{2}) \cdot ⟨ \nabla_{⊥}^{2} E_{0} {(r)}^{2} ρ_{0} (r) ⟩, \end{array}

J_{n - 1} (Δ φ (Ω, z)) + J_{n + 1} (Δ φ (Ω, z)) = \frac{2 n J_{n} (Δ φ (Ω, z))}{Δ φ (Ω, z)} .

2021年，Thévenaz课题组在上述方案基础上继续研究，提出了基于Serrodyne的分布式F-SBS测量方案^[46]。该方案使用长度远小于声波周期的读取脉冲，读取共振声波的相位从而规避共振周期的掣肘，提升空间分辨率。实验验证的最高空间分辨率为0.8 m。

Figure 10. Full-Size Img PowerPoint

F-SBS demodulation by LPG. (a) Schematic diagram; (b) Experimental set-up^[45]

3.2 基于能量转移的探测方案

\begin{aligned} \frac{\partial A_{1}}{\partial z} = \frac{j ω_{1} Q_{P E}}{2 n c \bar{ρ}} A_{2} U \\ \frac{\partial A_{2}}{\partial z} = \frac{j ω_{2} Q_{P E}}{2 n c \bar{ρ}} A_{1} U^{*}, \end{aligned}

Figure 13. Principle of OMTDR. The energy transferred between the dual-frequency components of the pulses, and their Rayleigh scattering lights are used to demodulation[47]

Figure 13. Full-Size Img PowerPoint

Principle of OMTDR. The energy transferred between the dual-frequency components of the pulses, and their Rayleigh scattering lights are used to demodulation^[47]

实验过程中使用一根225 m长的单模光纤作为待测光纤，将末端25 m去掉涂覆层使其暴露在空气中，再将这部分中的5 m置于酒精中，如图16所示。实验结果如图17和图18所示，可以清晰地分辨出空气段与酒精段，上升和下降沿陡峭，信噪比较高。空气中测得的增益谱宽为0.45 MHz，酒精中测得的增益谱宽为2.21 MHz，与理论值符合良好。在数据处理过程中，由于使用了分段差分算法，其窗长为1 m，使得OMTDA系统空间分辨率退化为2 m，但相对于已有方案仍然提升了一个数量级。

Figure 17. Full-Size Img PowerPoint

Distributed results of OMTDA. (a) The energy transfer process along the fiber; (b) Distributed F-SBS gain spectrum^[48]

2020年，本团队提出了高空间分辨率的F-SBS分布式传感方案——光力时域分析技术(opto-mechanical time-domain analysis, OMTDA)^[35]。这种方案装置简单，解调算法便捷，消除了横向声波场寿命对空间分辨率的限制，且因其简单的后处理过程和更高的信噪比，不会在解调过程中损失空间分辨率，从而将空间分辨率提升了一个数量级以上。

于是有：

\begin{aligned} \frac{d P_{1} (Ω, z)}{d z} = & - \frac{ω_{1} Q_{E S} Q_{P E}}{2 \bar{ρ} n^{2} c^{2} Ω_{0, m} Γ_{0, m}} \\ \cdot \frac{{(Γ_{0, m} / 2)}^{2}}{{(Γ_{0, m} / 2)}^{2} + {(Ω - Ω_{0, m})}^{2}} P_{1} (z) P_{2} (z) \\ = & - g_{0, m}^{(Ω)} P_{1} (z) P_{2} (z), \end{aligned}

$i = 1,2$分别代表高频和低频光，满足${\omega _1} - {\omega _2} = \varOmega $。光波和声波分别满足麦克斯韦方程和物质密度方程：

\begin{aligned} \frac{d P_{2} (Ω, z)}{d z} = & \frac{ω_{2} Q_{E S} Q_{P E}}{2 \bar{ρ} n^{2} c^{2} Ω_{0, m} Γ_{0, m}} \\ \cdot \frac{{(Γ_{0, m} / 2)}^{2}}{{(Γ_{0, m} / 2)}^{2} + {(Ω - Ω_{0, m})}^{2}} P_{1} (z) P_{2} (z) \\ = & g_{0, m}^{(Ω)} P_{1} (z) P_{2} (z), \end{aligned}

该方案的原理核心在于，满足相位匹配的两调频脉冲产生的TAW仍是相干的。因此，可以使用长调频脉冲作为激发脉冲，先将声波场激发至稳态，而后用较短的调频脉冲读取稳态TAW。这样，既可以满足声波场所需的较长激发寿命，也可以满足高空间分辨率的实用需求。其具体原理如图15所示。

根据光功率与电场强度的关系$P = 2nc{\varepsilon _0}{\left| A \right|^2}$，可以得到两束光功率随距离的变化规律：

如式(5)所示，F-SBS频移与光纤包层直径呈反比关系，通过OMTDA技术实现对光纤的分布式直径测量^[12]，结果如图19所示。这种方法无需截断光纤，可以实现无损的直径测量，并能够实现米级分辨力的分布式测量。由于较窄的频谱宽度和较高的频谱测量精度，这种方法测量得到的共振频率反演回光纤直径能得到相当高的测量精度，实验验证与电镜分析表明，该方案的直径测量精度可达3.9 nm，远超主流商业测量方案(~100 nm)，相较于传统成像技术存在很大优势。

Figure 14. Distributed sensing results of OMTDR. (a)~(c) are the distributed F-SBS spectrums measured when the fiber under test placed in air, ethanol, and water[47]

Figure 14. Full-Size Img PowerPoint

Distributed sensing results of OMTDR. (a)~(c) are the distributed F-SBS spectrums measured when the fiber under test placed in air, ethanol, and water^[47]

由于采用了光纤中较弱的瑞利散射作为测量信号，上述方案难以获得高信噪比的测量结果。为了实现横向声波场的窄带激发，微秒级长脉冲的引入也使该方案的空间分辨率限于百米量级。F-SBS效应的弱强度与横向声波场较长的寿命成为了提升分布式F-SBS传感器空间分辨率的两只拦路虎。复杂的传感系统与较差的系统稳定性使得F-SBS分布式传感远达不到实用标准。

2009年，Kang等在光子晶体光纤中激发F-SBS的过程中，使用双频光激发F-SBS效应，不断提高注入光功率，观测到了高频光和低频光间的能量转移现象^[39]。这一过程与后向SBS类似，高频泵浦光在散射过程中产生了斯托克斯光，斯托克斯光与低频光频率相同，从而能量由高频光转移至低频光。可以由高频光、低频光、声波场间的三波耦合过程描述。考虑光波与声波在时间与空间的强度演化项为${A_i}\left( {{\textit{z}},t} \right)$和$U\left( {\textit{z},t} \right)$，有光场$ {E_i} $和声场$ \rho $：

Figure 20. (a) Experimental setup for polarization separation assisted OMTDA; (b) Temporal trace and frequency components of activation and probing pulses[49]

Figure 20. Full-Size Img PowerPoint

(a) Experimental setup for polarization separation assisted OMTDA; (b) Temporal trace and frequency components of activation and probing pulses^[49]

U (z) = \frac{ε_{0} Q_{E S}}{Ω_{0, m} Γ_{0, m} [j - 2 (Ω - Ω_{0, m}) / Γ_{0, m}]} A_{1} {A_{2}}^{*} .

Figure 18. Full-Size Img PowerPoint

Results of acoustic impedance sensing. (a) The linewidth of spectrums along the fiber; (b) F-SBS spectrums measured in air and ethanol^[48]

Figure 19. Results of distributed diameter measurements[12]. (a) Diameter distribution before and after etching and its comparison with the SEM results (A-F); (b) Diameter variations along the FUT; (c) Representative images of the fiber cross section at A, B, C and E captured by SEM

Figure 19. Full-Size Img PowerPoint

Results of distributed diameter measurements^[12]. (a) Diameter distribution before and after etching and its comparison with the SEM results (A-F); (b) Diameter variations along the FUT; (c) Representative images of the fiber cross section at A, B, C and E captured by SEM

\frac{\partial^{2} E}{\partial z^{2}} - \frac{n_{e f f}}{c} \frac{\partial^{2} E}{\partial t^{2}} = \frac{1}{ε_{0} c^{2}} \frac{\partial^{2} P^{N L}}{\partial t^{2}},

综上所述，OMTDA作为一种行之有效的分布式F-SBS测量手段，其有效性和实用性已经得到了实验验证，尤其在物质识别、光纤直径测量等领域，其不仅有相当高的空间分辨率，还兼具高信噪比和高测量精度。

g_{0, m}^{(Ω)} (Ω, z) = g_{0, m} \frac{{(Γ_{0, m} / 2)}^{2}}{{(Γ_{0, m} / 2)}^{2} + {(Ω - Ω_{0, m})}^{2}} .

在光纤一端注入双频长脉冲以激发F-SBS。当光频率差满足F-SBS共振条件时，能量由高频光转移至低频光。脉冲的背向瑞利散射可以反应入射光的两个频率成分分别在光纤各个位置处的功率，通过将二者分离开逐个分析即可获取光纤不同位置处的${P_1}$和${P_2}$，改变调制频率即可实现不同频率下的增益谱扫描。由于${\varOmega _{0,m}}$一般在百兆赫兹量级，通过传统的光学滤波器件难以将其分离，Zadok课题组通过后向布里渊散射的窄带增益特性将其分开，额外引入一路背向传输的高能连续光做布里渊滤波器，进行窄带滤波，其频率相较原频光移动${\varOmega _{{\rm{BSBS}}}} \pm {\varOmega _{0,m}}/2$，从而实现对两个成分的定频增强，实现$g_{0,m}^{\left( \varOmega \right)}\left( {\varOmega , \, {\textit{z}}} \right)$的分布式解调。该工作使用了窄线宽激光源，其瑞利散射光会因脉冲内的散射信号干涉出现剧烈的强度抖动，这会严重影响$ {P_{1,2}} $在距离上的测量稳定性和准确性。对此，Zadok课题组提出对脉冲光和放大光进行相同的相位编码，并对激光器进行波长调谐，而后进行大量平均以消除瑞利噪声。由于在空气中$ {{\rm{R}}_{0, \, m}} $模声波场的寿命在微秒量级，该工作使用了1 μs的长脉冲激发声波场以达到稳态，这决定了该技术的空间分辨率将在100 m左右。同时，因为二氧化硅电致伸缩效应较弱，噪声较强，为了获取足够的信号强度，需要对信号进行大量的平均和后处理，这也导致系统的空间分辨率继续劣化。通过剥除目标光纤段的涂覆层增强其信号，并对信号进行窗长为1 μs的移动平均，最终在3 km带涂覆层的光纤中实现了100 m裸纤的信号识别以及酒精和水的物质辨别，结果如图14所示。

\begin{aligned} g_{0, m}^{(Ω)} (Ω, z) = & \frac{P_{1} (Ω, z)}{P_{2} (Ω, z) [P_{1} (Ω, z) + P_{2} (Ω, z)]} \\ \cdot \frac{d [P_{2} (Ω, z) / P_{1} (Ω, z)]}{d z} . \end{aligned}

\begin{aligned} ρ (r, z, t) = ρ_{0} (r) U (z, t) e^{j (Ω t - q z) + c . c .} \end{aligned},

Figure 16. Full-Size Img PowerPoint

Schematic diagram of the fiber under test^[48]

为了增强横向声波，采用双频长激发脉冲光进行预激发，使横向声波场达到稳态，再用双频短脉冲光读取声波场，而后用BOTDA系统分别测量读取脉冲两频率分量的分布式能量转移情况，经扫频和后处理即可得到高信噪比的分布式F-SBS谱。在后处理过程中，对高频和低频相对应的光功率分布做除法，得到能量转移的积累过程，再微分，得到分布式F-SBS增益谱。因为不需要读取脉冲激发声波场，实验中用到的读取脉冲光脉宽从数百纳秒降至10 ns(理论空间分辨率为1 m)。

上述推导过程未考虑光纤衰减。根据上述关系也可以反演出$g_{0,m}^{\left( \varOmega \right)}\left( {\varOmega ,{\textit{z}}} \right)$与${P_1}\left( {\varOmega ,{\textit{z}}} \right)$和${P_2}\left( {\varOmega ,{\textit{z}}} \right)$的关系：

因此，只要测定了${P_1}$和${P_2}$在不同频率和位置处的功率，即可反演出F-SBS的增益空间分布谱。据此，研究人员提出了一系列的测量方法，可以实现F-SBS增益谱分布式的解调。2018年，Zadok课题组提出使用高能双频脉冲光的背向瑞利散射强度获取高频光与低频光的分布式能量强度，从而实现分布式前向布里渊散射谱解调的测量方案^[47]。由于光路结构与光时域反射计(optical time-domain reflectometry, OTDR)类似，该技术被命名为光力时域反射技术(optomechanical time-domain reflectometry, OM-TDR)。其具体原理如图13所示。

\begin{aligned} \frac{\partial^{2} ρ}{\partial t^{2}} - & \bar{Γ} \nabla^{2} \frac{\partial ρ}{\partial t} - {v_{L}}^{2} \nabla^{2} ρ \\ = \nabla \cdot f = - \frac{1}{2} ε_{0} (a_{1} + 4 a_{2}) \nabla^{2} (E_{1} {E_{2}}^{*}) \end{aligned} .

首先，采用能量转移而非相位测量进行分布式解调。F-SBS在光纤中强度较弱，远低于其他三阶非线性过程，这导致其对探测光的相位调制也较弱，信噪比低。相位解调方案使用单频脉冲读取TAW，声波场在读取脉冲持续时间内是持续衰减的。另外，分布式相位还原过程无法避免微分的引入，微弱的相位噪声导致微分的结果发生崩坏。而使用调频脉冲作为读取脉冲，由于激发脉冲已将声波场激发至稳态且激发脉冲与读取脉冲产生的TAW相干，读取脉冲持续时间内声波场会维持稳态。另外，能量转移过程可以通过BOTDA直接进行测量，实验现象更加直观，信噪比也更高。

E_{i} (r, z, t) = E_{0} (r) A_{i} (z, t) e^{j (ω_{i} t - k_{i} z) + c . c .},

\begin{aligned} \frac{\partial A_{1}}{\partial z} = - \frac{j ω_{1} ε_{0} Q_{E S} Q_{P E}}{2 \bar{ρ} n c Ω_{0, m} Γ_{0, m} [j - 2 (Ω - Ω_{0, m}) / Γ_{0, m}]} A_{1} {| A_{2} |}^{2}, \\ \frac{\partial A_{2}}{\partial z} = \frac{j ω_{2} ε_{0} Q_{E S} Q_{P E}}{2 \bar{ρ} n c Ω_{0, m} Γ_{0, m} [j - 2 (Ω - Ω_{0, m}) / Γ_{0, m}]} A_{2} {| A_{1} |}^{2} . \end{aligned}

Figure 15. Full-Size Img PowerPoint

Schematic diagram of OMTDA^[35]

将式(20)和式(21)分别代入式(22)和式(23)中，可以得到光场与声场的演化方程。考虑声波场被激发到稳态的情况，忽略时间偏导项，有：

为了进一步提升空间分辨率，2021年本团队提出基于偏振分极的OMTDA技术，实现了0.8 m的空间分辨率^[49]，具体方案如图20所示。偏振噪声是限制方案信噪比和空间分辨率的重要因素之一，OMTDA方案中，激发脉冲的调制频率被设置远离读取脉冲，这是为了规避激发脉冲的信号串扰。但经过验证，激发脉冲仍会对最终解调的信号强度有所影响。通过在保偏光纤中分离激发与探测过程可以有效解决上述问题。使用偏振分束器(polarization beam splitter, PBS)将激发脉冲和读取脉冲分别注入待测保偏光纤的快慢轴中，实现泵探分离过程。由于激发脉冲和读取脉冲处于不同的偏振模态，二者间的相互串扰可以忽略不计。通过精确调控探测光的偏振态，探测过程中的B-SBS的效率可以达到最大，从而有效提升信噪比。实验验证了0.8 m的空间分辨率，并演示了空气、酒精和涂覆层处光纤的F-SBS增益谱测量。

4. 结论和展望

本文首先分析了F-SBS的理论基础和传感原理，总结回顾了F-SBS的测量手段，并详细介绍了目前先进的分布式传感技术——光力时域分析技术。F-SBS作为一种新兴的传感机制，在外界物质识别、光纤结构检测乃至物质特性研究等领域都展现了十足的潜力，优良的性能促使其逐渐走向实用化和商业化。目前，诸多方案，尤其是分布式F-SBS测量技术的提出为F-SBS在不同场景的应用都做出了准备。随着技术的不断成熟，其空间分辨率、测量精度等参数都将继续不断优化，在未来环境污染监测、生物医疗、物质识别、光纤制造等领域将发挥重要作用。

利益冲突

所有作者声明无利益冲突

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- Li Tianfu, litianfu3307@163.com On this Site On Google Scholar
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
- Ba Dexin On this Site On Google Scholar
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
- Zhou Dengwang On this Site On Google Scholar
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
  - Postdoctoral Research Station for Optical Engineering & Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
- Ren Yuli On this Site On Google Scholar
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
- Chen Chao On this Site On Google Scholar
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
- Zhang Hongying On this Site On Google Scholar
  - Heilongjiang Provincial Key Laboratory of Quantum Control, School of Measurement and Communication Engineering, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China
- Corresponding author: Dong Yongkang, aldendong@163.com On this Site On Google Scholar
  aldendong@163.com
  - National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

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DOI: 10.12086/oee.2022.220021

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Li Tianfu, Ba Dexin, Zhou Dengwang, Ren Yuli, Chen Chao, Zhang Hongying, Dong Yongkang. Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering. Opto-Electronic Engineering 49, 220021 (2022). DOI: 10.12086/oee.2022.220021

Li Tianfu, Ba Dexin, Zhou Dengwang, Ren Yuli, Chen Chao, Zhang Hongying, Dong Yongkang. Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering. Opto-Electronic Engineering 49, 220021 (2022). DOI: 10.12086/oee.2022.220021

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- Received Date March 18, 2022
- Revised Date June 10, 2022
- Accepted Date July 07, 2022
- Published Date September 24, 2022
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物质名称	声阻抗/(kg·m⁻²·s⁻¹)	F-SBS谱宽/MHz	数据来源
空气	439.6	0.45	[35]
酒精	0.93×10⁶	2.21	[35]
水	1.483×10⁶	3.57	[36]
NaCl溶液(4%)	1.571×10⁶	3.78	[11]
NaCl溶液(8%)	1.664×10⁶	4.00	[11]
NaCl溶液(12%)	1.763×10⁶	4.24	[11]
聚酰亚胺(用作涂覆层)	3.60×10⁶	8.7(2.83)	[32]
丙烯酸酯(用作涂覆层)	3.39×10⁶	8.16(~8)	[37]
二氧化硅	13.19×10⁶	\	[32]

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Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering

Abstract

Keywords

1. 引　言

2. 前向受激布里渊散射的基本原理

2.1 F-SBS的发展概述和基本原理

2.2 前向受激布里渊散射的传感原理

3. 前向受激布里渊散射的探测手段

3.1 基于相位解调的探测方案

3.2 基于能量转移的探测方案

4. 结论和展望

利益冲突

References

Cited by

Periodical cited type(9)

Other cited types(8)

Author Information

Li Tianfu, litianfu3307@163.com On this Site On Google Scholar

Ba Dexin On this Site On Google Scholar

Zhou Dengwang On this Site On Google Scholar

Ren Yuli On this Site On Google Scholar

Chen Chao On this Site On Google Scholar

Zhang Hongying On this Site On Google Scholar

Corresponding author: Dong Yongkang, aldendong@163.com On this Site On Google Scholar

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Corresponding author: Dong Yongkang, aldendong@163.com

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Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering

Abstract

Keywords

1. 引 言

2. 前向受激布里渊散射的基本原理

2.1 F-SBS的发展概述和基本原理

2.2 前向受激布里渊散射的传感原理

3. 前向受激布里渊散射的探测手段

3.1 基于相位解调的探测方案

3.2 基于能量转移的探测方案

4. 结论和展望

利益冲突

References

Cited by

Periodical cited type(9)

Other cited types(8)

Author Information

Li Tianfu, litianfu3307@163.com On this SiteOn Google Scholar

Ba Dexin On this SiteOn Google Scholar

Zhou Dengwang On this SiteOn Google Scholar

Ren Yuli On this SiteOn Google Scholar

Chen Chao On this SiteOn Google Scholar

Zhang Hongying On this SiteOn Google Scholar

Corresponding author: Dong Yongkang, aldendong@163.com On this SiteOn Google Scholar

Copyright

About this Article

Cite this Article

Article History

Article Metrics

Related Articles

Links

Related Articles

Catalog

Corresponding author: Dong Yongkang, aldendong@163.com

Manuscript Submission

More Content

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Content

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1. 引　言

Li Tianfu, litianfu3307@163.com On this Site On Google Scholar

Ba Dexin On this Site On Google Scholar

Zhou Dengwang On this Site On Google Scholar

Ren Yuli On this Site On Google Scholar

Chen Chao On this Site On Google Scholar

Zhang Hongying On this Site On Google Scholar

Corresponding author: Dong Yongkang, aldendong@163.com On this Site On Google Scholar