Abstract

Conventional polarization-sensitive optical fiber sensors (POFS) sometimes can hardly detect external disturbances at some special locations where the polarization state of light has little change with the fixed analyzer. This phenomenon is the so-called polarization-induced signal fading that leads to alarm missing in the forward transmission POFS system and deteriorates locating accuracy in the polarization optical time-domain reflectometry system. To eliminate the fading phenomenon and maintain the high sensitivity along the whole sensing fiber, we propose a forward transmission polarization-sensitive optical fiber sensing scheme using polarization-maintaining fiber with the slow axes 45° aligned splicing at both the input and detection ends. Theoretical and experimental results indicate that the system works at the most sensitive state and the signal fading phenomenon is eliminated. This system promises potential applications in perimeter security and physical parameters measurement.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Polarization-sensitive optical fiber sensors (POFS) can measure the physical parameters such as vibrations [13], electromagnetic field [4,5], and polarization mode dispersion (PMD) [68], etc., by detecting the state of polarization (SOP) of the light. They usually can be divided into forward and backward transmission system. The back-transmission system is also known as the polarization optical time-domain reflectometer (POTDR).

In the POTDR system, the SOP of light after the disturbance point fluctuates randomly along the fiber. Even under the same disturbance loads, its change may still be very small at some positions, which are called “signal fading” points. This unavoidable signal fading effect of the traditional POTDR is mainly due to the quite weak birefringence characteristic of single-mode fiber (SMF) [9]. This effect also exists in the forward transmission system. Because of the signal fading effect, the sensitivity to external disturbance varies greatly along the fiber, which may lead to location errors or alarms missing in the POFS system.

To suppress the fading phenomenon, some solutions on the transmitting end have been reported. Reference [9] proposed to use three polarizers with orthogonal directions on the Poincare sphere to detect the change of SOP in any direction. To realize the three polarizers scheme for each wavelength channel, actually, nine polarizers are needed. That would be very complex, thus high-cost. And Ref. [10] proposed to suppress the signal fading using probe pulses with ergodic SOPs in a POTDR system. To achieve the best results, it required that the vibration should be persisted during the period of ergodic SOPs, which means the response time of the proposed system would be increased for n (n is the number of the ergodic SOPs and is 100 in this paper) times compared to the traditional POTDR system. So, it can be concluded that this scheme is time-consuming and is more suitable for the measurement of long-lasting vibration with a fixed frequency.

Whereas some other solutions modified the receiving end. Usually, a single polarizer is used to detect the change of SOP. However, the polarizer’s sensitivity to the SOP change is related to the initial SOP and its moving trail, which brings in signal fading and inaccurate measurement. Instead of the single polarizer scheme, Ref. [11], used a polarization beam splitter (PBS) to obtain the variation of light’s SOP. As the two outputs of the PBS present opposite responses, the final signal trace obtains a 3 dB signal to noise ratio (SNR) enhancement. However, the signal fading problem is not well relieved. Recently, a simple method is proposed to use two polarizers with 45° alignment [12]. These two polarizers present complementary sensitivities to the SOP change. Thus, the signal fading can be obviously suppressed to some extent. All of the schemes mentioned above are based on partial Stokes vector measurement, thus unable to analyze the full SOP information. To realize full SOP detection, mainly two methods have been reported, namely the amplitude-division method [13] and the mechanical modulation method [14]. However, they are either too complex or unsuitable for dynamic measurement.

In conventional POFS systems, SMF is used as the sensing fiber, which can be regarded as a quite weak birefringence waveguide. The birefringent axis of SMF rotates randomly along the fiber, and the birefringence index also slightly varies randomly. Considering the small disturbance applied on the sensing fiber, the SOP of output light draws a small arc of a circle on the Poincare sphere. The size and plane of the circle are random. The polarization signal decays if the circle is small and/or the SOP rotation direction is perpendicular to the polarizer.

On the contrary, polarization-maintaining fiber (PMF) has a fixed birefringent principal axis. The plane of the circle that the emitted light SOP rotates on is fixed. And the size of the circle can be adjusted by rationally allocating the light intensity to the fast and slow axes. Then the signal fading can be avoided by setting the circle as the largest one and adjusting the SOP rotation direction to be parallel to the polarizer. The whole system is then able to work at the most sensitive state. Therefore, using PMF as the sensing fiber can eliminate the polarization-induced signal fading along the entire fiber length.

In this paper, a fading-free POFS is proposed and demonstrated. It mainly consists of PMF, a phase modulator, and an in-line polarizer. The PMF pigtail of the light source is 45° aligned splicing with the PMF slow axis to obtain the equal intensity of light transmitted along the fast and slow axes of PM sensing fiber. The polarizer axis is also 45° aligned with the slow axis of the PM sensing fiber. And the phase difference of the orthogonally polarized lights reaching the polarizer is controlled to be about 90° by a phase modulator. Experimental results show that such design successfully eliminates signal fading existing in the conventional system. As a severe time-domain depolarization effect will be induced by the high birefringence index of the PMF [3], PMF is not suitable as the sensing fiber for the backscattering-based POTDR. Therefore, only the forward POFS system is considered.

2. Theoretical analysis of the signal fading

2.1. Theory

In a traditional polarization-based forward transmission POFS system, the SMF is used as the sensing fiber. The SOP change caused by external disturbance is transformed into intensity variation after a polarizer. The polarizer shows different sensitivities to different SOP changes, which brings signal fading phenomenon along the sensing fiber. To investigate the fading phenomenon, a numerical simulation is conducted using the wave plate model [3].

This model is shown in Fig. 1. The sensing fiber consists of thousands of birefringence wave plates. Sin and Sout are the Stokes vectors of input and output light respectively. In the i-th wave plate, θ is the angle between the fast axis and x-axis; δ is the phase delay.

 

Fig. 1. Wave plate model of a sensing fiber link.

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The Muller matrix of each wave plate can be written as follows [15]:

$$ M_{i}=\alpha\left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & \cos ^{2} 2 \theta_{i}+\sin ^{2} 2 \theta_{i} \cos \delta_{i} & \cos 2 \theta_{i} \sin 2 \theta_{i}\left(1-\cos \delta_{i}\right) & -\sin 2 \theta_{i} \sin \delta_{i} \\ 0 & \cos 2 \theta_{i} \sin 2 \theta_{i}\left(1-\cos \delta_{i}\right) & \sin ^{2} 2 \theta_{i}+\cos ^{2} 2 \theta_{i} \cos \delta_{i} & \cos 2 \theta_{i} \sin \delta_{i} \\ 0 & \sin 2 \theta_{i} \sin \delta_{i} & -\cos 2 \theta_{i} \sin \delta_{i} & \cos \delta_{i} \end{array}\right] $$
where α is the loss coefficient of the corresponding wave plate.

Then, the Stokes vector of output light can be defined as follows:

$${S_{\textrm{out}}} = M{S_{in}} = {M_N}{M_{N - 1}} \ldots {M_1}{S_{\textrm{in}}}.$$
Assuming the x-axis is the polarization axis of the polarizer, its Muller matrix is
$${M_p} = \frac{1}{2}\left[ \begin{array}{cccc} 1 &1 &0 &0\\ 1 &1 &0 &0\\ 0 &0 &0 &0\\ 0 &0 &0 &0 \end{array} \right].$$

Then, the Stokes vector of the light after the polarizer is

$${S_p} = {M_p} \ast {S_{out}} = \frac{1}{2}\left[ \begin{array}{cccc} 1 &1 &0 &0\\ 1 &1 &0 &0\\ 0 &0 &0 &0\\ 0 &0 &0 &0 \end{array} \right]\left[ \begin{array}{l} {s_{out0}}\\ {s_{out1}}\\ {s_{out2}}\\ {s_{out3}} \end{array} \right] = \frac{1}{2}\left[ \begin{array}{c} {s_{out0}} + {s_{out1}}\\ {s_{out0}} + {s_{out1}}\\ \textrm{ 0}\\ \textrm{ 0} \end{array} \right]$$
where sout0, sout1, sout2, sout3 are Stokes vector parameters of Sout.

Therefore, the light intensity after the polarizer is

$$I = \frac{1}{2}({{s_{out0}} + {s_{out1}}} ).$$

2.2. Simulation

To verify the signal fading phenomenon in the SMF-based forward transmission system, simulations are performed using the model described in Section 2.1. The simulation parameters are listed in Table 1.

Tables Icon

Table 1. Parameters used in the simulation.

In the simulation, the total sensing fiber length L is 100 m, and wave plate l is 1 m. The angle between the wave plate’s fast axis and the x-axis θ obeys uniform distribution in [0,2π] and their phase delay δ has a standard normal distribution [3]. The input polarization state (Stokes vector) is Sin = [1; 1; 0; 0]. Actually, in this paper, the input polarization state does not affect the final results. Assuming the sensing fiber is slightly perturbed with small strain introduced, the direction of the main axis θ of the wave plate is unchanged, and only the strain-induced phase variable δ is changed. A 10 Hz sinusoidal perturbation signal with a maximum amplitude of 10 degrees is imposed to each wave plate successively. For each wave plate, the time-domain signal of the polarizer is recorded as shown in Fig. 2(a). Then its corresponding spectrum [Fig. 2(b)] is obtained after the fast Fourier transform (FFT). For each waveplate (location), the sensitivity is defined as the intensity at the vibration frequency in the corresponding spectrum. Finally, the distribution of the sensitivity variation along the fiber is recovered as shown in Fig. 2(c), where the sensitivities near 0 are fading points.

 

Fig. 2. Signal fading phenomenon in the SMF-based forward transmission system. (a) Time-domain signal. (b) the FFT of the signal. (c) Sensitivities distribution. (d) SOP trace of a fading point. (e) SOP trace of a sensitive point.

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Through Poincare representation, we find that at the fading point, the circle where the SOP rotates is small and nearly perpendicular to the polarizer. While at the most sensitive point, the circle is large and nearly parallel to the polarizer as shown in Figs. 2(d) and 2(e). As described in Eq. (3), the polarizer is placed along S1-axis.

As the increasing external stress will cause the SOP rotating around the stress principle axis and drawing a closed circle on the Poincare sphere [16], we find that there are mainly three types of polarization fading cases as shown in Figs. 3(a)–3(c). First, when the circle that the SOP rotates on is quite small [Fig. 3(a)], the SOP can be considered unaffected by external disturbance; Second, the circle is perpendicular to the polarizer [Fig. 3(b)]. And third, the circle is parallel to the polarizer, but with a SOP moving direction perpendicular to it [Fig. 3(c)]. The most sensitive situation away from the above three fading cases can be obtained as shown in Fig. 3(d). It should meet the following conditions: the circle that the SOP rotates on is the largest one and parallel to the working axis of the polarizer; meanwhile, the SOP moving direction is parallel to the polarizer, which can be hardly satisfied all along SMF.

 

Fig. 3. (a-c) Fading conditions and (d) the most sensitive situation. P: polarizer.

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2.3. Proposed PMF-based fading-free forward transmission system

As analyzed above, the SMF is prone to signal fading due to its weak and random birefringence feature. As for PMF, the case is more deterministic and controllable, thus it provides the possibility to implement a fading free sensing system with the largest sensitivity as depicted in Fig. 3(d).

The proposed PMF-based fading-free forward transmission system is shown in Fig. 4. The blue line represents PMF. The relationship between SOP trace and polarizer in the procedure to achieve the most sensitive situation is shown in Fig. 5. Step 1, the continuous wave (CW) generated by a laser is coupled into a PM sensing fiber link. There is a fiber splicing point with the slow axes 45° aligned in the front end of the PMF, which makes the linearly polarized light equally coupled into the fast and slow axes of the PM sensing fiber link. It means that along the sensing fiber link, the SOP rotates on the largest circle (S1=0 seen from the Poincare sphere). Step 2, at the receiving end, the sensing signal passes through an in-line polarizer with PM pigtails and is detected by a PD. The optical axis of the polarizer is 45° offset to the slow axis of the PM sensing fiber. This is equivalent to place the polarizer along the S2-axis, which makes the polarizer parallel to the circle. Step 3, by controlling the polarization-dependent phase modulator, the phase difference between the orthogonally polarized light reaching the polarizer is set around 90°. It means that the SOP is set to a left-handed circular or a right-handed circular status (as indicated by the yellow dot). This ensures that the SOP moving direction is parallel to the axis of the polarizer. In general, Step 1 adjusts the circle where the output light SOP rotates to the largest one, which avoids the first signal fading case as Fig. 3(a); Step 2 keeps the circle parallel to the polarizer, which settles the second fading case in Fig. 3(b). Step 3 adjusts the input light phase to bias the output light SOP moving direction parallel to the polarizer, which solves the third issue in Fig. 3(c).

 

Fig. 4. Configuration of signal-fading-free PMF-based forward transmission system. LD: laser diode, PZT: piezo-transducer, PD: photodetector, AWG: arbitrary waveform generator.

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Fig. 5. Relationship of SOP trace and polarizer in the most sensitive situation. P: polarizer.

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Finally, the Jones vector expression of the light signal reaching the polarizer is:

$$\boldsymbol{E}=\left[\vec{E_x}, \vec{E_y}\right]^{T} = \left[E_{x}e^{j{\delta_{x}}}, E_{y}e^{j{\delta_{y}}}\right]^{T}.$$

Then, the output light intensity passing through 45° placed polarizer is:

$$ I_{o}=\left|E_{x} e^{j \delta_{x}} \cos (\pi / 4)+E_{y} e^{j \delta_{y}} \sin (\pi / 4)\right|^{2}=E_{x}^{2} / 2+E_{y}^{2} / 2+E_{x} E_{y} \cos \left(\delta_{x}-\delta_{y}\right) .$$

As $E_{x}^{2}=E_{y}^{2}=I_{i}/2$, when $\left|\delta_{x}-\delta_{y}\right|=90^{\circ}$, $I_{o}=I_{i}/2$. Ii is the total input light intensity before polarizer. So, the phase difference can be kept around 90° by adjusting the phase modulator to bias the output light intensity around half of the total intensity.

3. Experimental results and discussion

To verify the fading-free capability of the system experimentally, a series of identical vibrations events have been carried out in the SMF-based forward transmission system and the PMF-based forward transmission system, respectively. Figure 6 depicts the PMF-based system where the blue optical fibers are PMFs. In comparison to the PMF system, the SMF-based system uses SMF fiber as the sensing fiber without the phase modulator unit. The phase modulator (MPZ-LN-20) is adjusted by the AWG manually to bias the signal intensity of PD1 around half of its maximum (the signal intensity of PD2). To simplify the experiment, the sensing fiber link is 39-m long and consists of eight 3-m long optical fiber patch cords and one 15-m fiber spool wrapped on a piezo-transducer (PZT) plate in series. A 10 Hz sinusoidal vibration generated by a fiber stretcher (OPTIPHASE PZ3) is applied to the 9 test points (the connection points of the optical fiber patch cords) successively by moving the PZT from the first test point to the ninth point. The fiber stretcher contains a PZT whose driving voltage is set at 50 Vpp by amplifying the 1 Vpp output voltage of the AWG by 50 times. The PMF in the fiber stretcher ensures that the perturbation unit is equal to a wave plate, meanwhile maintains the PMF structure of the proposed scheme. A CW laser (Koheras BASIK MIKRO E15) with less than 100 kHz linewidth and 16 dBm output power is chosen as the light source. The photodiodes with 125 MHz bandwidth are used to transform the light signals to electrical signals. The attenuator is used to keep the received optical power undersaturation by observing the electrical signal of PD2.

 

Fig. 6. Setup of the PMF-based forward transmission system. V-Amp: Voltage Amplifier, OSC: oscilloscope.

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Then the AC electrical signals are sampled by an oscilloscope (PicoScope 3000 Series) shown in Fig. 7(a). The sampling rate is 1 kSa/s. By Fast Fourier transform (FFT), the measured 10 Hz sinusoidal vibration intensity is obtained as shown in Fig. 7(b). Figures 7(a) and 7(b) are the signals at the 5th test points in the SMF-based system. The generated amplitude of the peak frequency in the spectrum is regarded as the sensitivity of the corresponding point. Figure 7(c) shows the measured sensitivity curves along sensing fiber link of SMF-based forward transmission system in solid line and that of the PMF-based forward transmission system in dotted line. Severe signal fading cases appear at the 2nd, 3rd, 6th, and 9th test points in the SMF-based system. And there is no signal fading phenomenon in the PMF-based system. The small sensitivity fluctuation of the proposed system is mainly due to the imperfect manual implementation of the feedback control. It can be expected that by an automatic feedback control unit, the sensitivity curve will be smoother. It should be noted that this system is not a distributed optical fiber sensor system. However, we can take multiple measurements for the sensitivity test by moving the PZT from the first test point to the ninth point. The result of Fig. 7(d) shows that the noise level of the system is about 2 × 10−4 V/√Hz and the SNR would reach 22.6 dB. Here, the SNR is defined as the amplitude ratio of signal amplitude to the background noise level, i.e. SNR = 10 × log10 (Asignal/Anoise).

 

Fig. 7. Sensitivities of SMF-based and PMF-based forward transmission systems. (a) Time-domain result. (b) frequency domain result. (c) Sensitivities distribution. (d) Noise level

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So far, the proposed scheme has been theoretically and experimentally validated based on PMF. However, this method still needs to be improved in several aspects. In fact, PMF is not suitable as the sensing fiber for the POTDR due to the severe time-domain depolarization effect caused by the high birefringence index of the PMF. Besides, the most sensitive state is achieved only when the disturbance introduces no polarization mode coupling (PMC). Otherwise, the circle that the SOP rotates on will diminish, thus degrading the sensitivity. Finally, the proposed system cannot locate. To realize spatially resolved sensing, we can adopt the time delay estimation method [5,17,18] by improving the proposed system.

4. Conclusion

A novel fading-free PMF-based forward transmission polarization-sensitive optical fiber sensing system is proposed in this paper. First, three types of signal fading cases in SMF is analyzed and presented. Then, a PMF-based system is designed to meet the requirements of the most sensitive situation: the circle that the SOP rotates on is the largest one and parallel to the polarizer; meanwhile, the SOP moving direction is parallel to the polarizer. Finally, experimental results showed that the proposed system can effectively eliminate the signal fading effect. This system promises potential applications in perimeter security and physical parameters measurement.

Funding

National Natural Science Foundation of China (61722108, 61931010); National Key Research and Development Program of China (2018YFB1801205); the Innovation Fund of WNLO.

Disclosures

The authors declare no conflicts of interest.

References

1. X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017). [CrossRef]  

2. H. Wu, J. Liu, L. Lu, X. Sun, D. Atubga, and Y. Rao, “Multi-Point Disturbance Detection and High-Precision Positioning of Polarization-Sensitive Optical Time-Domain Reflectometry,” J. Lightwave Technol. 34(23), 5371–5377 (2016). [CrossRef]  

3. C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016). [CrossRef]  

4. M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017). [CrossRef]  

5. Z. Qin, Z. Cheng, Z. Zhang, J. Zhu, and F. Li, “New method for lightning location using optical ground wire,” Chin. Opt. Lett. 4(12), 712–714 (2006).

6. B. Huttner, B. Gisin, and N. Gisin, “Distributed PMD Measurement with a Polarization-OTDR in Optical Fibers,” J. Lightwave Technol. 17(10), 1843–1848 (1999). [CrossRef]  

7. J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017). [CrossRef]  

8. N. Cyr, H. Chen, and G. W. Schinn, “Random-Scrambling Tunable POTDR for Distributed Measurement of Cumulative PMD,” J. Lightwave Technol. 27(18), 4164–4174 (2009). [CrossRef]  

9. C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017). [CrossRef]  

10. X. Wang, J. Hu, F. Wang, Y. Yong, Y. Zhang, M. Xue, X. Zhang, and S. Pan, “Multi-vibration detection by probe pulses with ergodic SOPs in a POTDR system,” Opt. Express 26(22), 28349 (2018). [CrossRef]  

11. Z. Zhang and X. Bao, “Continuous and Damped Vibration Detection Based on Fiber Diversity Detection Sensor by Rayleigh Backscattering,” J. Lightwave Technol. 26(7), 832–838 (2008). [CrossRef]  

12. M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

13. R. M. A. Azzam, “Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light,” Opt. Acta 29(5), 685–689 (1982). [CrossRef]  

14. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995). [CrossRef]  

15. H. Dong, M. Tang, and Y. Gong, “Measurement errors induced by deformation of optical axes of achromatic waveplate retarders in RRFP Stokes polarimeters,” Opt. Express 20(24), 26649–26666 (2012). [CrossRef]  

16. Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017). [CrossRef]  

17. W. Yuan, B. Pang, J. Bo, and X. Qian, “Fiber Optic Line-Based Sensor Employing Time Delay Estimation for Disturbance Detection and Location,” J. Lightwave Technol. 32(5), 1032–1037 (2014). [CrossRef]  

18. C. Ma, T. Liu, K. Liu, J. Jiang, Z. Ding, X. Huang, L. Pan, M. Tian, and Z. Li, “A Continuous Wavelet Transform Based Time Delay Estimation Method for Long Range Fiber Interferometric Vibration Sensor,” J. Lightwave Technol. 34(16), 3785–3789 (2016). [CrossRef]  

References

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  1. X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017).
    [Crossref]
  2. H. Wu, J. Liu, L. Lu, X. Sun, D. Atubga, and Y. Rao, “Multi-Point Disturbance Detection and High-Precision Positioning of Polarization-Sensitive Optical Time-Domain Reflectometry,” J. Lightwave Technol. 34(23), 5371–5377 (2016).
    [Crossref]
  3. C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
    [Crossref]
  4. M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
    [Crossref]
  5. Z. Qin, Z. Cheng, Z. Zhang, J. Zhu, and F. Li, “New method for lightning location using optical ground wire,” Chin. Opt. Lett. 4(12), 712–714 (2006).
  6. B. Huttner, B. Gisin, and N. Gisin, “Distributed PMD Measurement with a Polarization-OTDR in Optical Fibers,” J. Lightwave Technol. 17(10), 1843–1848 (1999).
    [Crossref]
  7. J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
    [Crossref]
  8. N. Cyr, H. Chen, and G. W. Schinn, “Random-Scrambling Tunable POTDR for Distributed Measurement of Cumulative PMD,” J. Lightwave Technol. 27(18), 4164–4174 (2009).
    [Crossref]
  9. C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
    [Crossref]
  10. X. Wang, J. Hu, F. Wang, Y. Yong, Y. Zhang, M. Xue, X. Zhang, and S. Pan, “Multi-vibration detection by probe pulses with ergodic SOPs in a POTDR system,” Opt. Express 26(22), 28349 (2018).
    [Crossref]
  11. Z. Zhang and X. Bao, “Continuous and Damped Vibration Detection Based on Fiber Diversity Detection Sensor by Rayleigh Backscattering,” J. Lightwave Technol. 26(7), 832–838 (2008).
    [Crossref]
  12. M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.
  13. R. M. A. Azzam, “Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light,” Opt. Acta 29(5), 685–689 (1982).
    [Crossref]
  14. A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995).
    [Crossref]
  15. H. Dong, M. Tang, and Y. Gong, “Measurement errors induced by deformation of optical axes of achromatic waveplate retarders in RRFP Stokes polarimeters,” Opt. Express 20(24), 26649–26666 (2012).
    [Crossref]
  16. Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
    [Crossref]
  17. W. Yuan, B. Pang, J. Bo, and X. Qian, “Fiber Optic Line-Based Sensor Employing Time Delay Estimation for Disturbance Detection and Location,” J. Lightwave Technol. 32(5), 1032–1037 (2014).
    [Crossref]
  18. C. Ma, T. Liu, K. Liu, J. Jiang, Z. Ding, X. Huang, L. Pan, M. Tian, and Z. Li, “A Continuous Wavelet Transform Based Time Delay Estimation Method for Long Range Fiber Interferometric Vibration Sensor,” J. Lightwave Technol. 34(16), 3785–3789 (2016).
    [Crossref]

2018 (1)

2017 (5)

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017).
[Crossref]

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

2016 (3)

2014 (1)

2012 (1)

2009 (1)

2008 (1)

2006 (1)

1999 (1)

1995 (1)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995).
[Crossref]

1982 (1)

R. M. A. Azzam, “Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light,” Opt. Acta 29(5), 685–689 (1982).
[Crossref]

Aerssens, M.

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

Ambirajan, A.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995).
[Crossref]

Atubga, D.

Azzam, R. M. A.

R. M. A. Azzam, “Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light,” Opt. Acta 29(5), 685–689 (1982).
[Crossref]

Bao, X.

Bo, J.

Bohata, J.

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

Cao, C.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Chen, H.

Chen, Q.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Chen, X.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Cheng, Z.

Cyr, N.

Ding, Z.

Dong, H.

Fu, S.

X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017).
[Crossref]

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Gisin, B.

Gisin, N.

Gong, Y.

Gusarov, A.

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

Hu, J.

Huang, X.

Huang, Z.

Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

Huttner, B.

Jaros, J.

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

Jiang, J.

Komanec, M.

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

Li, F.

Li, Z.

Liu, J.

Liu, K.

Liu, T.

Look, D. C.

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995).
[Crossref]

Lu, J.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Lu, L.

Lu, Y.

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

Ma, C.

Megret, P.

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

Moreau, P.

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

Pan, L.

Pan, S.

Pan, Y.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Pang, B.

Pisarik, S.

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

Qian, X.

Qin, Z.

Rao, Y.

Schinn, G. W.

Shum, P.

X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017).
[Crossref]

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Song, M.

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

Sun, X.

Tang, J.

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Tang, M.

Tian, M.

Wang, C.

X. Wang, C. Wang, M. Tang, S. Fu, and P. Shum, “Multiplexed polarization OTDR system with high DOP and ability of multi-event detection,” Appl. Opt. 56(13), 3709–3713 (2017).
[Crossref]

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Wang, F.

X. Wang, J. Hu, F. Wang, Y. Yong, Y. Zhang, M. Xue, X. Zhang, and S. Pan, “Multi-vibration detection by probe pulses with ergodic SOPs in a POTDR system,” Opt. Express 26(22), 28349 (2018).
[Crossref]

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Wang, X.

Wang, Z.

Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

Wu, C.

Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

Wu, H.

H. Wu, J. Liu, L. Lu, X. Sun, D. Atubga, and Y. Rao, “Multi-Point Disturbance Detection and High-Precision Positioning of Polarization-Sensitive Optical Time-Domain Reflectometry,” J. Lightwave Technol. 34(23), 5371–5377 (2016).
[Crossref]

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Wuilpart, M.

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

Xia, Q.

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

Xue, M.

Yin, C.

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

Yong, Y.

Yuan, W.

Zhang, X.

X. Wang, J. Hu, F. Wang, Y. Yong, Y. Zhang, M. Xue, X. Zhang, and S. Pan, “Multi-vibration detection by probe pulses with ergodic SOPs in a POTDR system,” Opt. Express 26(22), 28349 (2018).
[Crossref]

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Zhang, Y.

Zhang, Z.

Zhao, C.

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Zhou, C.

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Zhou, Y.

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Zhu, J.

Zhu, W.

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

Zvanovec, S.

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

Appl. Opt. (1)

Chin. Opt. Lett. (1)

IEEE Photonics J. (2)

C. Wang, Y. Zhou, H. Wu, C. Zhao, J. Tang, C. Zhou, S. Fu, P. Shum, and M. Tang, “Temporal depolarization suppressed POTDR system for quasi-distributed instantaneous intrusion sensing and vibration frequency measurement,” IEEE Photonics J. 8(2), 1 (2016).
[Crossref]

Z. Huang, C. Wu, and Z. Wang, “Stress Direction Measurement Based on Polarization State in Optical Fibers Using the Quaternion Method,” IEEE Photonics J. 9(6), 1–11 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (3)

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

M. Wuilpart, M. Aerssens, A. Gusarov, P. Moreau, and P. Megret, “Plasma Current Measurement in Thermonuclear Fusion Reactors Using a Photon-Counting POTDR,” IEEE Photonics Technol. Lett. 29(6), 547–550 (2017).
[Crossref]

J. Bohata, J. Jaros, S. Pisarik, S. Zvanovec, and M. Komanec, “Long-Term Polarization Mode Dispersion Evolution and Accelerated Aging in Old Optical Cables,” IEEE Photonics Technol. Lett. 29(6), 519–522 (2017).
[Crossref]

J. Lightwave Technol. (6)

Opt. Acta (1)

R. M. A. Azzam, “Division-of-amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of All Four Stokes Parameters of Light,” Opt. Acta 29(5), 685–689 (1982).
[Crossref]

Opt. Eng. (1)

A. Ambirajan and D. C. Look, “Optimum angles for a polarimeter: part I,” Opt. Eng. 34(6), 1651–1656 (1995).
[Crossref]

Opt. Express (2)

Other (1)

M. Song, C. Yin, Q. Xia, Y. Lu, and W. Zhu, “Development of distributed POTDR with analyzers of different SOP directions,” in AIP Conference Proceedings (2017), pp. 1–6.

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Figures (7)

Fig. 1.
Fig. 1. Wave plate model of a sensing fiber link.
Fig. 2.
Fig. 2. Signal fading phenomenon in the SMF-based forward transmission system. (a) Time-domain signal. (b) the FFT of the signal. (c) Sensitivities distribution. (d) SOP trace of a fading point. (e) SOP trace of a sensitive point.
Fig. 3.
Fig. 3. (a-c) Fading conditions and (d) the most sensitive situation. P: polarizer.
Fig. 4.
Fig. 4. Configuration of signal-fading-free PMF-based forward transmission system. LD: laser diode, PZT: piezo-transducer, PD: photodetector, AWG: arbitrary waveform generator.
Fig. 5.
Fig. 5. Relationship of SOP trace and polarizer in the most sensitive situation. P: polarizer.
Fig. 6.
Fig. 6. Setup of the PMF-based forward transmission system. V-Amp: Voltage Amplifier, OSC: oscilloscope.
Fig. 7.
Fig. 7. Sensitivities of SMF-based and PMF-based forward transmission systems. (a) Time-domain result. (b) frequency domain result. (c) Sensitivities distribution. (d) Noise level

Tables (1)

Tables Icon

Table 1. Parameters used in the simulation.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

M i = α [ 1 0 0 0 0 cos 2 2 θ i + sin 2 2 θ i cos δ i cos 2 θ i sin 2 θ i ( 1 cos δ i ) sin 2 θ i sin δ i 0 cos 2 θ i sin 2 θ i ( 1 cos δ i ) sin 2 2 θ i + cos 2 2 θ i cos δ i cos 2 θ i sin δ i 0 sin 2 θ i sin δ i cos 2 θ i sin δ i cos δ i ]
S out = M S i n = M N M N 1 M 1 S in .
M p = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] .
S p = M p S o u t = 1 2 [ 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ] [ s o u t 0 s o u t 1 s o u t 2 s o u t 3 ] = 1 2 [ s o u t 0 + s o u t 1 s o u t 0 + s o u t 1  0  0 ]
I = 1 2 ( s o u t 0 + s o u t 1 ) .
E = [ E x , E y ] T = [ E x e j δ x , E y e j δ y ] T .
I o = | E x e j δ x cos ( π / 4 ) + E y e j δ y sin ( π / 4 ) | 2 = E x 2 / 2 + E y 2 / 2 + E x E y cos ( δ x δ y ) .

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