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Abstract
We report the numerical and experimental study of probe pulse deformation in a forward-pumped distributed Raman amplifier on a 40-km standard single mode fiber. Distributed Raman amplification can improve the range of OTDR-based sensing systems, but it could result in pulse deformation. A smaller Raman gain coefficient can be used to mitigate pulse deformation. The sensing performance can still be maintained by compensating for the decrease in the Raman gain coefficient by increasing the pump power. The tunability of the Raman gain coefficient and pump power levels are predicted while keeping the probe power below the modulation instability limit.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin optical time-domain reflectometry (BOTDR) is a fiber-based sensing technique based on spontaneous Brillouin scattering for distributed fiber-optic sensing [1]. The technique allows the data separation of strain and temperature measurements using only one fiber by analyzing the back-reflected Brillouin signal frequency shift and Brillouin power. [1,2]. A BOTDR interrogator scheme using a polarization-diverse coherent receiver suited for distributed sensing at distances up to 100 km is reported in [3]. The work shows that distributed temperature sensing based on Brillouin signal power and strain sensing based on the shift in Brillouin frequency is a viable approach to reduce the cross-sensitivity between the two parameters. Further enhancement of signal to noise ratio (SNR) and sensing range in BOTDR systems can be achieved by employing amplification schemes like distributed Raman amplification [4,5] and remotely pumped amplification in Erbium doped fibers (EDF) [6]. The sensing range of single side interrogated repeater-less BOTDR has been extended to 250 km using Raman amplification and remotely pumped EDF in [7]. Similar work was performed on Brillouin optical time-domain analysers (BOTDA) [8–10], and phase-sensitive Rayleigh optical time-domain reflectometry ($\varphi$-OTDR) for distributed acoustic sensing [9,11]. Implementing higher-order Raman amplification [12] and a bi-directional or backward pumping scheme [13,14] can lead to improved sensitivity and flatness of OTDR-based sensing systems than single-wavelength forward Raman pumping schemes. Optical pulse coding/decoding techniques can further enhance the signal-to-noise ratio and hence improve the accuracy and spatial resolution in Brillouin sensing systems. [15–18].
One challenge with amplifier-assisted sensing systems arises when the probe pulse is temporally deformed as a result of the amplification process [10]. Such deformation occurs when the amplification process is not temporally invariant due to local gain depletion. In the case of Raman amplification using a co-propagating pump field, the combined effect of pump depletion and pump-probe walk-off along the sensing fiber can result in significant deformation of the probe pulse [10]. In the conventional case of anomalous fiber dispersion, the pump propagates faster than the probe so that the leading edge of the probe pulse experiences a smaller gain than the trailing edge. Unfortunately, an asymmetrically deformed pulse will experience a frequency shift due to a self phase modulation induced chirp [10]. For Brillouin sensing, such a frequency shift may result in a bias in the temperature and strain estimation which is highly nontrivial to account for. Thus, while pre-tailoring the shape of the probe pulse can sometimes be advantageous [19,20], keeping the pulse shape unaltered during transmission in the sensing fiber is, however, essential in all of the above-mentioned schemes for distributed fiber-optic sensing.
In this paper, the Raman gain coefficients for standard single mode fiber (SSMF) and TrueWave reduced slope (TW-RS) fiber are characterized, and pump depletion is studied using CW pump and probe sources. The probe pulse deformation is characterized using a CW pump source and a pulsed probe source. A quantification of pulse deformation is defined, and it is used to evaluate the simulated and measured pulse deformations. We show that utilizing a smaller Raman gain coefficient allows mitigation of the pump depletion which reduces probe pulse deformation, while the probe power at the end of the fiber can be maintained by increasing the pump power. Additionally, we numerically analyze the frequency shift that happens due to pulse deformation, and show that utilizing a smaller Raman gain coefficient can reduce such frequency shifts. By considering the modulation instability (MI) limit, the highest possible pump and probe powers that could be used while tuning the Raman gain coefficient are predicted. As a result, we show that implementing distributed Raman amplifiers with a smaller Raman gain coefficient can enhance the fiber sensing system SNR and signal reach while avoiding pump depletion. We also show that using a fiber with lower dispersion reduces the amount of deformation to the pulse shape.
This paper is organized as follows. In section 2, the depolarized effective Raman gain coefficient characterization and pump depletion studies using the CW pump and probe sources are presented. The study on probe pulse deformation with pulsed probe setup is given in section 3. The effect of group velocity dispersion on probe pulse deformation is given in section 4. In section 5, a numerical analysis is carried out, where the highest possible pump powers that will keep the probe pulse deformation below a fixed level at different Raman gain coefficient settings are predicted numerically while considering the MI threshold limitations. In section 6, the mitigation of probe frequency shift due to pulse deformation is studied by simulation.
2. Raman gain coefficient characterization and pump depletion study
For CW sources of pump and probe, the forward pumped Raman-amplification process is described by the following two coupled pump and probe rate equations [21]:
Figure 1 shows the experimental setup used to study the pump depletion. An Ando (AQ4321D) laser, which can be tuned from 1520 nm to 1620 nm (corresponds to pump and probe frequency shift $\Delta \nu =\nu _P-\nu _{Pr}$ of 9 to 21 THz) is used as the probe laser and a depolarized Keopsys KPS-BT2-RFL-1455-30-FA laser with a wavelength of 1455 nm is used as the pump. The transmission part of the Raman amplifier is only studied in this paper. Hence, the Brillouin scattering must be avoided. For that, a phase modulator driven by a 2 GHz sinusoidal RF signal is used to broaden the linewidth of the probe laser. EDFAs operating in the C-band (Keopsys KPS-STD-BT-C-30-PB-111-FA-FA) and the L-band (JDS Uniphase OAB1492+20FP4) are used to amplify the probe at the respective probe wavelengths. The output from EDFA is controlled by a VOA. The pump and probe are combined using a WDM and co-propagated in the 40-km SSMF. The input pump and probe powers are monitored using a power meter connected to the 1$\%$ port of a 20-dB coupler. The end of the fiber is connected to an OSA (YOKOGAWA AQ6375) using the 1% port of another 20-dB coupler. The output probe spectrum is measured on the OSA, when the pump and probe signals are co-propagating in the fiber and the measurement is repeated while the pump is turned off. From the two measurements, the on-off gain $G_A$ is obtained. The fiber attenuation coefficients of SSMF at the pump and probe wavelengths are measured as $\alpha _P(\Delta \nu = {0}\;\textrm{THz})= {0.246}\;\textrm{dB/km}$, $\alpha _{Pr}(\Delta \nu = {13.2}\;\textrm{THz})= {0.191}\;\textrm{dB/km}$.
Fig. 1. Experimental setup used for studying the pump depletion. (EDFA: Erbium-doped fiber amplifier, WDM: wavelength division multiplexer, VOA: variable optical attenuator, OSA: optical spectrum analyzer, RF: radio frequency)
First, the small signal on-off gain, $G_A$, is measured by tuning the probe wavelength from 1520 nm to 1620 nm. By inversely calculating Eq. (2), the Raman gain coefficient $g_R(\lambda )$ of SSMF and TW-RS fibers can be obtained from the measured $G_A$. The results are shown in Fig. 2(a), where the peak gain is 13.2 THz away from the pump frequency. The TW-RS fiber has a larger $g_R(\lambda )$ than SSMF. In the measured frequency shift range, the obtained Raman gain spectra are almost identical in the shape compared to the expected Raman spectrum in fused silica fiber [22]. These obtained Raman gain coefficients $g_R(\lambda )$ are used to study the pump depletion and the following probe pulse deformation study.
Fig. 2. (a) Measured Raman gain spectra as a function of the pump and probe frequency shift in SSMF (red) and TW-RS (blue) fibers. Markers show the standard deviation errors of the measurements. (b) Output probe power as a function of pump power at three $g_R$ values at an input probe power of 10 dBm. Simulation results are shown in solid lines. The dashed line shows the simulated undepleted output power. Measured results are shown in triangular markers.
The pump depletion is measured in different pump powers from 0.4 W to 1.2 W at three different Raman gain coefficients $g_R=0.377 \mbox {, } 0.306\mbox { and } 0.173 \, {}\;{\textrm{(W km)}^{-1}}$ by setting frequency shift at 13.2, 15.1 and 15.7 THz respectively. The input probe power $P_{Pr,in}$ is set at 10 dBm. The results are shown in Fig. 2(b), and compared with corresponding numerical simulations. In the study, the output probe power $P_{Pr.out}$ in decibel is estimated based on the measured on-off gain $G_A$, using the equation $P_{Pr,out}=G_A+P_{Pr,in}-\alpha _{Pr}L$. These obtained output powers are plotted as a function of the pump power for different $g_R$ together with corresponding simulation results in Fig. 2(b). For lower pump power, the output probe power matches with the undepleted output probe power, but for higher pump power, the two lines deviate, showing the impact of pump depletion. The pump depletion increases significantly when using a larger $g_R$. The measured output power agrees well with the simulated output probe power given in solid lines in the same figure, confirming the fact that a larger $g_R$ results in larger pump depletion. The results show that, when using $g_R=0.377 \mbox {, } 0.306\mbox { and } 0.173 \, {}\;{\textrm{(W km)}^{-1}}$, the output probe power can be kept approximately the same as 15 dBm while the pump powers are set at 0.55, 0.65 and 1.10 W, respectively. Hence, it is practically possible to utilize a smaller Raman gain coefficient to avoid pump depletion while maintaining the output probe powers by increasing the pump power for a constant input probe power.
3. Tuning the Raman gain coefficient for mitigating the probe pulse deformation
To study the probe pulse propagation in the fiber, the following amplitude propagation equations are considered [21]:
Figure 3 shows the experimental setup used for measuring probe pulse deformation. Similar to the CW probe setup shown in Fig. 1, the probe signal is spectrally broadened first using a phase modulator. Then, using an intensity modulator (JDSU OC-192 10Gb/s) driven by a pattern generator (HP 8130A), the CW probe source is converted to a pulse train of 50 ns pulse widths and 100 ns separation between the pulses. At the end of the fiber, the pulsed probe and pump signals are separated using a second WDM. The residual pump is dumped, and the amplified probe pulse is filtered by an ASE filter (Koshin Kogaku TFM/FC) to remove the ASE noise from EDFAs. Another VOA is used to avoid saturation in the photodiode. The probe pulses are acquired by the PP-10G 10 Gbps photodiode. Then the traces are analyzed using a Lecroy LT262 oscilloscope which has a bandwidth of 350 MHz and operates in Random Interleaved Sampling (RIS) mode at 50 GS/s. The acquired traces are low-pass filtered during post-processing to reduce the noise. Finally, the filtered traces are normalized to the average power at the leading edge of the pulse.
Figure 4 shows the normalized input probe pulses. The simulated pulses are approximated to a 30th order super Gaussian pulse using the equation:
Fig. 4. Measured and simulated input probe pulses are shown using blue solid lines and black dashed lines, respectively.
Fig. 5. Measured and corresponding simulated probe traces are shown using solid lines and black dashed lines, respectively. (a) output probe pulses for $g_R = {0.377}\;{\textrm{(W km)}^{-1}}$, (b) output probe pulses for $g_R = {0.173}\;{\textrm{(W km)}^{-1}}$. The measured trace using input peak probe powers of $P_{Pr}=21\mbox { and }18\mbox { dBm}$ are shown in blue and red solid lines, respectively. The measured traces at different input peak probe powers are separated in time for better visualization. The pump power is set at 0.2 W.
To quantify the probe pulse deformation, a deformation factor $\eta$ is defined as the ratio of power in the trailing edge to the power in the leading edge:
In the equation, $\widetilde {P_{Pr}^{+,-}}$ is the power at the trailing and the leading edge of the output pulse normalized to the leading edge of the pulse. Thus, $\eta$ is a measure of the deformation of the output pulse compared to the input pulse. If $\eta = 1$, the pulse is not deformed, but rather evenly amplified or attenuated during propagation and thus it keeps the original properties. The variation of $\eta$ with $g_R$ for four different input peak probe powers is shown in Fig. 6(a). Experimentally, the pulse deformation is measured at two frequency shifts at 13.2 THz and 15.7 THz, corresponding to $g_R$ of ${0.377}\;{\textrm{(W km)}^{-1}}$ and ${0.173}\;{\textrm{(W km)}^{-1}}$. As the peak probe power increases, the deformation on the pulse also increases, but the deformation is more pronounced for larger $g_R$ values. For $g_R = {0.173}\;{\textrm{(W km)}^{-1}}$, the deformation is close to one, for all input peak probe powers in both simulated and measured output probe pulses. At $g_R = {0.377}\;{\textrm{(W km)}^{-1}}$, the deformation factor, $\eta$, of the measured output probe pulse deviates from the simulated pulses. The narrow transient in the deformed peak may not be fully resolved due to the limitation of oscilloscope bandwidth. This may be the reason for the discrepancy between the measurement and simulation when using larger $g_R$. Despite this deviation, the tendency of larger pulse deformation for larger Raman gain is clearly evident in both the simulated and measured output traces for all input peak probe powers of the pulses.Fig. 6. (a) Variation of deformation factor $\eta$ with $g_R$ for SSMF at four different input peak probe powers with pump power $P_P = {0.2}\;\textrm{W}$. $\eta$ for the two measured pulses at $g_R= {0.173}\;{\textrm{(W km)}^{-1}}$ and ${0.377}\;{\textrm{(W km)}^{-1}}$ are shown using markers and the simulated results are shown by lines. (b) Deformations of two probe pulses with the same output average probe power of 10 dBm, but different $g_R$ values of ${0.173}\;{\textrm{(W km)}^{-1}}$ and ${0.377}\;{\textrm{(W km)}^{-1}}$ and pump powers 0.4 W and 0.2 W, respectively. The input peak probe power $P_{Pr}= {21}\;\textrm{dBm}$ is the same for both traces. The measured traces at different configurations are separated in time for better visualization. Simulated traces are shown using dashed lines and measured traces using solid lines.
Practically, fiber sensing systems that use Raman amplification normally keep a fixed input peak probe power, while varying pump power to improve the sensing performance. Hence, the mitigation of probe pulse deformation is also studied on the 40 km of SSMF for different pump powers while keeping the input probe power the same. Figure 6(b) shows two output probe pulses with the same average output probe power of 10 dBm at different configurations as $g_R= {0.173}\;{\textrm{(W km)}^{-1}},\,P_P = {0.4}\;\textrm{W}$ and $g_R= {0.377}\;{\textrm{(W km)}^{-1}},\,P_P = {0.2}\;\textrm{W}$, respectively. The same input peak probe power is set at 21 dBm. The relative power of the deformed pulse peak at the trailing edge is reduced by 22% by tuning the pump and probe frequency shift to utilize a smaller $g_R$. The output probe power is maintained by compensating for the lower gain by increasing the pump power.
4. Mitigating probe pulse deformation using a fiber with lower dispersion
In section 2 and 3, pump depletion and pulse deformation in a 40-km SSMF were considered. The probe pulse deformation is a combined effect of pump depletion and group velocity dispersion, i.e. the walk-off between the pump and probe pulses due to the difference in group velocity of the two wavelengths. When using a fiber with lower group velocity dispersion, the pump and probe have less temporal walk-off. To study the effect of dispersion on pulse deformation, the above simulations and measurements are repeated on a 43-km TW-RS fiber. TW-RS has a larger Raman gain coefficient and a lower group velocity dispersion between the pump and probe wavelengths compared to SSMF [23]. For this group velocity dispersion effect study, two similar $g_R$ for SSMF and TW-RS fibers are being used, namely $g_R(\Delta \nu = {13.2}\;\textrm{THz})= {0.377}\;{\textrm{(W km)}^{-1}}$ and $g_R(\lambda _{Pr}= {15.7}\;\textrm{THz})= {0.306}\;{\textrm{(W km)}^{-1}}$, respectively. The walk-off parameter $\Delta \beta _1$ for the TW-RS fiber at $g_R= {0.306}\;{\textrm{(W km)}^{-1}}$ is ${-0.34}\;\textrm{ns/km}$, which is significantly smaller than the $\Delta \beta _1$ for SSMF at $g_R$ of ${0.377}\;{\textrm{(W km)}^{-1}}$, namely ${-1.74}\;\textrm{ns/km}$. The simulated and measured probe pulses at the end of the 43-km TW-RS fiber for two different input peak probe powers of 18 dBm and 21 dBm are shown in Fig. 7. Comparing these output pulse shapes with those in SSMF at $g_R= {0.377}\;{\textrm{(W km)}^{-1}}$ shown before in Fig. 5(b), it is seen that the TW-RS pulse is flatter than in the SSMF because the deformation is lower. The amount of the deformed peak at the trailing edge of TW-RS fiber is significantly smaller than that of the SSMF. When using 18 dBm input peak probe power, the deformed peak width at the end of 40-km SSMF is 13.2 ns, while for the 43-km TW-RS fiber, it is 2.7 ns. While the relative power between the trailing and leading edge of the pulses is 1.33 in SSMF and 1.1 in TW-RS fiber. Hence, by using a lower dispersion TW-RS fiber, the deformed peak width is reduced by 79.5%, and the deformed peak is reduced by 17.2%. Therefore, a lower dispersion fiber can preserve the original pulse shape in Raman amplification. The pump and probe signals propagate with less temporal separation, as there is lower group velocity dispersion between the pump and probe wavelengths. Both the leading and trailing edges experience a more similar depleted pump power level, which results in a significantly less deformation peak compared to SSMF. Moreover, the Brillouin backscattering power and Kerr effect inversely scale with ${A_{eff}}$. Hence, all these factors together with the fiber attenuation factor should be considered while selecting the fiber for fiber sensing.
Fig. 7. Probe pulse deformation at the output of 43-km TW-RS fiber for two different input peak probe powers when the pump power is 0.2 W, and Raman gain coefficient is set as $g_R= {0.306}\;{\textrm{(W km)}^{-1}}$. The simulated pulses are shown using the dashed lines with markers and the measured pulse using solid lines.
5. Numerical analysis on the tunability of Raman gain coefficient
The constraint of tuning the Raman gain coefficient and compensating with higher pump power is modulation instability (MI). This can occur when the probe power exceeds the MI critical power threshold, which results in detrimental effects on the fiber sensing. Due to pulse deformation, the deformed peak is likely to exceed this limit in the amplification process even though the input probe power is still lower than the critical power. Hence, it is necessary to keep the probe power below such limit throughout the fiber during the amplification process.
In the following analysis, the highest possible pump powers corresponding to different measured Raman gain coefficients of 40-km SSMF are numerically predicted. The deformation factor $\eta =1.5$ is set as a limit. This limit is chosen such that the impact of the deformation becomes visible on the frequency traces of the sensing system, which is discussed in more detail in the next section. The input peak probe power is set at 22 dBm. The critical probe power of 23 dBm is considered as the MI threshold above which the MI can happen and degrade the sensing systems’ performance [5,24]. The results are shown in Fig. 8, the predicted highest pump power that could be used increases as the $g_R$ decreases. It shows that, when using smaller $g_R$ the deformation factor can be kept approximately the same at $\eta =1.5$, while allowing higher pump powers. The output probe power at the leading edge also increases when using smaller $g_R$, this is due to the amplifier gain being higher when using higher pump power. This also proves that using a smaller $g_R$ can reduce pulse deformation, while maintaining the output probe power level by increasing the pump power. However, a limitation of using smaller Raman gain coefficients $g_R$ and increasing the pump power is determined by the MI threshold on probe power. The maximum peak probe power in the fiber shown in the magenta line starts to exceed the MI critical power of 23 dBm, when the Raman gain coefficient is smaller than ${0.2}\;{\textrm{(W km)}^{-1}}$ and the pump power is larger than 27 dBm (0.5 W). It shows that when limiting the deformation to $\eta =1.5$, the smallest Raman gain coefficient that can be used is $g_R= {0.2}\;{\textrm{(W km)}^{-1}}$ and the highest pump power is 0.5 W, for an input peak probe power of 22 dBm. For all these configurations, the powers at the leading edge of the deformed output probe pulses are higher than the peak probe power without amplification, which shows that even with a small $g_R$ the distributed Raman amplification can improve the SNR of the sensing systems.
Fig. 8. Numerically predicted pump powers for different $g_R$ settings when the allowed deformation is $\eta =1.5$ in a 40-km SSMF Raman amplifier system. The input peak probe power is set at 22 dBm. The highest input pump powers are shown in a blue solid line, the red solid line shows the output probe power at the leading edge, and the corresponding $\eta$ is shown in the green line. The output peak probe power without using Raman amplification is shown using the red dashed line, the maximum peak probe power throughout the fiber is shown using the magenta line, the gray area is the limit of smallest $g_R$ below which MI can occur, and the black dashed line shows the assumed MI critical power of 23 dBm.
Practically, a low input peak probe power can be useful to avoid MI when using Raman amplification. For 40 km of SSMF, by using an input peak probe power of 13 dBm, the pump power can be increased to 32.7 dBm (1.82 W) and a smaller Raman gain coefficient of $g_R= {0.136}\;{\textrm{(W km)}^{-1}}$ can be utilized. It needs to be noticed in Fig. 6(a), the studies using input peak probe power of 24 and 27 dBm exceed the MI limit when using Raman amplification. Even though the MI effect is not clearly observable in the temporal trace for this short-length transmission in 40 km SSMF, the MI could still severely deteriorate the performance of the fiber sensing systems.
Moreover, when using a fiber sensing system with a longer length, higher pump power is needed to compensate for the small Raman gain coefficient to maintain the SNR at the remote end. In this case, the highest probe power along the fiber is more likely to exceed the MI critical power, which may limit the tunability of the Raman gain coefficient. Such predictions on the tunability of the Raman gain coefficient and pump power can be carried out for any Raman amplifier system to mitigate the probe pulse deformation based on the sensing system requirements.
6. Numerical analysis of mitigating frequency shift due to pulse deformation
The probe pulse deformation can result in a small shift of the probe frequency spectrum due to self phase modulation (SPM) [10]. This frequency shift does not occur when the probe pulse maintains a rectangular-like shape. However, as the probe pulse is deformed, it shows a gradual intensity variation across the pulse resulting in a SPM induced frequency shift. The frequency shift can affect the fiber sensing systems that rely on Brillouin frequency shift, since this could for instance incorrectly be interpreted as a change of temperature and strain. Hence, mitigating probe pulse deformation is useful to minimize Brillouin frequency shift estimation errors. The frequency shift is studied on the 40-km SSMF using simulations. The frequency spectrum of input and output probe pulses are shown in Fig. 9. The center of the deformed output probe pulse frequency spectrum is shifted by 18 MHz at the end of the 40-km SSMF. Compared to the input spectrum, which can be described as a sinc function, the output probe spectrum is not only shifted to the lower frequency, but also shows asymmetry, as the red-shifted side has more power. In fiber sensing systems based on Brillouin scattering, both the shift and the asymmetry in the probe frequency can distort the Brillouin spectrum and result in the Brillouin peak frequency shift. The Brillouin peak frequency shift induced by probe pulse deformation has been reported in [25], and the measured peak Brillouin frequency is shifted by 3 MHz in a 34 km of optical fiber (Sumitomo Z-PLUS Fiber ULL) while using a pump power of 0.6 W and input peak probe power of 17 dBm. Therefore, the deformation in probe pulses in Raman amplification could result in a relevant Brillouin frequency shift estimation error.
Fig. 9. Comparison of simulated input (blue) and output (red) probe pulses and the corresponding spectra in 40-km SSMF, when using $P_P = {0.6}\;\textrm{W}$, $P_{Pr,in}= {15}\;\textrm{dBm}$ and $g_R= {0.377}\;{\textrm{(W km)}^{-1}}$.
Figure 10(a) shows the simulated probe frequency shift induced by pulse deformation between the start and the end of 40-km of SSMF. The absolute frequency shift at different input peak probe power for different pump powers is shown here. The simulated result shows that, the absolute frequency shift increases with input probe and pump powers. For $g_R= {0.377}\;{\textrm{(W km)}^{-1}}$, the highest frequency shift is approximately 18 MHz for the pump power of 0.6 W, as shown with the blue solid line. When using a smaller Raman gain coefficient $g_R= {0.173}\;{\textrm{(W km)}^{-1}}$, the frequency shift is decreased to 6 MHz using the same pump power, as shown with the red solid line. In Fig. 10(b), the frequency shift is plotted as a function of output probe power at the leading edge of the deformed pulse. The frequency shift increases when having higher output probe powers at the leading edge. When using the same input peak probe power of 13 dBm, the frequency shift can be decreased by 1.6 MHz by decreasing $g_R$ from 0.377 to 0.173 ${\textrm{(W km)}^{-1}}$, while the output probe power is maintained at 10 dBm by compensating for smaller Raman gain coefficient by increasing the pump power from 0.2 W to 0.4 W. The typical resolution of frequency estimation at the end of a long fiber in a Brillouin-based OTDR sensing system is in the order of 1 MHz to 2 MHz [25]. If the frequency shift induced by pulse deformation is larger than 2 MHz, it will result in an error in frequency shift estimation due to temperature or strain changes. For example, the configuration in Fig. 6(b) where $g_R= {0.377}\;{\textrm{(W km)}^{-1}},\,P_P = {0.2}\;\textrm{W}$ and $P_{Pr}= {21}\;\textrm{dBm}$, gives the deformation factor $\eta \approx 1.5$. These studies are within the MI threshold as described in Fig. 8. The corresponding probe frequency shift can be numerically estimated as $|\Delta \nu |= {11}\;\textrm{MHz}$. When using 40-km SSMF as the sensing fiber, such frequency shift can be translated to ${10}^{\circ }\textrm {C}$ temperature estimation error or ${244}\;\mathrm{\mu}{\varepsilon}$ strain estimation error [3]. This shows that, while using Raman amplification in a fiber sensing system, mitigating probe pulse deformation is necessary to reduce the probe frequency shift error.
Fig. 10. (a) Absolute frequency shift between start and end of 40-km SSMF with the respect to input probe pulse as a function of input peak probe power. Simulation results using $g_R = {0.377}\;{\textrm{(W km)}^{-1}}$ and $g_R = {0.173}\;{\textrm{(W km)}^{-1}}$ are shown in blue and red, respectively. The input pump powers are 0.6, 0.4, and 0.2 W and using shown using different line styles. (b) The absolute frequency shift varies with output leading edge probe power, the results for $g_R = {0.377}\;{\textrm{(W km)}^{-1}}$ and $P_P = {0.2}\;\textrm{W}$ and for $g_R = {0.173}\;{\textrm{(W km)}^{-1}}$ and $P_P = {0.4}\;\textrm{W}$ are shown in blue dotted and red dashed lines, respectively. The gray dashed line indicates the same output probe power of 10 dBm, the round marker shows the cases when the input probe peak powers are the same, namely 13 dBm.
7. Conclusion
In this paper, pump depletion in distributed Raman amplifiers is studied both through simulations and experiments. The pump depletion and group velocity dispersion in the fiber can cause deformation in probe pulses in a Raman amplifier system. Using a pulsed probe source, this probe pulse deformation is studied for different values of the Raman gain coefficient, and for both SSMF and TW-RS fibers with different dispersion profiles. The results show that using a smaller Raman gain coefficient can reduce pump depletion and mitigate the probe pulse deformation by detuning the pump and probe frequency shift. The output probe power, and with it the SNR at the far end of the sensing fiber, can still be maintained by increasing the pump power. Fibers with smaller dispersion between the pump and probe wavelengths can also reduce the deformations in the output probe pulse. For a 40-km SSMF with an input peak probe power of 22 dBm, the highest possible pump power for a fixed deformation factor of $\eta =1.5$ is predicted between 23 to 27 dBm when $g_R$ is tuned from ${0.377}\;{\textrm{(W km)}^{-1}}$ to ${0.2}\;{\textrm{(W km)}^{-1}}$ before MI occurs. The probe frequency shift due to pulse deformation is predicted for different Raman gain coefficients and pump powers. It is also possible to maintain the output power and reduce the frequency shift by using a smaller $g_R$ while increasing the pump power. For a distributed Raman amplifier using 40 km of SSMF, the probe frequency shift can be reduced from 18 MHz to 6 MHz by tuning the Raman gain coefficient from ${0.377}\;{\textrm{(W km)}^{-1}}$ to ${0.173}\;{\textrm{(W km)}^{-1}}$ when the pump power is 0.6 W and the input peak probe power is 15 dBm. Even with a smaller Raman gain coefficient, the implementation of a distributed Raman amplifier can still improve the sensing signal reach. Hence, when including distributed Raman amplification schemes in a fiber sensing system that has the requirements on probe pulse shape, it is better to utilize a smaller Raman gain coefficient and use sensing fibers with lower group velocity dispersion. In the already deployed systems, changing the sensing fiber to a lower dispersion fiber is not practically possible. In such cases optimizing the pump frequency for a smaller $g_R$ can be a better option. Choosing a fiber with a smaller dispersion can be beneficial when implementing new fiber sensing systems. These conclusions still hold if the length of the sensing fiber is longer than 40 km. In a sensing system with a longer length, the effective probe reach is mainly determined by the length of the fiber where the maximum probe power is reached. This in turn depends on the available pump power, the Raman gain coefficient, the fiber attenuation coefficient, and input peak probe power. The probe pulse deformation mainly occurs within the length over which the pump depletion happens, after that the pulse deformation stays the same. These factors together with the MI limit determine the degree of freedom in utilizing distributed Raman amplification in OTDR-based fiber sensing systems. It is also important when using a remote optically pumped amplifier (ROPA) to further improve the sensing performance. Single-sided sensing systems with forward pumping schemes are considered in this paper. Higher-order, backward, or bidirectional pumping schemes are out of the scope of this paper, but the conclusions made here also apply to these schemes, as pump depletion is inevitable in all Raman amplifier systems.
Funding
Innovationsfonden (0224-00074B).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors on reasonable request.
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