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Abstract
A Brillouin optical time domain analysis (BOTDA) system utilizing tailored compensation for the propagation loss of the pump pulse is demonstrated for long-range and high-resolution distributed sensing. A continuous pump wave for distributed Brillouin amplification (DBA pump) of the pump pulse co-propagates with the probe wave, where gradual variation of the spectral width is additionally introduced to the DBA pump to obtain a uniform Brillouin gain along the position. In the experimental confirmation, a distributed strain measurement along a 51.2 km fiber under test is presented with a spatial resolution of 20 cm, in which the measurement error (σ) of less than 1.45 MHz and the near-constant Brillouin gain of the probe wave are maintained throughout the fiber.
© 2017 Optical Society of America
1. Introduction
Distributed fiber sensors based on Brillouin scattering have been intensively studied so far for more than two decades with the growth of social and industrial needs for real-time structural health monitoring of large civil structures and materials [1–6]. Brillouin optical time domain analysis (BOTDA) is one of the representative sensing schemes which utilizes the stimulated Brillouin scattering (SBS) between a pulsed pump and a continuous-wave (CW) probe. The measurement range of the BOTDA system is limited by the drop of signal to noise ratio (SNR) as a result of the depletion of the pump pulse according to the propagation along a fiber under test (FUT). For obtaining a larger SNR the simplest way is to use a pump pulse with higher optical power, however the peak power is limited by the onset of a nonlinear effect called modulation instability (MI) which considerably broadens its spectrum [7]. When the peak power of the pump pulse is kept below the threshold (~20 dBm) of the MI and the double-sideband probe configuration (i.e. Stokes and anti-Stokes waves) is adopted to suppress the pump depletion originating from the energy transfer to the probe wave by the SBS itself, the Rayleigh scattering becomes the main cause of the pump depletion which gives a uniform propagation loss of ~0.2 dB/km in a conventional optical fiber [8]. As a possible solution distributed Raman amplification (DRA) was introduced to compensate for the loss of the pump, which allows the enlargement of the measurement range to over 100 km [9-10]. However, the DRA-BOTDA system requires high pumping power of an order of Watts and the relative intensity noise of the Raman pump is translated to the detected signal, which deteriorates the overall measurement performance. The technique of optical pulse coding is also an effective way to enhance the SNR of a BOTDA system [11-12], at the cost of increased system complexity to apply coded pulse sets of uniform amplitude and coding/decoding processes. The use of frequency division multiplexing and in-line EDFAs is also demonstrated for extending the sensing range of a BOTDA system [13]. Recently J. Urricelqui et al. proposed the use of distributed Brillouin amplification (DBA) to compensate for the loss of the pump pulse [14], in which a continuous DBA pump wave with a broadened spectral width (125 MHz) by frequency modulation co-propagates with the probe wave. The DBA method is advantageous over the DRA scheme since it can be operated at much lower power level of the additional pump, which results in smaller amount of noise added to the signal [14]. However, the injection of the DBA pump wave cannot provide uniform compensation along the fiber due to the propagation loss of the DBA pump itself, so the pump pulse is not amplified sufficiently in the front and middle of an FUT when the amplification is optimized at the end of the fiber.
In this paper we present a tailored pump compensation scheme for the BOTDA system where the spectral width of the DBA pump is varied in time to compensate for the effect of propagation loss of the DBA pump itself. By this implementation the Brillouin gain provided by the DBA pump exactly counter-balances the propagation loss of the pump pulse at all the positions, leading to a near-constant Brillouin gain of the probe wave along an FUT. In experiments, we demonstrate distributed measurements of the Brillouin frequency (νB) along a 51.2 km optical fiber with a 20 cm spatial resolution where the measurement error (σ) below 1.45 MHz and the uniform Brillouin gain are maintained throughout the fiber.
2. Principle
Figure 1 schematically shows the configuration of the BOTDA system with the tailored pump compensation. The probe and DBA pump co-propagate along an FUT as a continuous wave (CW) in the opposite direction to the propagation of the pump pulse. For distributed measurement, the frequency offset (Δν) between the pump pulse (νp) and probe (νs) is swept in the vicinity of νB while that between the center of the modulated DBA pump (νas) and νp is fixed at νB.
Fig. 1 Schematic of the BOTDA system with the tailored pump compensation where the direction of each wave is pointed by an arrow. The green square indicates the starting position of the pump pulse.
In the FUT, the SBS occurs between the DBA pump and pump pulse as well as the pump pulse and CW probe. At the same time, each optical wave experiences the propagation loss caused by the Rayleigh scattering. When the other nonlinear effects such as the MI and stimulated Raman scattering are ignored by assuming the peak power of the pump pulse (PP) is below the threshold (~20 dBm), the evolution of the power of the probe (i.e. the Stokes sideband, PS), the anti-Stokes sideband (PAS), the DBA pump (PD), and PP in a double-sideband probe configuration is governed by the following coupled differential equations:
where gB is the Brillouin gain coefficient, Aeff is the effective area of the fundamental mode, and α is the attenuation constant of the optical fiber, respectively. The terms in the form of gBPiPj/Aeff in Eqs. (1) – (4) represent the increment or decrement by the Brillouin gain or loss, respectively. If dPP/dz in Eq. (2) is equal to 0 one obtains a uniform Brillouin gain of the probe along the FUT in Eq. (3). For simplification we ignore the Brillouin loss of the DBA pump given by the pump pulse in Eq. (1). The Brillouin gain and loss of the pump pulse by the two sidebands in Eq. (2) effectively cancel each other when the power of each wave does not exceed ~4 mW in the double-sideband probe configuration [8]. Under this condition, Eqs. (1) and (2) are reduced to:The solution of Eq. (5) is which yields the condition for the uniform Brillouin gain of the probe by Eq. (6) as follows:
The left-hand side of Eq. (7) represents the Brillouin gain by the DBA pump as a function of z while the right-hand side is constant. When a frequency modulation is applied to the DBA pump the spectral width is broadened and the spectral power density is decreased, which causes the reduction of the Brillouin gain of the pump pulse. If we assume the width (w) of the broadened spectrum is much larger than the intrinsic Brillouin gain bandwidth (ΔνB ~30 MHz), the reduction rate of the Brillouin gain of the pump pulse is nearly equal to w/ΔνB [15]. When this rate is introduced to Eq. (7), one finally obtains a formula for w as a function of position (or time) for the uniform Brillouin gain of the probe as follows:
where c is the speed of light in vacuum and ng is the group refractive index in the optical fiber.3. Experimental setup
The experimental setup of the BOTDA system with tailored pump compensation is depicted in Fig. 2. Two distributed feedback laser diodes (LD 1 and LD 2) at a wavelength of 1550 nm were used for the pump-probe wave and the DBA pump wave, respectively. Two sidebands were generated by an electro-optic modulator (EOM) and a microwave generator for the probe for which a polarization switch was introduced for the polarization-diversity scheme to suppress the polarization-dependent gain fluctuation of the SBS. A semiconductor optical amplifier (SOA) and a pulse generator were used to generate a rectangular pump pulse, where the duration of the pulse was varied from 40 to 60 ns to apply the differential pulse-width pair (DPP) technique [16] for a spatial resolution of 1 m (50/40 ns), 50 cm (50/45 ns) or 20 cm (52/50 ns) depending on the measurement condition. The pump pulse was propagated in the opposite direction to the probe at a repetition rate of 1 kHz after being amplified by an Er-doped fiber amplifier (EDFA). A current modulation in the shape of a triangular wave was applied to the LD 2 by an arbitrary waveform generator (AWG) to broaden the spectrum of the DBA pump, where the amplitude of the RF wave exponentially increases according to Eq. (8). The initial and final amplitude corresponds to the frequency deviation of ± 100 MHz to ± 1 GHz that was synchronized to the propagation of the pump pulse as shown in Fig. 1. It is worth noting that the 10-fold increase in the frequency deviation is to compensate for the propagation loss of ~10 dB in the test fiber (~51 km). A polarization scrambler was additionally used to the DBA pump to suppress the polarization dependence of the gain, and the DBA pump was combined with the probe by a 90/10 coupler after being amplified by an EDFA. The FUT is a 51.2 km single-mode fiber which contains three 30 cm test sections near the end of the fiber as shown in the inset ‘A’. The input power of the probe, the pump pulse (peak power) and the DBA pump to the FUT was −1 dBm, + 17 dBm, and + 11 dBm, respectively, controlled by the EDFA’s. For distributed measurement the optical frequency of the probe was swept by a 2 MHz step, and only the lower-frequency component of the two sidebands was received by a 5 GHz photo detector and a 2 GS/s data acquisition board through two optical filters and an EDFA. The time trace was averaged 4096 times for noise suppression.
Fig. 2 Experimental setup for the BOTDA system with tailored pump compensation. Inset ‘A’ shows the configuration of the FUT where three 30 cm test sections are located near the fiber end with one loose section between two strain-applied sections: AWG, arbitrary waveform generator; PS, polarization scrambler; PSW, polarization switch; SOA, semiconductor optical amplifier; EDFA, Er-doped fiber amplifier; EOM, electro-optic modulator; FBG, fiber Bragg grating; TBF, tunable bandpass filter; PD, photo detector; DAQ, data acquisition.
Figure 3 shows the shape of the RF waveform applied to the LD 2 for current modulation, the amplitude of which is exponentially increased according to Eq. (8). The base of modulation is a triangular function at 100 kHz. Considering the length of the FUT of about 51 km, the DBA pump power was dropped to ~1/10 of its initial value with the attenuation coefficient α of ~0.2 dB/km. Since the spectral width of the LD 2 was measured to be proportional to the RF amplitude the expected amplitude ratio between both ends is 10. However, the initial amplitude (0.025) of the RF waveform is set slightly smaller than the expected value (0.03) considering the finite gain bandwidth of 30 MHz in the SBS. The initial spectral width of 200 MHz was determined considering the maximum drift of relative frequency difference between the two LD’s (several tens of MHz) and the possible variation of the νB at the front of the fiber. The modulation width of the DBA pump varies from 200 MHz to 2 GHz in Fig. 3, which we believe is sufficient to cover the deviations of local BFS in most applications. Since only the ratio between initial and final width is important in our scheme, one may adapt the modulation width considering the measurement conditions.
Fig. 3 The RF waveform applied to the LD 2. The exponential change of the amplitude is determined by Eq. (7) with the attenuation coefficient (0.2 dB/km) and the length (51.2 km) of the FUT.
In addition to the tailored pump compensation by the DBA the DPP method was adopted for high spatial resolution. In experiments, we applied a 50/40 ns pair for the calibration measurement of uniform Brillouin gain along the position, a 50/45 ns pair for the comparison with former DBA method with a fixed spectral width, and finally a 52/50 ns pair for distributed measurement with a 20 cm spatial resolution.
4. Experimental results
Figure 4 compares the BGS distributions measured by three different schemes with the same power of the pump and probe waves with a spatial resolution of 1 m (i.e. DPP method with a 50/40 ns pulse pair): (a) ordinary BOTDA without DBA pump, (b) BOTDA with the DBA pump of a fixed spectral width, (c) BOTDA with the DBA for tailor compensation (our scheme). One can clearly see that the maximum Brillouin gain at the front of the fiber is uniformly maintained throughout the FUT in Fig. 4(c) while the gain is gradually decreased in Fig. 4(a) or decreased at middle positions in Fig. 4(b). The maximum Brillouin gain according to the position is plotted in Fig. 4(d) where one can confirm the advantage of the proposed scheme.
Fig. 4 Distribution map of the BGS measured with a 50/40 ns pulse pair (a) without BDA pump, (b) with a DBA pump of a fixed spectral width, and (c) with the BDA pump for tailored compensation. (d) Maximum Brillouin gain according to the position.
To investigate the effect of the tailored compensation in detail we performed another measurement using a 50/45 ns pulse pair with the fixed and the tailored DBA pump waves. Figure 5 shows the measurement error (σ) of the νB according to the position where it is confirmed that the tailored scheme provides lower measurement error in comparison to the fixed DBA method. It should be noted that, in the experiment, the power level of the DBA pump of the fixed spectral width was set to have the same Brillouin gain in the front and rear ends of the fiber, which is to keep the power of the pump pulse below the threshold of the MI throughout the FUT. In the case of the DBA pump with a fixed spectral width the Brillouin gain by the DBA pump is much larger in the rear half of the fiber than in the front half. We think the intensity noise transferred from the DBA pump contributes to the steeper increase of the measurement error in the region of 40 – 50 km, while more gradual increase is observed in our tailored compensation. We believe further research is needed to clearly understand the origin of noise in the proposed system.
Fig. 5 Error (σ) of the νB according to the position with the DBA pump of a fixed spectral width and the DBA pump for tailored compensation measured using a 50/45 ns pulse pair.
We performed the final distributed measurement with the DBA pump for the tailored compensation where a 52/50 ns pulse pair was used for a 20 cm spatial resolution. The shape of the pump pulse after passing through the FUT with (gray-black) or without (blue-violet) the tailored DBA pump is depicted in Fig. 6(a) where no significant distortion by the tailored DBA is observed. The difference between the two DPP pulses is shown in Fig. 6(b) where the duration of ~2 ns corresponding to a 20 cm spatial resolution is confirmed. The measurement results are depicted in Fig. 7. The distribution map of νB is seen in Fig. 7(a), and Fig. 7(b) is the zoomed view of the dashed box in Fig. 7(a) which is around the test sections near the end of the fiber. One can clearly see the increase of the νB in the strain applied sections (1 and 3) by the strain while that of the loose section (2) is unchanged, which confirms the high spatial resolution of the measurement. The different length observed in the sections (1) and (3) is the result of the finite sampling distance (~5 cm) by which the 30 cm sections may appear as 5 or 6 points. Figure 7(c) shows the measurement error (σ) according to the position, where it is notable that an average error of about 1.2 MHz is maintained along the fiber with the maximum value of about 1.45 MHz (near the position of 20 km). The strain dependent change of νB measured in one of the strain applied sections (section 1) is plotted in Fig. 7(d) which decently fits a line with a slope of 0.0405 MHz/με. The strain coefficient for an ordinary SMF is usually between 0.045 MHz/με to 0.05 MHz/με. We think the smaller value of our result is attributed to the mitigation effect by the epoxy and the acrylate coating of the fiber.
Fig. 6 (a) The shape (i.e. output power) of the pump pulse with (gray/black) or without (blue/violet) the tailored DBA pump with a 52/50 ns pulse pair after passing through the FUT. (b) Difference between the DPP pulses with (black) or without (blue) the tailored DBA pump after passing through the FUT. Note that different scales are used for the cases with or without the DBA pump.
Fig. 7 Measurement result with a 20 cm spatial resolution: (a) Distribution map of νB. (b) Zoomed view of the test section near the end of the FUT (dashed box in (a)). (c) Measurement error (σ) according to the position. (d) Change of νB as a function of strain in the test section 1 in (b).
5. Conclusions
The BOTDA system with tailored compensation for the propagation loss of the pump pulse based on the DBA has been proposed and experimentally demonstrated. We showed that the tailored scheme can provide an enhanced measurement accuracy compared to the former DBA-based scheme with a fixed spectral width. The presented measurement result of 51.2 km range / 20 cm resolution corresponds to the number of effective sensing points of more than 250k, and the value of evaluation parameter for the performance of a BOTDA sensor, called figure-of-merit (FoM), in this experiment is calculated to be about 40 [17]. Currently the measurement range is limited to ~50 km which is due to the onset of SBS of the incident DBA pump which seems to be attributed to the imperfect frequency modulation with the triangular wave where the shape of the frequency change is not exactly triangular and the non-negligible intensity modulation which is inevitable in the current modulation. We believe the use of a compensated modulation waveform for uniform spectral broadening might be helpful for increasing the SBS threshold [18-19], however further study is needed to find out the ultimate limiting factor of the sensing range.
Funding
National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2015R1A2A2A01007078); Chung-Ang University Research Scholarship Grants in 2016.
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