In polarization optical time domain reflectometry (POTDR) system, the performance of polarimetric measurement is constrained by the low signal to noise ratio (SNR) due to the weak Rayleigh backscattering and the degradation of the degree of polarization (DOP) of signal light. Therefore, it is indispensable to improve the SNR without sacrificing the DOP of backscattered signal for a sufficient dynamic range. In this paper, a Simplex coded POTDR (sc-POTDR) system is proposed and demonstrated. The relationships between the signal’s DOP and coding length/bit width are studied. Both numerical simulations and experimental results show that the length of Simplex code has no impact to the signal’s DOP and the temporal depolarization effect can be suppressed just by reducing the bit width. Applying 511-bit Simplex code, a coding gain of 10.125 dB has been demonstrated. By taking advantage of high DOP and the coding gain, the changes of polarization state caused by a mechanical event in a long fiber link have been detected and located precisely.
© 2017 Optical Society of America
Optical time domain reflectometry (OTDR) system has been widely used in the measurement of characterization of optical fibers . In OTDR system, an optical pulse is injected to the fiber links under test as a probe, then the Rayleigh backscattered and Fresnel reflected signals are collected by photodetector . The signal-to-noise ratio (SNR) of the system is determined by the peak power and pulse width of the probe pulse as well as the performance of photodetector. In this case, since the peak power of the probe pulse and the sensitivity of photodetector can’t be increased easily, the SNR of the OTDR system can be effectively improved by increasing the pulse width, which will however deteriorate the spatial resolution at the same time. In order to improve the SNR without sacrificing the spatial resolution, various coding techniques have been proposed and applied in conventional OTDR system  and distributed sensing systems based on OTDR . Biorthogonal Codes have been used in conventional OTDR system, and the SNR is enhanced up to 9.04 dB . Distributed temperature sensing based on Raman-OTDR with pulse coding is demonstrated  and Brillouin-based distributed temperature sensor employing pulse coding provides up to 7 dB SNR improvement .
As one kind of the OTDR system, polarization optical time domain reflectometry (POTDR) was proposed in 1980’s for measuring the spatial distributions of physical fields by detecting local polarization properties of single-mode fibers (SMF) . In a general way, backward Rayleigh scattering (BRS) light is detected as the sensing signal in the POTDR system [9,10]. As a result of imperfect manufacturing and the influence of external environmental factors, the birefringence of the fiber is randomly distributed, which makes the polarization states of signal light from different part of the sensing fiber change randomly. Although the POTDR suffers from the same low SNR problem as other OTDR systems, the application of coding techniques in POTDR system is not straightforward. When a light pulse covering a certain fiber length propagates along the sensing fiber, BRS lights arrive at the photodetector (PD) from different position have different polarization states, resulting in the intensity superimposition on the PD and further leading to the temporal depolarization effect. In an incomplete-POTDR system, the degree of polarization (DOP) of signal light determines the dynamic range of the system . Therefore, the signal’s DOP of an incomplete-POTDR system cannot be neglected when trying to improve the SNR by coding techniques. Unfortunately, few research has been conducted to investigate the suitable coding technique for POTDR. The relationships among the signal’s DOP, the selection of coding pattern, the coded pulse length and the bit width should be investigated in details.
In this paper, a Simplex coded POTDR system has been proposed and demonstrated for the first time to the best of the authors’ knowledge. Firstly, the dynamic range of the incomplete-POTDR system is defined in order to describe the relationship between signal’s DOP and system performance. As we can see from the mathematical definition, the higher the signal’s DOP is, the better the system performance will be. Secondly, a phase plate model is employed for simulation to study the relationship among signal’s DOP, width of single probe pulse and the bit width/coding length of Simplex code. From the results of simulation, the conclusion about Simplex coded POTDR system (sc-POTDR) can be drawn: 1) the coding length has no impact to the signal’s DOP changing; 2) the signal’s DOP mainly depends on the bit width of the Simplex code. In other words, no matter how long the code is, the signal’s DOP will not change as long as the bit width is kept constant. So Simplex coding can be used in POTDR system to overcome the tradeoff between SNR and the spatial resolution without introducing any extra temporal depolarization. At last, the simulation results have been verified experimentally by using 31- to 511-bit Simplex codes and excellent coding gain has been achieved, which agrees with theoretical analysis. Benefiting from these advantages, the changes of polarization state caused by a mechanical event between two sections of single mode fiber has been detected and located without average processing.
2. Theory and simulation
2.1 Relationship between DOP and dynamic range of a POTDR system
A phase-plate model is adopted to describe the fiber link, where the fiber is regarded as thousands of cascaded phase plates with linear birefringence. The Stokes vector and Mueller matrix are used to describe light and fiber respectively, then each segment of fiber is given by 
The coherent length of the light source used in POTDR is assumed to be much shorter than the optical pulse width, so light scattered back from different locations will superimpose by intensity at the receiver. The Stokes vector of scattered light which is detected at the fiber input can be defined as follows
Equation (2) is described discretely, where n denotes the location of optical pulse front edge. It is deduced from the continuous form that can be found in . r denotes the Rayleigh scattering coefficient. k denotes the number of segments from which the scattered light will arrive at the receiver spontaneously, which is in fact half the pulse width. is the total roundtrip Muller matrix from the input port to the i-th phase plate while R = diag(1,1,1,-1) . Sin denotes the Stokes vector of injected light. The DOP of the received optical signal is given by 
In an incomplete POTDR system, the light described by Eq. (2) will propagates through a polarizer before it arrives at the photodetector. As has been discussed in our previous publication , the light intensity after the polarizer is
According to Eq. (4), when the Stokes vector of the light arriving at the receiver changes, the light intensity after polarizer will have maximum and minimum values. When a disturbance event occurs at a fiber position, the detected signal intensity after this position in an incomplete POTDR system will wholly change. The normalized dynamic range of the effective optical power carrying polarimetric information in an incomplete POTDR system is thus defined as 
From Eq. (5) we can draw a conclusion that the DOP of the signal determines the dynamic range of POTDR system. Since the birefringence is randomly distributed along the fiber link, the DOP of the superimposed light will degrade, which reduces the range of signal power variation caused by disturbance event.
2.2 Relationship between DOP and parameters of coded optical pulse
In order to overcome the tradeoff between SNR and spatial resolution, various coding techniques have been proposed and applied in conventional OTDR systems and distributed sensing systems based on OTDR technique. In the process of decoding, plenty of correlation operations are used for enhancing the signal and reducing noise based on the fact that noise is randomly distributed and the signal is predictable. As the birefringence of the fiber is randomly distributed which makes the polarization states of signal light from different part of the sensing fiber change randomly, correlation coding techniques such as Golay code  and pseudo-random code  may be inappropriate for POTDR system. Therefore, the linear code is applicable to POTDR system such as Simplex code . A longer coded optical signal which actually injects higher energy will provide better SNR but it might lead to the fading of DOP in POTDR system, resulting in the deterioration of dynamic range. Thus it will be necessary to investigate the relationship between signal’s DOP and parameters of pulse coding (bit width, coding length).
For this purpose, we have performed simulations using the aforementioned model. The SOP of input light (Stokes vector) is Sin = [1;1;0;0] and the Rayleigh scattering coefficient is 10−7. A fiber link of 20 km is established with the length of each segment set at 0.2 m. The Mueller matrixes used for describing sensing fiber are generated only once, which means all the simulations are performed on the same sensing fiber. The DOP of BRS light can be calculated by the Stokes parameters with Eq. (3). Both conventional single pulse POTDR (sp-POTDR) system and Simplex coded POTDR (sc-POTDR) system are simulated for comparison.
For the case of single pulse, the pulse width is set from 10 ns to 50 μs. For coded pulse, the coding length is set from 31-bit to 511-bit while the bit width is set from 20 ns to 200 ns. To make a clear comparison, we calculate the mean value of DOP along the fiber link in each case. The simulation is repeated for 25 times so the standard deviation of average DOP in each case is calculated and plotted. The results are shown in Fig. 1.
From Fig. 1(a), the DOP decreases with the growth of pulse width. Finally it is stabilized at about 0.3 to 0.35, and this phenomenon is in consistency with the theoretical prediction  in which the minimal DOP of Rayleigh backscattered light is 1/3. The results of sc-POTDR system which are shown in Fig. 1(b) indicate that the DOP of the coded pulse does not change obviously unless the bit width changes. The bit widths used in Fig. 1(b) are also indicated in Fig. 1(a) as crosses, from which we can see that the DOP of sc-POTDR is the same as the DOP of sp-POTDR if their bit widths are the same regardless of coding length.
In fact, Simplex coding have very similar effect on POTDR and OTDR systems, i.e., recovering the system response of one bit by decoding the responses to a number of coded sequences. It has to be emphasized that the light source must be incoherent, otherwise the decoding process, which is actually linear matrix operation, would fail to take effect. Then it is not hard to understand that the DOP of coded POTDR only depends on the bit width, rather than the length of the whole sequence.
In coded OTDR, coding gain is used to represent the SNR enhancement over conventional OTDR under same measurement time, and its theoretical value is derived as Eq. (6) . In POTDR system, it is defined as the ratio between SNR of N-bit sc-POTDR and SNR of N times average sp-POTDR system on the condition that two systems have the same bit width. Since coherence is not considered in POTDR, the coding gain has the same expression as in OTDR.
As a conclusion, the Simplex coding can be used in POTDR system to overcome the tradeoff between SNR and spatial resolution without introducing any extra temporal depolarization. Long length Simplex code with narrow bit width will provide the incomplete POTDR system with high SNR, high spatial resolution and high dynamic range. These characteristics have been validated experimentally in the next section.
3. Experimental configuration and results
3.1 Experimental setup
The scheme of sc-POTDR system is shown in Fig. 2. This system is capable of modulating the optical probe pulse according to the given codes, sampling the backscattered signal and transmitting data for signal processing. With a LabVIEW program, the arbitrary waveform generator (AWG) can read and export the Simplex code sequence with different coding length through general-purpose interface bus (GPIB). The light source is a DFB laser with 1550 nm central wavelength, 0.15 nm spectral width and the output power is fixed at 10 dBm. Acoustic-optical modulator (AOM) is used to modulate the continuous wave (CW) light source into coded optical signal according to the AWG output. When the AWG exports the coded signal to AOM, a trigger signal is also exported to the oscilloscope at the same time. In the sc-POTDR system, the bit width is set at 100ns constantly, while the pulse width for sp-POTDR ranges from 100 ns to 50 μs. The sensing fiber consists of two sections of SMF, with the length of 25.5 km and 2.4 km respectively. Between the two sections of SMF, a polarization controller (PC) is used to introduce a polarization disturbance event in the experiment.
At the receiver, the Rayleigh backscattered light transmits through a fiber bench. Within the fiber bench, a fixed polarizer and a rotatable quarter-wave plate are used for the polarimetric measurement. The photodetector used in this experiment is a highly sensitive photodetector based on PIN-FET with 10MHz bandwidth. By changing the angle between the fast axis of quarter-wave plate and the optical axis of the polarizer four times, the DOP distribution of the fiber link can be calculated from the received POTDR traces. We choose the optimum angles −45°, 0°, 30° and 60° in our measurements . It is convenient to use Matlab for decoding detected signal and restoring stokes parameters off-line.
In sp-POTDR system, because of the low SNR of the system, for each angle setting, 25000 traces are recorded for averaging. The average DOP of signal with different pulse width are measured and the results are drawn in Fig. 3(a). It is clearly observed from Fig. 3(a) that the average DOP of signal falls to 1/3 with the pulse width widening. The results are in accordance with the simulation. According to Eq. (5), we can infer that increasing the width of optical probe pulse is not feasible for POTDR system. Overlong pulse width not only decrease the spatial resolution, but also cause serious temporal depolarization leading to significant deterioration of system dynamic range. According to Eq. (5), the low dynamic range will lead to less effective power fluctuation when a disturbance occurs on the fiber link that changes the polarization state, even though the optical signal intensity is strong enough.
In the sc-POTDR system, signal’s DOPs of different coding length are measured and the results are drawn in Fig. 3(b). As the coding length gets larger, the signal’s DOP remains unchanged and is consistent with sp-POTDR system with 100 ns pulse width (about 0.71). With the comparison of sc-POTDR and sp-POTDR, the feasibility of Simplex code for POTDR has been validated by simulation and experiment.
In Fig. 4(a), we illustrated experimental results obtained by single pulse (gray line) and 511-bit (black line) Simplex codes of 100 ns bit width. SNR of the POTDR system is improved significantly by 511-bit Simplex code. Actually the coding gains of 7~511 bit Simplex code are measured, and the experimental and theoretical results are shown in Fig. 4(b). Apparently, excellent agreement with the theoretical predictions has been observed over different coding lengths.
Besides the coding gain, in POTDR system, it is more interesting to examine the system response of Stokes parameters using the Simplex code. In the contrast experiments, the Stokes parameters of sp-POTDR and 511-bit sc-POTDR system with 100ns bit width were measured while the state of fiber link keeps static. In order to acquire accurate POTDR waveform for comparison, 50,000 repeated sampling was taken in sp-POTDR system. The measuring results of s1, one of the Stokes parameter, is shown in Fig. 5(a). We can see that s1 of sp-POTDR and sc-POTDR match very well. The calculation results of s2 and s3 have very similar features compared with s1 thus they are not presented. In this paper, subsection correlation calculation is defined which is used to measure the Stokes parameters similarities between sp-POTDR and sc-POTDR. The subsection correlation calculation window consists of 500 sampling points (sampling rate: 250Msam/s) and it slides along with the fiber link to obtain the distribution of correlation coefficient continuously. The correlation coefficient r of the Stokes parameters between sp-POTDR and sc-POTDR can be defined as followsFig. 5(b). As we know, the correlation coefficient higher than 0.6 is considered to be highly correlated between two sets of data. According to Fig. 5(b), the Stokes parameters (s1, s2, s3) of sp-POTDR and sc-POTDR show excellent agreement except for the end of the fiber link because of low SNR, which means that the Simplex coding does not affect the accurate measurement of Stokes parameters.
According to the results of simulation and experiment, the Simplex coding in POTDR system can overcome the tradeoff among SNR, spatial resolution and system dynamic range. We further demonstrate its application in determining and locating the mechanical event disturbance using POTDR system without averaging process. In experiments shown in Fig. 2, a polarization controller (PC) is inserted between two sections of single mode fibers (one is about 25.5 km, the other is about 2.4 km). The sc-POTDR system signal is collected before and after the change of the PC. The results are depicted in Fig. 6(a), while its partial enlarged detail around where the disturbance occurs (denoted by circle) is plotted in Fig. 6(b). As shown in Figs. 6(a) and 6(b), when we twist the PC, the status of polarization before the location of PC is almost constant (the POTDR trace coincide with the other) while the POTDR traces after the location of PC separate with each other. In order to find the disturbing point, POTDR traces are processed by subsection correlation calculation defined in Eq. (7). As we know, the smaller the correlation coefficient is, the more significant difference of two traces will be. By setting a suitable threshold of correlation coefficient (0.3 is used in this experiment), we can easily locate the disturbing point at 25.5 km as plotted in Fig. 6(c).
In this paper, we numerically and experimentally demonstrated a SNR improved sc-POTDR system using Simplex coding for the first time, to the best of the authors’ knowledge. The 511-bit Simplex code provides a coding gain of 10.125 dB without performing any average processing which overcomes the trade-off among the dynamic range, spatial resolution, SNR and DOP. Moreover, the changes of polarization state caused by a mechanical event along the single mode fiber link has been detected and located accurately by using a 511-bit sc-POTDR system with 100ns bit width. Long Simplex code provides POTDR system the sufficient SNR to avoid average processing which is time-consuming. We believe that the sc-POTDR will pave the way to the application of instantaneous intrusion sensing and vibration frequency extraction based on the polarization measurement with the help of real-time digital signal processing circuits.
National Natural Science Foundation of China (61290311, 61331010, 61275069, 61205063, 61307091); 863 High Technology Plan of China (2013AA013402); the National Key Technologies R&D Program (2016YFB1200104); Program for New Century Excellent Talents in University (NCET-13-0235).
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