Open Access
Add to BibSonomy
Abstract
In distributed optical fibre sensors, distributed amplification schemes have been investigated in order to increase the measurement range while avoiding the limitation imposed by the fibre attenuation and the nonlinear effects. Recently, the use of Raman amplification with an engineered intensity modulation has been demonstrated as an efficient way to produce a virtually lossless trace employing a single-end configuration. In this paper, we propose the combination of this technique with a simultaneous second order Raman pumping scheme for increasing the measurement range. The optimal modulation profile has been numerically analyzed and we experimentally demonstrate a sensor able to detect perturbations along 70 km of fibre, with a minimal SNR penalty along the total length. Thanks to this new approach, the sensitivity in the worst point is considerably improved, and the ASD noise floor is also reduced. The measurement range is extended approximately 15 km compared with the equivalent first order pumping case.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed optical fibre sensors (DOFS) are a promising technology for vibration sensing, as low-cost and widespread telecommunication cable can be efficiently transformed into an acoustic sensor [1]. These sensors represent a cost-effective method to measure at every point along an optical fiber that can be deployed in any unusual environment.
In the general configuration of time-domain DOFS, a series of pulses are sent into the fibre under test (FUT) and the return of the backscattered signal due to the Rayleigh process is recorded and analyzed against time. This analysis provides us with information about perturbations as well as temperature and strain changes. Unfortunately, the trace power decays with distance due to fibre attenuation and the measurement range is limited to a few tens of kilometers. To face this problem, the pulse probe energy can be increased at the input by means of enlarging the pulse width or increasing the peak power. However, the first solution reduces the spatial resolution whereas the second alternative produces the advent of nonlinear impairments such as modulation instability (MI). The use distributed amplification based on nonlinear effects (Raman, Brillouin or parametric) to compensate for the fibre attenuation is an alternative solution that allows us to extend the measurement range without compromising the resolution [2–6]. Several Raman pumping schemes, including the use of bidirectional pumps or higher order schemes [7,8], have been investigated in order to achieve a close-to-perfect compensation of the attenuation losses. These schemes can minimize simultaneously the amplified spontaneous emission (ASE) noise and the nonlinear impairments. However, these techniques require extremely high average pump powers (which have implications for eye safety), and a pump source launched at the opposite fibre end, which is not generally possible in real implementations. Recently, single-end implementations of virtual transparency in DOFS has been proposed [9,10]. These configurations use Raman and Brillouin amplification in which perfect compensation is obtained by means of engineering the time-domain gain through the modulation of the pump intensity. Thanks to these configurations, the nonlinear effects and the ASE are reduced and the pump energy is saved. Here, Brillouin assistance in distributed sensors presents several drawbacks such as a narrow gain bandwidth that is inhomogeneous along the fibre and fluctuates with temperature changes. Moreover, the Brillouin effect produces an amplification exclusively between counter-propagating signals and, consequently, only the backscattered signal is amplified by a co-propagating pump. By using Raman assistance in distributed sensors, both the probe and the backscattered signal are amplified. In addition, higher order cascaded Raman can be implemented through a single-end pumping scheme. In these configurations the maximum gain is pushed further into the fiber span [11–13]. In DOFS, due to this fact, the probe power can be kept reasonably high along a longer distance and the backscattered signal is amplified further into the fiber span, when it is less energetic, resulting on an extension of the measurement range. Besides that, as semiconductor lasers, limited to 400-500 mW output power, are typically used as the pump laser, the extra gain produced by the second order pumping scheme cannot be easily obtained with a first order configuration.
In this paper, the combination of a higher order cascaded Raman amplification and the optimization of the gain profile through the modulation of the pump intensity are exploited in order to obtain the best performance in terms of measurement range. Although the use of a second order pump counteracts the power saving obtained by the pump modulation, the combined effect is advantageous in terms of noise reduction. We propose an amplification scheme based on two co-propagating pumps at 1365 nm and 1455 nm, respectively. The amplitude of the 1455 nm laser is modulated by an arbitrary signal whereas the 1365 nm laser can be either continuous or pulsed. This implementation is theoretically and numerically analyzed and validated for a chirped pulse phase-sensitive optical time-domain reflectometer (CP $\phi$-OTDR [14]) along more than 70 km. To our knowledge, this is the first implementation of DOFS with second order Raman and pump modulation and, also, the first application of second order Raman amplification to CP $\phi$-OTDR system.
A SOA with a time-dependent gain at detection can also be used for producing an equalized trace at the photodetector. However, this implementation is probably worse in terms of the OSNR of the trace, which in the end is the target of all these amplification schemes. In this case, the SOA will normally have a worse noise figure than Distributed Raman amplification.
2. Theoretical analysis
Prior to the beginning of the analysis, we should note that it can be extended for any kind of ideal time-domain DOFS. In real DOFS, the backscattered signal is unwanted amplified due to the walk off between signals at different wavelength and the impossibility of instantly switch off the pumps. In sensors where the absolute amplitude of signal or spectral shape of signal, such as Raman DTS or Brillouin OTDR, a deeper analysis should be performed. Nevertheless, in the next section, we will focus on the implementation of the optimal amplification strategy for CP $\phi$-OTDR. In [9], we can found a complete analysis of the first order Raman asistance with pump modulation in DOFS. Here, this model is extended for the second order case.
As it was previously mentioned, the operating principles of a $\phi$-OTDR are akin to those of a radar echo. A probe pulse is launched on one end of a fibre span and the counterpropagating trace, produced by a backscattering Rayleigh process at any point of the fibre, is detected by a photodetector at the same fibre end. The analysis as a function of the time of flight of the pulse along the fibre give us information about the position where a physical change occurs. In our system, the wavelength of the probe pulse is 1550 nm. Synchronously, two other optical signal at 1455 nm and 1365 nm, respectively, are launched at the same point of the fibre. These signals are called $P_\lambda$ where $\lambda$ can take the values $s$, $p1$ and $p2$ for 1550 nm, 1455 nm, and 1365 nm. $P_s$ is the pulse probe used in our sensor and $P_{p1}$ and $P_{p2}$ are the Raman pumps to produce a cascaded amplification. In order to simplify the model we can make some assumptions: Firstly, given the relatively small values of dispersion-induced walk-off in standard sensing fibres ($\sim$ 1 ns km$^{-1}$) and the relatively broad pulses (typ. 10’s of ns, at least) used in CP $\phi$-OTDR, it is reasonable to assume that the dispersion walk-off between signals is negligible, as long as the duration of each gated pump is longer than the sum of the duration of the pulses at its Stokes frequency plus the corresponding dispersion walk-off. Secondly, and given the attenuation coefficients in standard fibre, we assume that the value of the pump power decays slowly enough to consider a complete overlap between the probe pulse and a portion of the Raman pump signals. Under these premises, the attenuation/amplification processes can be separately analyzed for the probe pulse and the counterpropagating signal. Therefore, the Raman pumps can be split into two different parts ($P_{\lambda,a}(z)$ and $P_{\lambda,b}(z, t)$) for independently amplifying the probe pulse and the trace, respectively. Thereby, $P_{p1}= P_{p1,a} + P_{p1,b}$ where $P_{p1,a}$ is a gated signal and $P_{p1,b}$ is an arbitrary signal. Regarding $P_{p2}$, it usually is a continuous pump or a gated signal and, consequently, the initial values on z of $P_{p2,a}$ and $P_{p2,b}$ take a constant value with time. Finally, the probe is defined as ($P_{s,a} (z)$) and the backscattering signals at any point of the fibre is written as ($P_{s,b} (z, z')$). Note that z’ is used to distinguish the scattered point and the propagation distance z. It is also important to know that the pumps launched at $t$ amplify the backpropagating signal scattered at $z'$ in the point z, where t and z’ are related by the expression $t=2(z-z')/v_g$ where $v_g$ is the group velocity. Hence, the temporal dependence of the equation can be removed and the general set of equations for describing the power evolution of each signal is written as:
Fig. 1. Schematic of the Raman and Rayleigh interactions in the proposal approach. The typical pump profiles are included.
Secondly, we evaluate the system 1–3 for the backscattering signal $P_{s,b}$ and the portion of the pumps ($P_{p2,b}$, $P_{p1,b}$) to amplify it. In this case, as the trace power is low, the pump depletion of $P_{p1,b}$ is neglected. Thus, we can solve independently the equations for the pumps (1–2). For the undepleted regime, the evolution of $P_{p1,b}$ is described by,
where $\tilde {P}_{p1,b} (t)$ is the initial profile of $P_{p1,b}$ and $z_{eff}$ is the effective length equal to $z_{eff}=(1-exp(-\alpha _{p2}z))/\alpha _{p2}$. Subsequently, the Eq. (4) is introduced in Eq. (3) in order to calculate the Raman gain experienced by a backscattered signal:Here, we should remember that the time of the initial profile can be substituted by $t=2(z-z')/v_g$. Our objective is to obtain an optimum profile of $\tilde {P}_{p1,b} (t)$ that produce a perfectly compensated trace. It means, the signal produced at a further point of the fibre will require a higher Raman gain as it has experienced a higher attenuation and, consequently, its signal amplitude is minimal. Then, the total attenuation losses (two times $\alpha _sz'$ as the probe and the backscattering signal are equally attenuated) should be compensated by the Raman amplification for the probe and for the backscattering signal. $G (z') = 2\alpha _sz' +G_p (z')$ where $G_p (z')$ is the probe amplification because of $P_{p1,a}$ and $P_{p2,a}$.
Following this process, the performance of our proposal is numerically estimated. The most relevant fibre parameters for the simulation are: $\alpha _{p2} = 0.31$, $\alpha _{p1} = 0.25$ dB km$^{-1}$, $\alpha _s = 0.19$ dB km$^{-1}$, $g_{R1} = 0.44$ W$^{-1}$km$^{-1}$ and $g_{R2} = 0.55$ W$^{-1}$km$^{-1}$. Note that some parameters have changed with respect to our previous work as the fibre span is different, so the optimal profile for $1^{st}$ order Raman amplification alone is also slightly different. Moreover, the power of $P_{p1}$,a is also reduced in our second-order scheme to avoid nonlinear impairments when the second order pump is activated. For the modulated pump, the repetition rate is equal to the probe rate (1 KHz). Initially, we estimate the power evolution for the probe ($P_{s,a}$) and the part of the pumps accompanying it ($P_{p1,a}$ and $P_{p2,a}$) by means of solving the system 1–3 for this signals. Secondly, the power evolution of $P_{p1,b}$ and $P_{p2,b}$ are calculated and, the result is used for determining the trace read at the photodetector. At this point, an iterative algorithm which calculates the optimal profile of $P_{p1,b}$ for other pump parameters can be used. In the first iteration, the system is solved without any $P_{p1,b}$ and, subsequently, this pump is activated for the values where the power trace decays below a defined threshold with respect to the initial power level. The pump power is increased up to the value that the power trace reaches the initial power level. The resultant $P_{p1, b}$ is a staircase function as it is shown in Fig. 2(a) for three different configuration of $P_{p1,a}$ and $P_{p2}$. The third configuration (represented by the yellow line) is close to the optimal used in the experimental section. As it was mentioned, amplifying the probe is more efficient. So, we chose the maximum value of $P_{p1,a}$ that avoids the nonlinear effect. This value for the second order scheme is 0.32 W. The pump power for the 1365 nm is limited to 0.2 W because, in the experimental section, a Raman laser is used and these lasers introduced a big amount of RIN. Although the steps are not regular both in time and power increment, the result can be fitted by a linear increasing function. Two fitting line are also represented. The first one (named fitting 1) is the optimal profile that minimize the trace excursion for 100 km. However, this profile implies a high peak power. In real implementation, the 1455 nm laser is limited at 400 mW and this value is required for a perfect losses compensation for sensing 60 km. For this reason, another fitting is analyzed. Fitting 2 produce a higher amplification during the first 50 km and a perfect compensation of the attenuation losses at approximately 70 km. In the experimental section, the Fitting 2 is used as, apparently, it produces the best performance in our setup.
Fig. 2. Numeric results: (a) Optimal pump profile according to the iterative algorithm for (blue) $P_{p1,a}$ = 0 W and $P_{p2}$ = 0.2 W, (red) $P_{p1,a}$ = 0 and $P_{p2}$ = 0.5 W and (yellow) $P_{p1,a}$ = 0.32 W and $P_{p2}$ = 0.2 W. Two fitting line are included: (dashed purple) fitting 1 and (dotted green) fitting 2. (b) Trace profile for (blue) the optimal pump and (red and yellow) the fitting line.
3. Experimental results
In our setup, a conventional CP $\phi$-OTDR system is used to interrogate 100 km of fibre. Detailed information on the operation of this technique can be found in [14]. A semiconductor laser at 1550 nm is used to generate the probe pulse. The 100 ns pulses (corresponding to 10-meter spatial resolution) linearly chirped with $\approx$ 0.4 GHz of total pulse frequency content are launched at 1 KHz repetition rate. The counterpropagating trace photodetected with a 500 MHz bandwidth photodetector and recorded with a 1 GS/s digitizer, at the same fibre end where the pulse is injected. The peak power of the probe is adjusted for each pump profile in order to avoid the MI in the worst scenario corresponding to the continuous second order pump. A 1455 nm semiconductor laser is used in order to provide the first order Raman amplification. The semiconductor laser current is driven by an arbitrary waveform generator (AWG) and, consequently, its amplitude is modulated. The second order pump is produced by a 1365 nm Raman laser. One important limitation when these lasers are used for distributed amplification is the Relative Intensity Noise (RIN) transfer between the pumps and the signal [15]. Specifically, the RIN characteristic of this laser is approximately −100 dB/Hz. For this reason, its pump power is limited and the trace is 16 times averaged in order to remove this noise transfer. Next to the 1365 mm Raman laser, a variable optical attenuator (VOA) based on MEMS (microelectromechanical systems) technology is placed for gating this laser. Its extinction ratio is close to 22 dB. A complete scheme of the system is depicted in Fig. 3(a).
Fig. 3. (a) Experimental setup. Acronyms are: AWG (arbitrary waveform generator), OTA (operational transconductance amplifier), LD (laser diode), SG (signal generator), SOA (semiconductor optical amplifier), EDFA (erbium doped fibre amplifier), DWDM (dense WDM filter), WDM (wavelength division multiplexer), VOA (variable optical attenuator) and FUT (fibre under test). (b) The pump profiles studied.
The 1455 nm modulation profiles follow the previously analyzed waveform, consisting of a 37.5 $\mu$s pulse ($P_{p1,a}$) which amplifies the probe pulse and a linearly increasing function ($P_{p1,b}$) for amplifying the trace. The pump power of the gated pulse is limited at 320 mW to avoid the emergence of nonlinear impairment when the 1365 nm laser is activated. $P_{p1,b}$ is firstly optimized for obtaining a close to perfect compensation of the attenuation loses in the first order case (named profile 1). $P_{p1,b}$ is activated at 46.5 $\mu$s and its power linearly increases from 0 to 400 mW. The highest power part is truncated at this value due to the power limitation of the pump laser. The peak power is reached at 500 $\mu$s. This power is kept fixed until 800 $\mu$s (the round-trip time of the pulse in the 80 km fibre). Secondly, $P_{p1,b}$ take the values of fitting line 2 in the previous section (named profile 2). $P_{p1,b}$ is activated at 163.5 $\mu$s and the highest power is reached at 662 $\mu$s and the peak power is hold until 900 $\mu$s. Both pump profiles are shown in the inset of Fig. 3(b). Under these conditions, the average powers of ($P_{p1,b}$) are 223 mW and 207 mW, respectively, for the first order pump, which supposes a 44 $\%$ and 48 $\%$ power saving over the CW case. We compare the results using these profiles for three different possibilities: the first order case, when the 1365 nm laser is off; the CW second order case when the VOA is deactivated; the gated second order case when part of this signal is attenuated by the VOA. Here, the gated length is 100 $\mu$s pulse and the 1365 nm peak power is only 186 mW for both cases. As it was previously mentioned, this laser introduces a considerable amount of RIN. For this reason, a higher pump power at 1365 nm produces a noisy trace.
The traces read at the photodetector for the three different amplification schemes (a- first order amplification scheme; b- CW second order amplification scheme; c- gated second order configuration) when the pump at 1455 nm is modulated by profile 1 are shown in Fig. 4. For each fibre point, the maximum is related with the optical power of the measurement while the floor indicates the amount of ASE noise arriving at that moment. The variance of the trace is related to the OSNR of the signal and evidences the capability of taking a precise measurement at a particular trace position. When only the 1455 nm is activated (Fig. 4(a)), the trace is moderately over-amplified during the first kilometers of fibre and the noise floor is slightly increasing towards the fibre end in the trace. When the 1365 nm laser is also connected (Fig. 4(b)), both the trace and the noise floor are massively amplified. Finally, for the gated second order pumping scheme (Fig. 4(c)), the trace experiments an intermediate amplification and the noise floor is similar to the first configuration. Intuitively, the CW second order pump produces the best performance. However, to make a quantitative evaluation of the loss compensation achieved, the trace profile is represented in the Fig. 5(a). In this figure, we evaluate the standard deviation value of the measured trace, estimated over windows of 500 m. As it was previously mentioned the trace profile is almost flat for the first configuration during approximately 50 km and, subsequently, it decays until 5 dB at 80 km. An important improvement is reached by using the continuous pump. The trace profile is 10 dB increased for the 50 km. In the second fibre spool the trace profile is also decreasing and there is only a 5 dB improvement at 80 km. When the 1365 nm pump is gated, the performance is comparable to the CW case when the fibre length is relatively small, less than 30 km. Nevertheless, the improvement comparing to the first order pumping scheme is neglected beyond the 60 km.
Fig. 4. Traces for (a) the first order scheme (b) the CW second order scheme and (c) the gated second order configuration. The black dashed line indicates the ASE noise floor.
Fig. 5. Using the pump profile 1: (a) Trace profile for the first order case (red) the CW second order scheme (blue) and the gated second order configuration (yellow). (b) The ASD noise floor for the same configurations.
Nonetheless, the increment in the trace amplitude provides an incomplete piece of information about the quality of our proposal. To fully assess the improvement obtained, a demodulated measurement (i.e. a strain value recovered from the chirped-pulse traces) should be shown. To do that, the best estimation is the strain Amplitude spectral density (ASD) noise floor in all fibre positions. The strain ASD noise floor is a measurement used to describe the sensitivity in an acoustic sensor. The ASD is the square root of the strain power spectral density (PSD). More specifically, the strain ASD noise floor can be calculated by: $ASD_{nf} = \sigma /\sqrt {f/2}$ where $\sigma ^2$ is the strain standard deviation and f is the acoustic sampling frequency [16]. The Fig. 5(b) gives us information about this assessment. In terms of ASD noise floor, the increment of the trace amplitude translates into an extension of the measurement range by using the second order CW pumping assistance. Here, a noise threshold equal to $5\times 10^{-9}$ $\epsilon /\sqrt {Hz}$ is defined for quantifying the increment of the measurement range. For the first order case, we are able to measure 61 km whereas, for the second order pumping scheme, the measurement range is extended up to 73 km. For its part, the gated 1365 nm pumping scheme produce a small increment of the measurement range (only 5 km) in comparison with the first order configuration. Please note that in order to characterize the $2^{nd}$ order performance (which reaches 73 km) 100 km of fiber were used in this work, which does not allow for a direct comparison with the results of our previous work (where only 50 km were measured). Furthermore, apart from the use of a different optical hardware (fibre, filters, ambient conditions), slightly different setting was also used: lower pulse peak power was used (60 mW before and 50 mW here), which could be responsible for a certain degradation in the ASD noise floor in the best point of the fibre but leading to a lower accumulation of nonlinearities [16]. In any case, in this work we have prioritized a direct quantitative comparison between the first order and second order scheme, with identical equipment and ambient conditions, which shows a definite performance improvement in the second-order case, at least in terms of measurable range.
Afterwards, the performance by using the profile 2 is analyzed. In Fig. 6(a), the trace profiles, defined as it was calculated previously, are compared for the first and the second order scheme. Presently, the trace profile by using the continuous 1365 nm laser is almost flat along 90 km whereas, by using exclusively the 1455 nm pump, the trace is underamplified and its amplitude decays constantly after the first 10 km and the minimum is 6 dB less than the first kilometers, reached at 50 km. In the ASD noise floor figure (Fig. 6(b)), we observe that this trace amplitude degradation implies an increment of the noise floor and, therefore the measurement range is reduced to only 51 km. Nonetheless, the figure of the ASD noise floor is different for the second order configuration. Although the noise floor is grown in the first 60 km, the total measurement range is similar than using the previous pump profile and it supposes an extension of 19 km versus the first order case. In conclusion, a similar performance can be obtained using less amplification whenever the trace profile is almost constant.
Fig. 6. Using the pump profile 2: (a) Trace profile for the first order case (red) the CW second order scheme (blue). (b) The ASD noise floor for the same configurations.
4. Conclusions
In conclusion, a second order Raman amplification system with a 1455-nm modulated pump has been proposed in order to increase the measurement range in a time-domain DOFS by an almost ideal compensation of the attenuation loses. We have numerically estimated the optimal profile. Ideally, the 1455-nm pump is composed by a narrow pulse accompanying the probe and an increasing power profile for compensating the trace attenuation. This profile can be fitted by a linear function. Experimentally, a CP $\phi$-OTDR assisted by the proposed Raman amplification has been implement. In the 1455-nm pump, two different profiles have been studied. In both cases, the assistance by a CW 1365-nm pump produces an increment of the sensibility that translates into a reduction of the ASD noise floor and, consequently, the enlargement of measurement range. Nevertheless, the overamplification produced by a higher power pump does not imply a best performance. In addition, the improvement due to the use of a gated 1365-nm pump is small. Finally, a 70 km single-end DOFS has been demonstrated.
Funding
Comunidad de Madrid (SINFOTON2-CM: P2018/NMT-4326, TALENTO-CM 2017-T2/TIC-5227); European Research Council (OCEAN-DAS: ERC-2019-POC-875302); Ministerio de Ciencia, Innovación y Universidades (IJCI-2017-33856, RTI2018-097957-B-C31, RTI2018-097957-B-C33).
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 upon reasonable request.
References
1. M. R. Fernández-Ruiz, M. A. Soto, E. F. Williams, S. Martin-Lopez, Z. Zhan, M. Gonzalez-Herraez, and H. F. Martins, “Distributed acoustic sensing for seismic activity monitoring,” APL Photonics 5(3), 030901 (2020). [CrossRef]
2. G. P. Lees, H. H. Kee, and T. P. Newson, “Otdr system using raman amplification of a 1.65 μm probe pulse,” Electron. Lett. 33(12), 1080–1081 (1997). [CrossRef]
3. Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, “50-km single-ended spontaneous-brillouin-based distributed-temperature sensor exploiting pulsed raman amplification,” Opt. Lett. 28(18), 1651–1653 (2003). [CrossRef]
4. X. Angulo-Vinuesa, S. Martin-Lopez, J. Nuño, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Raman-assisted brillouin distributed temperature sensor over 100 km featuring 2 m resolution and 1.2 °c uncertainty,” J. Lightwave Technol. 30(8), 1060–1065 (2012). [CrossRef]
5. Z. N. Wang, J. J. Zeng, J. Li, M. Q. Fan, H. Wu, F. Peng, L. Zhang, Y. Zhou, and Y. J. Rao, “Ultra-long phase-sensitive otdr with hybrid distributed amplification,” Opt. Lett. 39(20), 5866–5869 (2014). [CrossRef]
6. J. Pastor-Graells, J. Nuño, M. R. Fernández-Ruiz, A. Garcia-Ruiz, H. F. Martins, S. Martin-Lopez, and M. Gonzalez-Herraez, “Chirped-pulse phase-sensitive reflectometer assisted by first-order raman amplification,” J. Lightwave Technol. 35(21), 4677–4683 (2017). [CrossRef]
7. S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order raman amplification,” Opt. Express 18(18), 18769–18778 (2010). [CrossRef]
8. Y. Fu, R. Zhu, B. Han, H. Wu, Y.-J. Rao, C. Lu, and Z. Wang, “175-km repeaterless botda with hybrid high-order random fiber laser amplification,” J. Lightwave Technol. 37(18), 4680–4686 (2019). [CrossRef]
9. J. Nuño, H. F. Martins, S. Martin-Lopez, J. D. Ania-Castañon, and M. Gonzalez-Herraez, “Distributed sensors assisted by modulated first-order raman amplification,” J. Lightwave Technol. 39(1), 328–335 (2021). [CrossRef]
10. H. He, B. Luo, X. Zou, W. Pan, and L. Yan, “Enhanced phase-sensitive otdr system with pulse width modulation brillouin amplification,” Opt. Express 26(18), 23714–23727 (2018). [CrossRef]
11. S. Papernyi, V. Karpov, and W. Clements, “Third-order cascaded raman amplification,” in Optical Fiber Communication Conference and Exhibit, (2002), p. FB4.
12. S. Paperayi, V. Ivanov, Y. Koyano, and H. Yamamoto, “Sixth-order cascaded raman amplification,” in Optical Fiber Communication Conference and Exhibit, (2005), p. OThF4.
13. R. Chi, “Experimental optimization of the scheme of second-order raman amplifiers based on ultra-long span systems,” Results Phys. 18, 103195 (2020). [CrossRef]
14. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive otdr with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016). [CrossRef]
15. C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to signal rin transfer in raman fiber amplifiers,” J. Lightwave Technol. 19(8), 1140–1148 (2001). [CrossRef]
16. M. R. Fernández-Ruiz, L. Costa, and H. F. Martins, “Distributed acoustic sensing using chirped-pulse phase-sensitive otdr technology,” Sensors 19(20), 4368 (2019). [CrossRef]
