Brillouin gain bandwidth reduction in Brillouin optical time domain analyzers

Wenqiao Lin; Zhisheng Yang; Xiaobin Hong; Sheng Wang; Jian Wu

doi:10.1364/OE.25.007604

1. Introduction

Distributed optical fiber sensors based on Brillouin optical time domain analysis (BOTDA) have attracted lots of attention for the past decade due to its capability on measuring temperature or strain at each point along the sensing fiber [1,2]. In this technique, a pump pulse and a counter-propagating continuous probe wave, which are spectrally separated by the Brillouin frequency shift (BFS), initiate a power transfer between them through stimulated Brillouin scattering (SBS). The highest energy transfer takes place when the frequency offset between these two waves is exactly equal to BFS, and the amount of the energy transferred from pump to probe wave decreases as the frequency offset changes. Thus, by scanning the pump-probe frequency difference, Brillouin gain spectrum (BGS) with Lorentzian shape can be recovered. Since the temperature or strain change is linearly depending on the change of the center frequency of BGS, the distributed information on these physical quantities can be obtained by recognizing the local BGS peaks (i.e. BFSs) [1,2]. In order to get reliable BFS at each fiber position, post-processing such as Lorentzian fitting [3] or quadratic fitting [4] is usually performed on each corresponding BGS. Under this condition, and for a given signal-to-noise ratio (SNR) and fixed frequency scanning step, the frequency accuracy is highly related to the full width at half maximum (FWHM) of the BGS. As the BGS gets narrower by factor N, the frequency accuracy would be improved by factor $\sqrt{N}$ [4]. However, the measured BGS in the standard BOTDA system is the result of convolution between the natural Brillouin gain spectrum and the pulse spectrum [5]. This means that for a given spatial resolution, the FWHM of BGS is fixed. So even in the case of very bad spatial resolution (using very long width pump pulse), the BGS cannot be narrower than the natural Brillouin gain spectrum (about 30 MHz) [6], which is one of the critical limitations on the performance of a standard BOTDA sensor.

This intrinsic limitation also affects the performance of other techniques that make use of SBS effect, such as wideband phase shifting [7], microwave photonic filtering [8] and Brillouin-assisted high spectral resolution optical spectrum analyzer (SBS-OSA) [9,10]. An alternative strategy to overcome this Brillouin gain bandwidth limitation is to cool the fiber down to cryogenic temperatures [11], thus the bandwidth of 3 MHz can be achieved. At room temperature, the bandwidth of Brillouin gain spectrum could be reduced by using multistage Brillouin system [12], superposition of Brillouin gain/loss lines [13–15], or frequency domain aperture [16]. However, to the best of our knowledge, so far these above mentioned approaches are not suitable for BOTDA system, and there has been no relevant technique proposed for distributed sensing yet.

In this paper, a method to narrow the BGS in BOTDA system for improving the frequency accuracy is proposed for the first time to the best of our knowledge. The proposal is based on a pair of pump pulses with same pulse width and amplitude but different phase configurations. By taking the differential gain of the time-domain traces retrieved by using these two pump pulses, 2.5 m spatial resolution and the BGS with FWHM of 17 MHz can be obtained. With respect to the 51 MHz FWHM that corresponds to 2.5 m spatial resolution in standard single pulse BOTDA system, the BGS bandwidth in the proposal is reduced by factor 3 without SNR penalty, leading to $\sqrt{3}$ times frequency accuracy improvement. Moreover, benefiting from the narrower BGS, the rising/falling edge of BFS profile along the fiber is much sharper, resulting in more precise BFS estimation in case of complex temperature/strain distribution.

2. The principle of the proposal

The principle of the proposed method using a pair of pulses with same pulse width but different phase configurations is illustrated in Fig. 1, in which the red region denotes the pulse section with no phase shift, while the grey region represents the pulse section with $π$ -phase shift. The reference pulse with no phase shift has the finite width of $t_{1} + t_{2}$ , as shown in Fig. 1(a). The sensing pulse consists of two sections, in which the first section with the width of $t_{1}$ has no phase shift, while the phase of the second section with the width of $t_{2}$ has been shifted by $π$ , as depicted in Fig. 1(b). The differential gain can be obtained after subtracting the frequency-scanned time-domain traces retrieved by using these two pump pulses separately. Being similar with the methods that have been reported based on the differential pulse-width pair (DPP) BOTDA [17,18], the common section of the pulse pair proposed in this paper is also set to be long enough to substantially activate the steady-state acoustic wave (i.e. $t_{1} > > 12 n s$ [6]). But being different with DPP-BOTDA methods using the short-width second pulse sections ( $t_{2} < < 12 n s$ ) with either zero amplitude [17] or $π$ -phase shift [18,19], in our proposal the width of second section of the sensing pulse must be long enough ( $t_{2} > > 12 n s$ ) to ensure a differential BGS with larger peak power and narrower FWHM, which will be explained hereafter. Note that using this long-width second pulse section is the essential distinction between our proposal and other DPP-BOTDA methods.

Fig. 1 The schematic model of the proposal.

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2.1 Temporal response

In order to fully describe the principle of our proposal, the analytical expression of the differential gain on the probe wave is calculated by solving the well-known SBS three-wave coupled equations with slowly varying envelope approximation and negligible transverse field variations [6]:

\frac{\partial A_{p} (z, t)}{\partial z} + \frac{1}{V_{g}} \frac{\partial A_{p} (z, t)}{\partial t} = i \frac{1}{2} g_{2} A_{s} (z, t) Q (z, t),

\frac{\partial A_{s} (z, t)}{\partial z} - \frac{1}{V_{g}} \frac{\partial A_{s} (z, t)}{\partial t} = - i \frac{1}{2} g_{2} A_{p} (z, t) Q^{*} (z, t),

\frac{\partial Q (z, t)}{\partial t} + Γ_{A} Q (z, t) = i g_{1} A_{p} (z, t) A_{s}^{*} (z, t),

where

A_{p} (z, t)

,

A_{s} (z, t)

and

Q (z, t)

are slow varying complex envelopes of pump wave, probe wave and acoustic wave, respectively;

Γ_{A}

is the frequency detuning parameter, which equals to

i (Ω_{B}^{2} - Ω^{2} - i Ω Γ_{B}) / 2 Ω

, where

Γ_{B}

is the acoustic damping constant that is an parameter to determine the FWHM of the Brillouin gain spectrum

Δ ν_{B}

, as

Γ_{B} = 1 / τ_{A} = 2 π Δ ν_{B}

;

Ω_{B} / 2 π

and

Ω / 2 π

are Brillouin resonance frequency and pump-probe frequency difference, respectively.

g_{1}

and

g_{2}

are electrostrictive and elasto-optic coupling coefficients, respectively.

Under the small gain assumption, the probe amplitude $A_{s} (z, t)$ can be considered as the sum of a constant component $A_{S}^{0} (z, t)$ and a small varying component $a_{s} (z, t)$ coming from the Brillouin interacting. The variation signal $a_{s} (z, t)$ could be analytically obtained using Laplace transform, following a similar procedure presented in [20–23], but with the proposed pump pulse configuration shown in Fig. 1. Firstly, the mathematical expression of both reference pulse and sensing pulse used for solving the Eqs. (1)-(3) can be represented as:

A_{p} (z, t) = A_{p}^{0} {u (t - \frac{z}{V_{g}}) - u (t - t_{1} - \frac{z}{V_{g}}) + β [u (t - t_{1} - \frac{z}{V_{g}}) - u (t - t_{1} - t_{2} - \frac{z}{V_{g}})]},

where

A_{P}^{0}

is the peak amplitude of pump field,

t_{1}

and

t_{2}

are the widths of the first and second pulse sections, respectively. In the following analysis, the value of

t_{1}

is set as 30 ns, and

t_{2}

equals to 40 ns.

u (\cdot)

is the Heaviside step function, and the parameter

β

is related to the phase shift applied on the pump pulse, the value of which equals to “1” and “-1” for zero and

π

-phase shift, respectively. In other words, when

β = 1

, Eq. (4) represents the reference pulse, and when

β = - 1

, Eq. (4) denotes the sensing pulse. After calculation, the variations of probe signal observed at the start end of the fiber, attributed to a short fiber section

Δ z

at a given fiber location

z = z_{N}

, can be obtained:

\begin{array}{l} a_{s}^{} (z = 0, z_{N}, t) = g (z_{N}) \frac{I_{P}^{0} A_{S}^{0}}{2 Γ_{A}^{*}} Δ z {[1 - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] u (t - \frac{2 z_{N}}{V_{g}}) \\ + [(β - 1) [1 - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] + (β^{2} - β) [1 - \exp [- Γ_{A}^{*} (t - t_{1} - \frac{2 z_{N}}{V_{g}})]]] u (t - t_{1} - \frac{2 z_{N}}{V_{g}}) \\ - β [[1 - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] + (β - 1) [1 - \exp [- Γ_{A}^{*} (t - t_{1} - \frac{2 z_{N}}{V_{g}})]]] u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})} . \end{array}

Equation (5) describes the behavior of the probe amplitude variation resulting from the proposed pulse pair. This analytical solution provides clear physical insight of the SBS process for this BOTDA configuration. It should be noted that the $a_{s} (z = 0, z_{N}, t)$ obtained in Eq. (5) is the temporal waveform of the Brillouin gain at a given position $z_{N}$ , which is not the BOTDA trace that we normally acquired from the oscilloscope. Since every fiber, spanning the range from $z_{0}$ to $z_{L}$ , can be considered as a concatenation of M very short segments ( $M = (z_{L} - z_{0}) / Δ z$ ), the BOTDA trace, which is actually proportional to the sum of the contributions of individual segments, can be written as:

a_{s} (z = 0, t) = Re [\sum_{N = 0}^{L} a_{s}^{} (z = 0, z_{N}, t)] .

Here we use Eq. (5) to analyze the performance and investigate the parameters of our proposal, as previously did in all the other work using similar procedure [20–23]. By substituting the boundary conditions of the reference pulse ( $β = 1$ ) and the sensing pulse ( $β = - 1$ ) into the Eq. (5), respectively, the Brillouin temporal waveforms at position $z_{N}$ attributed to the reference and sensing pulse can be given by:

\begin{array}{l} a_{s}^{r e f e r e n c e} (z = 0, z_{N}, t) = g (z_{N}) \frac{I_{P}^{0} A_{S}^{0}}{2 Γ_{A}^{*}} Δ z \times \\ [1 - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] [u (t - \frac{2 z_{N}}{V_{g}}) - u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})], \end{array}

and

\begin{array}{l} a_{s}^{s e n s i n g} (z = 0, z_{N}, t) = g (z_{N}) \frac{I_{P}^{0} A_{S}^{0}}{2 Γ_{A}^{*}} Δ z \times \\ {[1 - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] [u (t - \frac{2 z_{N}}{V_{g}}) - 2 u (t - t_{1} - \frac{2 z_{N}}{V_{g}}) + u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})] \\ + 2 [1 - \exp [- Γ_{A}^{*} (t - t_{1} - \frac{2 z_{N}}{V_{g}})]] [u (t - t_{1} - \frac{2 z_{N}}{V_{g}}) - u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})]}, \end{array}

respectively, as depicted in Fig. 2(a).

Fig. 2 (a) The Brillouin temporal waveforms corresponding the reference and sensing pulses calculated by Eqs. (7) and (8) at Brillouin resonance frequency located at position z_N; (b) The differential Brillouin temporal response in the proposal. g_peak denotes the peak Brillouin gain at Brillouin resonance frequency.

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It can be seen that for both reference and sensing pulses, during the Brillouin interaction over the first pulse section, the Brillouin response gradually rises in an exponential trend. This behavior corresponds to the term $[1 - \exp [- Γ_{A}^{*} (t - 2 z_{N} / V_{g})]]$ that comes from the inertial feature of the acoustic wave according to Eq. (3). After that, the Brillouin response during the second section of the reference pulse keeps steady-state at the amplitude level of $g_{p e a k}$ , while that of the sensing pulse features an abrupt drop to $- g_{p e a k}$ at the beginning of the second pulse section due to the abrupt phase change [18–20], then turns back to its steady-state level ( $g_{p e a k}$ ) exponentially, as shown in Fig. 2(a).

The differential response between the reference pulse and sensing pulse can be extracted by subtracting $a_{s}^{s e n s i n g} (z = 0, z_{N}, t)$ from $a_{s}^{r e f e r e n c e} (z = 0, z_{N}, t)$ , which can be represented as:

\begin{array}{l} a_{s}^{p r o p o s a l} (z = 0, z_{N}, t) = a_{s}^{r e f e r e n c e} (z = 0, z_{N}, t) - a_{s}^{s e n s i n g} (z = 0, z_{N}, t) \\ = g (z_{N}) \frac{I_{P}^{0} A_{S}^{0}}{Γ_{A}^{*}} Δ z \times [\exp [- Γ_{A}^{*} (t - t_{1} - \frac{2 z_{N}}{V_{g}})] - \exp [- Γ_{A}^{*} (t - \frac{2 z_{N}}{V_{g}})]] \\ \times [u (t - t_{1} - \frac{2 z_{N}}{V_{g}}) - u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})] . \end{array}

In Eq. (9), the contribution of the exponential term $\exp [- Γ_{A}^{*} (t - 2 z_{N} / V_{g})]$ is actually very small inside the region $[u (t - t_{1} - 2 z_{N} / V_{g}) - u (t - t_{1} - t_{2} - 2 z_{N} / V_{g})]$ when $t_{1} = 30 n s .$ Therefore, the final differential temporal waveform expressed by Eq. (9) can be simplified as:

\begin{array}{l} a_{s}^{p r o p o s a l} (z = 0, z_{N}, t) \\ = g (z_{N}) \frac{I_{P}^{0} A_{S}^{0}}{Γ_{A}^{*}} Δ z \times \exp [- Γ_{A}^{*} (t - t_{1} - \frac{2 z_{N}}{V_{g}})] [u (t - t_{1} - \frac{2 z_{N}}{V_{g}}) - u (t - t_{1} - t_{2} - \frac{2 z_{N}}{V_{g}})], \end{array}

as the red line shown in Fig. 2(b). The blue line in Fig. 2(b) represents the Brillouin response in case of standard single pump pulse, the width of which is exactly the same as the second section (40 ns) of the sensing pulse in our proposal. It can be observed that the amplitude distributions of these two temporal waveforms are quite different. In case of our proposal, the amplitude at the beginning of the temporal waveform is maximum (twice the amplitude of the waveform in case of standard single pulse), then declines rapidly with exponential tendency. This amplitude distribution indicates that the Brillouin interaction mainly focuses at the front of the temporal waveform, while the interaction at the end of the waveform is very weak. Therefore, in our proposal, the spatial resolution is not the full duration (4 m) of this temporal waveform. In order to figure out in which duration the Brillouin interaction mainly takes places (i.e. figure out the spatial resolution), we use parameter

τ

to divide the temporal waveform into two parts, the duration of which are from

t_{1} + 2 z_{N} / V_{g}

to

t_{1} + τ + 2 z_{N} / V_{g}

, and from

t_{1} + τ + 2 z_{N} / V_{g}

to

t_{1} + t_{2} + 2 z_{N} / V_{g}

, respectively, as shown in Fig. 3(a).

Fig. 3 (a) The differential Brillouin temporal response in the proposal. $g_{p e a k}$ denotes the peak Brillouin gain at Brillouin resonance frequency; (b) the ratio between the contribution of the first section and second one versus $τ .$

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We consider that when the Brillouin information covered by the first part is far more than that covered by the second part (e.g. 10 times more), the contribution of the latter can be ignored. Thus, the spatial resolution can be considered as the width of the first part. Mathematically, the difference between the contributions of these two parts could be expressed as the ratio between the integrations of their corresponding time regions:

\frac{a_{s}^{1st} (z = 0, t)}{a_{s}^{2 n d} (z = 0, t)} = {\frac{R e [\int_{t_{1} + \frac{2 z_{N}}{V_{g}}}^{t_{1} + τ + \frac{2 z_{N}}{V_{g}}} a_{s}^{p r o p o s a l} (z = 0, z_{N}, t) d t]}{R e [\int_{t_{1} + τ + \frac{2 z_{N}}{V_{g}}}^{t_{1} {+t}_{2} + \frac{2 z_{N}}{V_{g}}} a_{s}^{p r o p o s a l} (z = 0, z_{N}, t) d t]} |}_{Ω = Ω_{B}} = \frac{\exp (- Γ_{A}^{*} τ) - 1}{\exp (- Γ_{A}^{*} t_{2}) - \exp (- Γ_{A}^{*} τ)} .

Figure 3(b) illustrates the calculated ratio according to Eq. (11) as a function of $τ$ . It can be found that the ratio increases dramatically as the value of $τ$ gets larger, and in order to ensure the contribution of the second part ignorable (i.e. the ratio reaches 10), the value of $τ$ should be 25 ns. It means that it is possible for the proposal to realize 2.5-m spatial resolution with no negative impact on the performance, which will be further experimentally demonstrated in this paper.

2.2 Spectral response

As the most important aspect of the proposed BOTDA method is that the BGS is much narrower than that using standard BOTDA method, it is necessary to study the spectral behavior of our proposal. The BGS corresponding to the reference pulse and the sensing pulse can also be simulated according to Eqs. (7) and (8), respectively, as the red curve and blue curve shown in Fig. 4(a). The BGS of sensing pulse is lower than that of the reference pulse is due to the negative Brillouin gain (the lower curve in Fig. 2(a)) resulting from the $π$ phase shift applied on the second pulse section. The differential BGS is obtained by simply subtracting the two BGS corresponding to the reference pulse and the sensing pulse, as the black curve shown in Fig. 4(a), which features FWHM of 17 MHz. As previously discussed, this differential BGS actually corresponds to 2.5-m spatial resolution in our proposal.

Fig. 4 (a) The simulated BGS corresponding to the reference pulse, sensing pulse and the subtraction response; (b) the simulated BGS of the proposal and the single-pulse method in cases of different pulse widths.

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In order to investigate the proposed BGS more intuitively, simulated BGS in cases of difference pulse widths (20 ns, 25 ns and 30 ns) in standard single pulse BOTDA method are depicted together with the BGS of our proposal in Fig. 4(b) for comparison, using the same amplitude scale as Fig. 4(a). From Fig. 4(b) it can be seen that with the same spatial resolution (25 ns single pulse), the FWHM of BGS using standard single pulse method (green curve) is 51 MHz, which is 3 times wider than the BGS of our proposal. We can also observe that the peak power of the proposed BGS (black curve) is 1.5 times higher than that of the BGS corresponding to 25 ns single pulse (green curve). However, practically, with respect to the single pulse method that only needs one time measurement, the noise level of our proposal has the penalty of factor $\sqrt{2}$ (~1.414) due to the subtraction process between two measurements [4]. Thus, for our proposal, the benefit on SNR from the 1.5 times higher power is cancelled out by the 1.4 times higher noise level. This means that the SNR of our proposal is almost the same as that of standard BOTDA method, so that the frequency accuracy improvement given by our proposal is purely from the narrowed BGS. Since the expression representing the frequency accuracy $σ_{ν}$ at a given fiber position z can be written as [4]:

σ_{ν} (z) = \frac{1}{S N R (z)} \sqrt{\frac{3}{4} δ \times Δ ν_{B}},

where

δ

denotes the frequency scanning step, the frequency accuracy improvement can be obtained by calculating the ratio (R) between the frequency accuracy for our proposal (

σ_{ν}^{p}

) and that for standard BOTDA method (

σ_{ν}^{s}

):

R = \frac{σ_{ν}^{p} (z)}{σ_{ν}^{s} (z)} = \sqrt{\frac{Δ ν_{B}^{p}}{Δ ν_{B}^{s}}} = \sqrt{3} .

3. Experimental demonstration and discussion

To demonstrate the feasibility of this proposed technology, the experiment is carried out as the setup presented in Fig. 5.

Fig. 5 Experimental setup of the proposal. PM: phase modulator; EOM: electro-optic modulator; PG: pattern generator; PC: polarization controller; PS: polarization switch; EDFA: erbium-doped fiber amplifier; PD: photodetector; DWDM: dense wavelength division multiplexing.

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The continuous-wave light from a narrow linewidth tunable laser with output power of 16 dBm operating at 1550 nm is split into two branches by a 50/50 coupler. On the probe branch, the light is modulated by an electro-optic modulator (EOM) to generate the carrier-suppressed double sideband (CS-DSB) signal. The modulating frequency is set to match the Brillouin frequency shift v_B. After that, the 2-tone probe with the power of −6 dBm/tone is injected into the far end of the sensing fiber after a polarization switch (PS) to avoid polarization fading effect. On the pulse branch, the optical beam is firstly pulsed by another EOM and then further phase modulated by a phase modulator (PM) to generate the pump pulse. By adjusting the bias voltage of the PM, zero-phase shift or $π$ -phase shift can be applied on the second pulse section, so that the reference pulse or sensing pulse can be achieved accordingly. After being amplified by an erbium doped-fiber amplifier (EDFA) to about 100 mW, the pulsed pump wave is launched into the start end of the sensing fiber, interacting with the counter-propagating 2-tone probe wave in the sensing fiber. On the receiving part, the lower tone of the 2-tone probe wave is extracted by using a dense wavelength division multiplexing (DWDM). At last, the BOTDA trace is finally detected by using a photodiode (PD) connected to an oscilloscope with 500 MSamples/s.

The proposal and the method based on conventional single-pulse BOTDA are both carried out with same probe and pump power for comparison. In order to provide a clear sight of the BGS, a 24.5-km-long sensing fiber with Brillouin resonance frequency of 10.871 GHz at room temperature of 26°C is used in this experiment for relatively high SNR performance. The width of the pump pulse in conventional BOTDA system is set to be 25 ns, corresponding to 2.5 m spatial resolution. For our proposal, the duration of zero phase section in the sensing pulse (first pulse section as shown in Fig. 1(b)) is set to be 30 ns, and the width of the $π$ -phase shift section (second pulse section as shown in Fig. 1(b)) is set as 40 ns, which are the same as the parameters set for previous simulation in this paper. As previously analyzed, after subtracting the BOTDA traces obtained using the 70 ns width reference pulse and the sensing pulse, the spatial resolution is supposed to feature as 2.5 m as well. Each BOTDA trace for both methods is averaged by 16 times, and a full frequency scanning range from 10.77 GHz to 11.01 GHz with step of 1 MHz is performed for recovering BGS.

The BGS obtained using reference pulse and sensing pulse, and the BGS after subtraction are shown as blue, red and black curves respectively in Fig. 6, which match the simulation results shown in Fig. 4(a) well, demonstrating the correctness of our analytical model. For comparison purpose, the measured and fitted BGS obtained using the proposal and the conventional single-pulse method at the end of sensing fiber are plotted in Fig. 7(a). It can be intuitively seen that in our proposal, the BGS linewidth is 1/3 times narrower and the BGS peak power is 1.5 times higher with respect to those in conventional single-pulse method, which match the simulation results shown in Fig. 4(b) very well. Furthermore, the FWHM of BGS at each fiber location after quadratic fitting [4] for both methods are also calculated from 20 independent experiments, as shown in Fig. 7(b). The FWHM of BGS along the fiber obtained by our proposal keeps ~17 MHz, while that obtained by conventional single-pulse method is around 51 MHz, showing exactly 3 times difference. As predicted before, from Fig. 7(a) one can observe that the BGS obtained by our proposal (red curve) is noisier, this is due to the noise penalty of factor $\sqrt{2}$ imposed by the trace differential process. In other words, this increased noise level ( $\sqrt{2}$ times) would annihilate the benefit brought by the 1.5 times higher peak power. After calculation, the SNR value at the end of fiber for the results obtained from both methods is 12 dB, which verifies our prediction. As a consequence, in our proposal, the potential improvement in terms of frequency accuracy is purely given by the 1/3 times narrower BGS, which is supposed to be factor $\sqrt{3}$ .

Fig. 6 The measured BGS induced by reference pulse, sensing pulse and the proposal respectively at the start of sensing fiber.

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Fig. 7 (a) The measured and quadratic fitted BGS at the end of sensing fiber; (b) the FWHM of BGS versus position for both methods.

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Figure 8(a) depicts the frequency error as a function of distance for both methods, which are calculated by the standard deviation of the estimated BFS obtained from 20 consecutive experimental measurements. It can be seen that the frequency error of estimated BFS at the end of fiber is about 2 MHz when using the conventional single-pulse BOTDA method, while error of about 1.1 MHz at the end of fiber is obtained by using the proposal. It means that when using the proposal, the frequency accuracy is improved by factor 2/1.1 = 1.8 ( $\approx \sqrt{3}$ ) with respect to that of the conventional single-pulse BOTDA method, which is in good agreement with the previous analysis.

Fig. 8 (a) The frequency error versus position calculated from 20 consecutive measurements; (b) the BFS profiles around the 2.5-m long hotspot.

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To verify the 2.5-m spatial resolution of our proposal as previously discussed, a 2.5-m-long hotspot with temperature of 46°C is implemented at the end of the sensing fiber. The conventional single-pulse BOTDA method is also carried out for comparison. For the sake of visual clarity, the estimated BFS profiles over the fiber region from 24.414 km to 24.454 km for both methods are plotted in Fig. 8(b). The 2.5-m spatial resolution can be obtained by both methods, while the rising/falling edge of the BFS profile at the hotspot of our proposal is sharper. This is because the FWHM of the BGS using our proposal is much narrower, so that the BGS at hotspot and the one outside the hotspot are easier to be separated. Figure 9 (a) shows the obtained BGS at 24.43 km (outside the hotspot) and at 24.437 km (inside the hotspot), respectively. It can be seen that the quadratic fitted curves for these two BGS are highly crossed, meaning that the fitting process in the transition region between the uniform fiber and the hotspot would be highly affected by the Brillouin information both inside and outside the hotspot, giving rise to slow rising and falling edges (from 24.434 km to 24.437 km, and from 24.437 km to 24. 44 km) in the BFS profile, as the blue curve shown in Fig. 8(b). Nevertheless, when using our proposal, as shown in Fig. 9(b), the quadratic fitted curves for these two BGS are almost separated, which affect less the fitting process in transition regions. This feature of our proposal provides the possibility to measure the BFS information more precisely in case of complex temperature/strain distribution.

Fig. 9 The BGS and the corresponding quadratic fitted curves inside and outside the hotspot obtained by using (a) standard single pulse BOTDA method; (b) our proposal.

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In order to demonstrate this point, another 2.5-m hotspot is implemented after the first one with 2.5-m distance separation. The BFS profiles obtained using both methods are shown in Fig. 10, in which the two hotspots are detected correctly by using both methods, thus the 2.5 m spatial resolution of our proposal is further verified. Note that the BFS of the fiber section between the two hotspots (around 24.438 km) is also correctly estimated using our proposal because of the sharp rising/falling edges of the BFS profile for both hotspots. However, the BFS in that fiber section obtained using the conventional single-pulse method is deviated from the correct value by 5 MHz. This is mainly because the rising/falling edge of the blue curve is much slower, so that the falling edge of the first hotspot and the rising edge of the second hotspot overlap in the middle section, disturbing the BFS determination of this section and giving rise to BFS estimation error.

Fig. 10 The BFS profiles around the two 2.5-m long hotspots.

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4. Conclusion

In conclusion, a novel BOTDA sensor using a pair of pulses with same pulse width but different phase shift has been proposed for narrowing the BGS. Theoretical analysis and experimental results have demonstrated that the spatial resolution of the proposal is 2.5 m, and the BGS bandwidth can be narrowed down to about 17 MHz, which is 3 times narrower than that of conventional single-pulse BOTDA method with the same spatial resolution (2.5 m), whilst keeping the same SNR level. It has been also demonstrated that this narrowing BGS has two following benefits: i) the frequency accuracy can be improved by factor $\sqrt{3}$ ; ii) the rising/falling edge of the BFS is much sharper, which could lead to more precise BFS estimation in case of complex temperature/strain distribution. The defect of our proposal is that the spatial resolution is fixed as 2.5 m, which limits the flexibility of the proposed BOTDA system. This drawback might be overcome by properly designing both amplitude and phase configuration in the pulses (but not just designing phase configuration as this paper), which is our next study topic in the near future.

Funding

863 program 2013AA014202, 973 program 2014CB340100, NSFC program 61307055, 61331008, 61335009, 61475022, 61471054, 61505011, MOE program 20130005110013, the Fundamental Research Funds for the Central Universities, and Beijing Municipal Commission of Education.

Acknowledgments

The authors would like to thank Dr. Marcelo A. Soto and Prof. Luc Thévenaz from EPFL for the valuable discussions.

References and links

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Brillouin gain bandwidth reduction in Brillouin optical time domain analyzers

Abstract

1. Introduction

2. The principle of the proposal

2.1 Temporal response

2.2 Spectral response

3. Experimental demonstration and discussion

4. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (10)

Equations (13)

Optics Express