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Abstract
In this paper, we propose and experimentally verify a method for optimizing the fault detection sensitivity of few mode fiber (FMF) link based on high-order spatial mode trend filtering. The employment of high-order mode trend filtering as a signal processing tool identifies meaningful level shifts from FMF optical time-domain reflectometer (FMF-OTDR) profile, which is associated with the problem of the minimization of the intrinsic random noise and modal crosstalk impact on the acquired data. A FMF link fault detection system is built, and the proposed method is utilized to detect the fault loss characteristics of 7.2 km 6-mode fiber with three fusion splice points with different fusion quality, and the detection results of each mode are compared with the results obtained by FMF-OTDR. The experimental results show that our proposed method can effectively improve the low fault detection sensitivity of high-order spatial mode caused by random noise and mode crosstalk.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the global data traffic increasing explosively, the development of new transmission technologies is a hot topic for research and competition between academic and industry. The mode division multiplexing (MDM) technology based on few-mode fiber (FMF), which can break through the non-linearity Shannon limit of traditional single-mode fiber (SMF) communication and multiply the capacity of optical fiber communication system by utilizing the orthogonality of spatial modes for spatial diversity multiplexing, is the most competitive expansion scheme to solve the “bandwidth crisis” of optical communication network in the future [1–6]. Faced with the rapid development of FMF research and development, application and the gradual construction of future FMF network [7–12]. In order to avoid the economic loss and service quality decline caused by the interruption of large-capacity service, and ensure the reliable operation of the FMF-based MDM systems, the fault detection and location of FMF link are of great significance.
At present, several technical schemes for fiber fault detection have been proposed, such as optical time domain reflectometer (OTDR) [13,14], optical frequency domain reflectometer (OFDR) [15,16], chaotic OTDR [17,18], and transmission reflection analysis (TRA) [19,20] technology, etc. All of the above methods are used to detect the fault by measuring the characteristics of basic mode LP01, which can realize the fault characterization of the SMF link with high dynamic range and high spatial resolution. However, for the FMF with multiple spatial modes, the transmission loss characteristics of each spatial mode are quite different. It is obviously inaccurate and incomplete to detect the FMF fault only by measuring the characteristics of basic mode LP01. In recent years, some methods for obtaining the mode loss [21] and crosstalk at a fusion splice point [22] in FMFs have been reported, which provides an idea for us to study innovative methods for FMF fault detection. In our previous work, we verify the fault detection sensitivity characteristics of different spatial mode. Compared with the LP01 mode, the high-order mode has high fault detection sensitivity. And then the fault detection and location method for FMF based on backscattered light of high-order modes is proposed and experimentally demonstrated [23]. However, in this method, due to the existence of dynamic spatial mode crosstalk at the splice point of FMF link, the high-order spatial mode fusion loss is greatly disturbed. The high-purity amplitude distribution of high-order spatial mode cannot be obtained, which reduces the fault detection sensitivity. On the other hand, the fault detection method based on higher-order mode mainly excites LP01 mode. By making use of the coupling characteristics between modes, the characterization and analysis of the fault events in the Rayleigh backscattering curve of each spatial mode (excited mode and coupled non-excited mode) are realized. It is known that the power of the backscattered light is very small, generally only $\textrm{1}{0^{ - 7}}{\sim }{10^{ - 6}}$ of the incident light power. For the FMF, the coupling coefficient between the modes is about −30 dB/km, then the Rayleigh scattering light coupled into the non-excited mode is only $\textrm{1}{0^{ - 11}}{\sim }{10^{ - 10}}$ of the whole incident light [24], which inevitably results in the low signal-to-noise ratio of the high-order mode backscattering light. Then, it leads to low detection sensitivity of micro event in high-order mode backscattering curve.
In this paper, in order to solve the above problems, we propose a high-sensitivity fault detection optimization method based on high-order spatial mode trend filtering. This method uses the piecewise linear optimal estimation of trend filter to estimate the trend of high-order mode backscattered signals with piecewise linear trend. The fault detection of 7.2 km six-mode fiber with three fusion splice points with different fusion quality is carried out, and the detection results of high-order mode are compared with the results obtained by the traditional FMF-OTDR. The experimental results show that the fault detection sensitivity of high-order spatial mode is effectively improved, and the accurate fault location is realized.
2. Principle and experimental setup
Figure 1 shows the schematic diagram of FMF fault detection based on high-order spatial mode trend filtering. By processing and analyzing the amplitude distribution of the high-order spatial mode backscattered light, the accurate characterization of the FMF link fault is realized. Under ideal conditions, the high-order spatial mode backscattering signal has high detection sensitivity for fusion splice, which can realize the comprehensive evaluation and accurate characterization for different fault events. However, due to the existence of dynamic spatial mode crosstalk caused by fusion splice point and the low signal-to-noise ratio (SNR) of high-order spatial mode backscattering signal, it is impossible to obtain the amplitude distribution characteristics of high-order spatial mode Rayleigh backscattered signal with high purity. Especially in long-distance FMF links, this reduces the fault detection sensitivity of high-order spatial mode, as shown in Fig. 1(a). In this paper, high-order spatial mode trend filtering can effectively improve the fault detection sensitivity, as shown in Fig. 1(b).
Fig. 1. The schematic diagram of FMF fault detection based on high-order spatial mode trend filtering.
In the fault detection sensitivity equation, $P{L_{bsi}}$ represents the fault detection sensitivity of mode i, which is the difference between the backscattering power ${P_{bsi}}\textrm{(}{z_0} - \Delta \textrm{z)}$ at the splice fault point ${z_0} - \Delta z$ and $P{L_{bsi}}\textrm{(}{z_0} + \Delta z\textrm{)}$ at ${z_0} + \Delta z$. When the $P{L_{bsi}}$ value of high-order mode reaches 0.2 dB, it will be considered as fusion splice fault. $\Delta z$ is determined by the spatial resolution of the system. We use subscripts $i(i = 1,2,3, \cdots ,6)$ to represent the mode labels (01, 11a, …,02) of FMF, respectively. $P{L_{FMF - OTDR}}$ and $P{L_{Proposed method}}$ are the fault detection sensitivity obtained by FMF-OTDR and our proposed method, respectively.
The backscattering curve of high-order spatial mode in the FMF can be divided into three parts: linear trend, step trend and statistical noise. Three main sources of noise are present in fault detection system of FMF link: ASE noise associates with the amplification of incident signal by EDFA. The shot noise (Poisson noise) is related to the photoelectric detection process of high-order spatial mode backscattered measurements. The thermal noise is mainly caused by the change of the current of the system device. Generally, it is caused by the micro thermal motion of the electron. The linear trend can represent the transmission loss coefficient of different spatial modes with distance, and the step trend can be expressed as the loss amplitude jump caused by fault events. The backscattering signals with different faults can be regarded as piecewise linear functions when the backscattered power is in logarithmic scale. In order to realize multi fault detection, the problem can be transformed into a multi-objective optimization problem:
According to Eq. (1), the piecewise linear estimation characteristic of trend filtering can be used to estimate the trend of the backscattered signals with different faults [25]. Then, the effective comprehensive evaluation of different fault events in FMF link is realized.
Therefore, the backscattering amplitude signal of high-order spatial mode can be decomposed into the sum of monotone linear functions with slope $\alpha \in \textrm{R}$ and intercept $\{{{\gamma_k}} \}_{k = 1}^N \in \textrm{R}$, that is the sum of ${\tilde{y}_k} = {\gamma _k} + \alpha k$. The $\frac{1}{2}\sum\limits_{k = 1}^M {{{({{y_k} - {\gamma_k} - ak} )}^2}}$ is the sum of squares of the residual error between the trend filtered signal and the original signal, which is used to measure the component of the overall signal trend fluctuation. The penalty term $\lambda \sum\limits_{k = 2}^M {|{{\gamma_k} - {\gamma_{k - 1}}} |}$ is the sum of absolute first difference in the component ${\gamma _k}$, which penalizes shifts on the level component. N is the total number of spatial positions, ${y_k}$ represents the backscattered signal observations of different spatial modes. The $\sum\limits_{k = 2}^M {|{{\gamma_k} - {\gamma_{k - 1}}} |}$ is ${\ell _1}$ norm, so it is called ${\ell _1}$ trend filtering.
As an adjustment parameter, non-negative real $\lambda$ is related to the number of jumping discontinuities in the filtered signal, which mainly used to control the number of fault events in the backscattering curve. It is necessary to consider not only the proximity of the model to the backscattered signal, but also the number of actual fault points. To overcome this dependency, we solve the problem for many different values of $\lambda$ and choose the best solution according to BIC metric [26]. The BIC criterion is defined as $\textrm{BIC = }n\ln (N) - 2\ln [L(\theta )]$. $L(\theta )$ represents the likelihood function value of Y, N is the number of samples, n is the number of parameters in the Y function. According to BIC minimum criterion that determines how good is an approximation by penalizing the number of jump discontinuities (fusion fault events). Then, under this condition, the optimal value of $\lambda$ is determined. The coordinate descent algorithm (CDA) [27] is used to solve the convex optimization problem of the objective function of Eq. (1). Finally, the trend filtering estimation of the amplitude signal of high-order spatial mode backscattering is realized, which greatly improves the fault location accuracy of FMF link.
Here, an experimental system of fault detection and location based on FMF-OTDR is built, as shown in Fig. 2. The structure scheme of a mode converter, a mode demultiplexer and FMF circulator is adopted. In this experiment, the mode converter and mode demultiplexer are realized by Photonic lantern A and B (PL A and PL B), respectively. The insertion losses (IL) of PL A and PL B used in the experiment is given in the Table 1, and the back-to-back mode crosstalk matrix of the PL A and PL B is measured by fusion-spliced with FMF-end of the PL A and PL B, as shown in Table 2. Firstly, the distributed feedback laser (DFB) generates a 1550 nm continuous wave (CW) light, which is modulated by an electro-optic modulator (EOM) driven by a signal generator (SG) to generate an optical pulse signal with pulse width of 300 ns at repetition rate of 4 kHz. Modulated optical pulse enters the mode converter (PL A) through the LP01 port (or LP11a or LP11b port, etc.) for mode conversion. Then, the PL A outputs the corresponding single excitation mode LP01 (or LP11a or LP11b, etc.). By utilizing the unidirectional transmission characteristics of the FMF circulator, the single excitation mode LP01 (or LP11a or LP11b, etc.) injects into the FMF circulator through port 1, and then outputs from port 2 entering into the fiber under test (FUT). The Rayleigh backscattering light of the excited mode and the non-excited mode (LP01, LP11a and LP11b mode, etc.) in the FUT return from port 2 to the FMF circulator, and then output from port 3 and enter into the PL B for spatial mode demultiplexing. Secondly, the backscattered light of excited mode (such as LP01) and the non-excited mode (such as LP11a or LP11b, etc.) of PL B output are detected by photoelectric (PD), and the detected electrical signals are sampled and averaged. Finally, the collected data are processed by digital signal, the trace of Rayleigh backscattering of each mode can be acquired for fault detection and location.
Fig. 2. High sensitivity fault detection system of FMF link based on high-order spatial mode trend filtering
Table 1. The IL of the PL A and PL B
Table 2. Back-to-back mode crosstalk matrix of PL A and PL B (unit: dB)
3. Experimental results and discussion
In the experiment, a 6-mode fiber with length of about 7.2 km is used as the fiber under test (FUT), and the detailed parameters are shown in Table 3. We utilize the manual mode of the fusion splicer for eccentric core fusion, the different offset value of about 1.0 μm, 0.5 μm and 1.5 μm can be realized can be realized, respectively. Then, three fusion splice points (A, B and C) with different fusion quality are introduced at the distance of 1 km, 3.1 km and 3.2 km, respectively. In order to achieve fast and efficient fault detection performance, a single spatial mode, i.e. LP01 mode, is excited. By using the coupling characteristics between spatial modes in FMF. The small events in the backscattering curves of each spatial modes (excited mode and coupled non excited mode) is characterized. Figure 3 shows the backscatter curve track of each spatial mode and the fault points A, B and C contained in each spatial mode.
Table 3. Parameters of the 6-mode FMF
According to the Fig. 3, the amplitude loss and location results of different fault points in each spatial mode are shown in Table 4. With the increase of mode order, the amplitude of fault loss at different fault points increases. It can be seen that no matter the low-order mode or the high-order mode, for the fault point C with large amplitude attenuation amplitude, can effectively realize the characterization and accurate positioning. However, for the detection of small fault events (fault points A and B), it can be seen from the table that only LP02 and LP21a with high detection sensitivity can realize fault location. For other spatial modes, due to the low signal-to-noise ratio of coupled non excitation modes and mode crosstalk at the fusion point, the fault identification cannot be carried out comprehensively and accurately. The fault events of the FMF link are missed or misjudged.
Table 4. Measurement results of fault points A, B and C of each spatial mode in the FMF
In order to improve the fault detection sensitivity and verify the fault detection performance of high-order mode trend filtering, the proposed method is used to process the backscattering amplitude of LP01 mode and non-excitation mode LP11a, LP11b, LP21a, LP21b and LP02, respectively. Figure 4 shows the distribution of the original Rayleigh backscattering of each spatial mode and the estimation results by using our proposed method. Then, the fault amplitude loss and location results of fault A, B and C of each mode are analyzed, and compared with the measurement results in Table 4.
Fig. 4. Experimental measurement results of fault points A, B and C of each spatial mode based on trend filtering.
It can be seen from Fig. 4(a), by using our proposed method, only fault point C with large amplitude attenuation is effectively detection for LP01 mode. This is also consistent with the detection results in the previous work, which further shows that the LP01 mode has low detection sensitivity for small fault points. As can be seen from Fig. 4(b), after the backscattering amplitude signal of LP11b mode is estimated by trend filtering, the originally unrecognized fault point A in LP11b mode can be effectively identified, and the fault amplitude attenuation is 0.339 dB. However, it is still unable to identify the B event with the amplitude attenuation of micro fault. As shown in Fig. 4(c) and 4 (d), after trend filtering estimation, LP11a spatial mode can be used to characterize the amplitude attenuation of fault B and C, and the values are 0.26 dB and 1.175 dB, respectively. The trend filtering estimation results for fault point A have some errors, but fault point B is effectively characterized on the original basis.
Figure 4(e) ∼ (j) shows the trend filtering estimation results of LP21a, LP21b and LP02 modes, as well as the amplification results of the corresponding fault points B and C. The analysis shows that the fault detection sensitivity of LP21a, LP21b and LP02 modes are effectively improved by using our proposed method. Meanwhile, the analysis shows that LP21a, LP21b and LP02 have high detection sensitivity for fault loss, and fault points A, B and C are effectively characterized, which can better realize fault event location. At the same time, the fault point B of LP21b spatial model could not be detected by FMF-OTDR, however, it can be effectively characterized by our proposed method. The results of amplitude loss and positioning measurement at different fault points in each spatial mode of 6-mode fiber are shown in Table 5.
Table 5. Measurement results of fault points A, B and C of each spatial mode in the FMF based on our proposed method
Similarly, through the analysis in Table 5, it can be seen that with the increase of mode order, the amplitude of fault loss under different fault points A, B and C increases. Compared with the measurement results in Table 1, the amplitude of fault loss of each mode estimated based on trend filtering is improved. The specific comparison results are shown in Fig. 5, where fault A, B, C and fault A’, B’, C’ represent the measurement results obtained by FMF-OTDR and our proposed method, respectively. The detection sensitivity of fault points A and C in high-order spatial mode LP02 is increased by 0.131 dB and 0.123 dB, respectively. The detection sensitivity at fault points A, B and C of LP21a is increased by 0.132 dB, 0.215 dB and 0.107 dB, respectively. At fault point A of LP21b mode is increased by 0.079 dB. Meanwhile, due to the low fusion crosstalk and signal-to-noise ratio of non-excited high-order spatial mode backscattering signal, LP11a and LP11b modes cannot achieve fault location. With our proposed method, the fault detection sensitivity is improved. Especially for the fault point B of LP11a, the fault point A of LP11b and the fault point B of LP21b mode, the fault detection results range from indeterminate to precise characterization. However, the corresponding loss amplitude at fault point B of LP21a and point C of LP11a has a certain downward trend, which is mainly caused by the close distance between the fusion splice point B and C. Under this condition, the dynamic mode crosstalk has a serious impact on the amplitude fluctuation of Rayleigh backscattering. This fluctuation causes some errors in the fusion splice loss obtained by trend filtering. To sum up, the results show that our proposed method can effectively improve the fault detection sensitivity, and realize more accurate and comprehensive evaluation of the fault point of FMF link.
4. Conclusion
In this paper, an optimization method of fault detection sensitivity based on high-order spatial mode trend filtering is proposed and experimentally verified. It solves the problem of low fault detection sensitivity caused by mode crosstalk and low signal-to-noise ratio of non-excited mode backscattering signal. A 6-mode fiber link fault detection system is built. The fault loss characteristics of 7.2 km FMF with three fusion splice points (A, B and C) with different fusion quality are analyzed and located. The detection results of each mode are compared with the results obtained by FMF-OTDR. The results show that the fault detection sensitivity of high-order spatial mode is improved effectively. Therefore, the fault detection and location method based on high-order spatial mode trend filtering successfully realizes the comprehensive evaluation and accurate characterization of the fault events in FMF link. It provides a strong guarantee for the fault detection of the FMF-based MDM systems.
Funding
Zhejiang Provincial Key Research and Development Program (2019c05010).
Disclosures
The authors declare no conflicts of interest.
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