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由于在1 550 nm窗口,单模光纤中材料色散占主导,可以假设光纤链路传输时延波动完全受材料色散的影响。对于波长为
$\lambda $ 的光信号来说,其在单模光纤中传播一段距离$L$ ,材料色散引起的群时延$\tau $ 为:$$\tau = \frac{L}{c}\left( {n - \lambda \frac{{{\rm d}n}}{{{\rm d}\lambda }}} \right)$$ (1) 式中:
$n$ 是光纤的折射率;$c$ 是真空中的光速。根据公式(1),长度一定的光纤中的传输时延主要受折射率
$n$ 和波长$\lambda $ 的影响。这意味着两个波长不同的光信号,在相同的光纤中传播速度不同。由材料色散的定义,可以得出单向传输时延关于温度的导数,即单波长单向传输时延波动为:$$\begin{array}{l} {\left. {\dfrac{{{\rm d}\tau }}{{{\rm d}T}}} \right|_{{\lambda _N}}} = \dfrac{1}{c}\left[ {\dfrac{{{\rm d}L}}{{{\rm d}T}}\left( {{n_{{\lambda _N}}} - {\lambda _N}\dfrac{{{\rm d}{n_{{\lambda _N}}}}}{{{\rm d}{\lambda _N}}}} \right)} \right. + \\ \quad \quad \quad \left. {\; L\left( {\dfrac{{{\rm d}{n_{{\lambda _N}}}}}{{{\rm d}T}} - {\lambda _N}\dfrac{{{{\rm d}^2}{n_{{\lambda _N}}}}}{{{\rm d}{\lambda _N}{\rm d}T}}} \right)} \right],\;\;N = 1,2 \\ \end{array} $$ (2) 其中
$N = 1,2$ 代表该表达式代入两个不同波长对应的两个函数。可以发现,不同波长对应的单向时延波动不相同。如果公式(2)中两个函数相减结果不等于零,则可以计算光纤路径中双波长传输延迟差的波动,表达式如下所示:$$\begin{array}{l} {\left. {\dfrac{{{\rm d}\tau }}{{{\rm d}T}}} \right|_{{\lambda _1} - {\lambda _2}}} = \dfrac{1}{c}\left[ {\dfrac{{{\rm d}L}}{{{\rm d}T}}\left( {\left( {{n_{{\lambda _1}}} - {n_{{\lambda _2}}}} \right) + {\lambda _2}\dfrac{{{\rm d}{n_{{\lambda _2}}}}}{{{\rm d}{\lambda _2}}} - {\lambda _1}\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}}}} \right)} \right. + \\ \quad \quad \quad \left. { L\left( {\dfrac{{\rm d}}{{{\rm d}T}}\left( {\left( {{n_{{\lambda _1}}} - {n_{{\lambda _2}}}} \right) + {\lambda _2}\dfrac{{{\rm d}{n_{{\lambda _2}}}}}{{{\rm d}{\lambda _2}}} - {\lambda _1}\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}}}} \right)} \right)} \right] \\ \end{array} $$ (3) 根据公式(3)提出了光纤单向时延波动测量方法,原理图如图1所示。本地站时钟A发送时间信号给两个激光器,分别以
${\lambda _1}$ 和${\lambda _2}$ 两个不同波长的光信号经过长距离光纤传输至终端站,经过光电探测器转换后由时间间隔测量设备测量出两个信号的到达时间差。则公式(3)中两个波长光信号之间的时延差波动可以在终端站测量得到。如果能够找到双波长时延差波动与单向传播时延波动之间的理论量化对应关系,则可以由实测的双波长传递时延差波动反推出单向时延波动。由公式(3)可知,两种波长的折射率和光纤长度都独立地受温度的影响,在此基础上可以计算和测量传输时延差的变化。由于光纤的热胀冷缩系数约为7 ppm/
${}^{\rm{o}}{\rm{C}}$ ,光纤长度随温度变化而导致的传输时延远小于材料色散,为方便计算,文中忽略光纤热胀冷缩对单向时延波动的影响。为了得到双波长时延差波动与单向传播时延波动之间的理论量化对应关系,定义比例系数
$M$ 是同一单模光纤内单波长光信号时延波动与双波长光信号时延差波动的比,忽略光纤的热胀冷缩效应,根据公式(2)和公式(3)可得比例系数$M$ 为:$$\begin{array}{l} M = \dfrac{{{{\left. {\dfrac{{{\rm d}\tau }}{{{\rm d}T}}} \right|}_{{\lambda _1}}}}}{{{{\left. {\dfrac{{{\rm d}\tau }}{{{\rm d}T}}} \right|}_{{\lambda _1} - {\lambda _2}}}}} = \dfrac{{\dfrac{L}{c}\left( {\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}T}} - {\lambda _1}\dfrac{{{{\rm d}^2}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}{\rm d}T}}} \right)}}{{\dfrac{L}{c}\left( {\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}T}} - \dfrac{{{\rm d}{n_{{\lambda _2}}}}}{{{\rm d}T}} + {\lambda _2}\dfrac{{{{\rm d}^2}{n_{{\lambda _2}}}}}{{{\rm d}{\lambda _2}{\rm d}T}} - {\lambda _1}\dfrac{{{{\rm d}^2}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}{\rm d}T}}} \right)}} \\ \quad \quad \quad \quad \quad = \dfrac{{\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}T}} - {\lambda _1}\dfrac{{{{\rm d}^2}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}{\rm d}T}}}}{{\dfrac{{{\rm d}{n_{{\lambda _1}}}}}{{{\rm d}T}} - \dfrac{{{\rm d}{n_{{\lambda _2}}}}}{{{\rm d}T}} + {\lambda _2}\dfrac{{{{\rm d}^2}{n_{{\lambda _2}}}}}{{{\rm d}{\lambda _2}{\rm d}T}} - {\lambda _1}\dfrac{{{{\rm d}^2}{n_{{\lambda _1}}}}}{{{\rm d}{\lambda _1}{\rm d}T}}}} \\ \end{array} $$ (4) 由上式可知,比例系数与温变范围、光波长、光纤折射率等条件有关。Sellmeier等式是描述特定光学介质材料的折射率随温度变化和波长的经验关系式。可以通过温度及波长的相关参数来精确预测光在特定介质中的色散关系,受温度和波长影响的折射率具有以下形式[12]:
$${n^2}\left( {\lambda ,T} \right) - 1 = \sum\limits_{i = 1}^3 {\frac{{{S_i}\left( T \right){\lambda ^2}}}{{{\lambda ^2} - \lambda _i^2\left( T \right)}}} $$ (5) 式中:
${S_i}(T)$ 是在特定温度下材料的共振强度参数,T是温度;$\lambda $ 是传播的光信号波长。在Sellmeier等式这种近似经验关系式下,共振强度参数${S_i}(T)$ 和波长参数不再具有直接的物理意义,而是用于生成与经验数据足够匹配的拟合参数。综上,光纤单向传输时延波动测量的基本原理是:通过精确测量温度和利用Sellmeier等式实时计算出给定光波长的光纤的折射率,进而计算出实际使用的双波长光信号对应的比例系数
$M$ ,从而可以将测得的双波长时延差波动乘以该比例系数$M$ ,最后反推出单向时延波动,如公式(6)所示:$${\text{单波长时延波动}} = {\text{测得双波长时延差波动}}*M$$ (6)
Fiber time delay fluctuations measurement based on one-way transfer
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摘要: 为了与现有光纤通信网络兼容,研究了一种基于单纤单向传输的光纤时延波动测量方法。基于色散温变效应和Sellmeier等式,建立了利用温度的准确测量和双波长光信号传输时延差波动反推单向时延波动的比例模型。令模型中的比例系数是单波长时延波动和双波长时延差波动的比,仿真研究了温度和波长差对比例系数的影响。搭建了75 km光纤单向时延波动测量实验平台,实验结果表明:实测比例系数−258.4接近于理论比例系数−277.3,对应单向传输时延波动误差为660 ps,实验结果验证了模型的正确性和基于单向传输的光纤时延波动测量的可能性。
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关键词:
- 单纤单向 /
- 时延波动测量 /
- 色散温变效应 /
- Sellmeier等式
Abstract: In order to be compatible with the existing optical communication network, a time delay fluctuations measurement based on "single-fiber one-way" transfer scheme was proposed. Based on the temperature-induced variation of group velocity dispersion effect and Sellmeier equation, a proportionality model for calculating the one-way delay fluctuations was established with detecting the delay difference fluctuations between two propagating optical signals at given different wavelengths and accurate temperature measurement. Assuming proportionality coefficient in the model was the ratio between one-way delay fluctuations and one-way dual wavelength delay difference fluctuations. By simulation, the impact of fiber link parameters, such as temperature and wavelength difference, on proportionality coefficient was discussed. The experimental platform for one-way time transfer over 75 km fiber was conducted and the experimental results show that the measured proportional coefficient is −258.4, close to the theoretical proportional coefficient −277.3, and the corresponding one-way delay variation error is 660 ps. The measured results validate the correctness of the proposed model as well as the possibility of fiber time delay fluctuations measurement based on one-way transfer. -
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