1. Introduction

Stimulated Brillouin scattering (SBS) in optical fibers is a nonlinear interaction between a relatively intense pump wave and a weaker, counter-propagating signal wave, which are coupled by a stimulated acoustic field [1]. Effective coupling requires that the difference between the optical frequencies of pump and signal matches the Brillouin frequency shift of the fiber ${\nu }_B$ ~10-11 GHz. Precise frequency matching is necessary, as the linewidth of the process for continuous pump waves is only about 30 MHz. Since the value of ${\nu }_B$ at a given fiber location varies with temperature and strain, the mapping of SBS interactions has been employed in the distributed sensing of both quantities for 25 years [2,3]. The most widely used measurement configuration is Brillouin optical time domain analysis (or B-OTDA), in which continuous signal waves are amplified by pump pulses, and the power of the output signal is observed as a function of time [3,4]. B-OTDA can reach 100 km range [5,6], and provide dynamic measurements [7], however the spatial resolution of the basic setup is restricted to the order of 1 m by the relatively long acoustic lifetime $\tau$ of about 5 ns [8]. Numerous methods were proposed to improve B-OTDA resolution (see a recent review in [9] and references therein). A resolution of 2 cm has been achieved along 2 km of fiber [10].

The magnitude of the stimulated acoustic wave at a given fiber location is given by the inner product between the complex envelopes of pump and signal at that point, weighted over an exponential window of duration $2\tau$ [11]. Therefore, the spatial profile of the acoustic wave is closely related to the temporal cross-correlation between the two counter-propagating optical complex envelopes [12]. This property is at the basis of Brillouin optical correlation domain analysis (B-OCDA), proposed initially by Hotate and coauthors 15 years ago [13]. In B-OCDA, continuous-amplitude pump and signal waves are judiciously modulated, in frequency or phase, so that the cross-correlation between their complex envelopes is restricted to discrete and narrow peaks [13,14]. Frequency modulation-based B-OCDA reached a spatial resolution of 1.6 mm [15]. The range of unambiguous measurements in the basic configuration was restricted to hundreds of resolution points, due to the generation of multiple, periodic correlation peaks. The measurement range was later extended through more elaborate frequency modulation patterns [14]. Recent advances in B-OCDA include phase modulation by long, binary sequences for an extended measurement range [16]; time gating for improved signal-to-noise ratios (SNRs) [14,17]; use of special phase codes for reduced off-peak residual interactions and improved SNR [18]; and the combination between B-OTDA and B-OCDA for the simultaneous interrogation of a large number of peaks [18]. State-of-the-art B-OCDA setups provide few-km range alongside cm-scale resolution [17–19].

To the best of our knowledge, B-OCDA configurations reported to-date make use of broadband modulation of narrowband optical carriers. The further scaling of resolution in B-OCDA would require higher modulation rates, towards 100 GHz. External electro-optic modulators, millimeter-wave generators, or programmable pattern generators at these rates are seldom available. Alternatively, large-signal direct current modulation of laser diodes was successfully employed in frequency modulation B-OCDA [15]. A modulator at the output of the laser diode was required to compensate for the parasitic intensity variations that are associated with this scheme [15].

Herein, we propose and demonstrate for the first time a B-OCDA configuration which employs the broadband amplified spontaneous emission (ASE) of fiber amplifiers, rather than modulated carriers, as the common source of Brillouin pump and signal. The ASE source is split in two replicas: one serves as a pump wave, and the other is modulated in suppressed-carrier, double-sideband format by a sine wave of radio frequency $\nu \approx {\nu }_B$ and serves as a signal wave. The coherence length of the ASE source can be well below a millimeter and it does not depend on high-rate modulation. The single, narrow peak of cross-correlation between the pump and the signal is scanned along a fiber under test by a variable optical delay line.

ASE-based B-OCDA raises several challenges: first, the SBS power gain over millimeter-scale sections of standard silica fibers is very small. To make matters worse, unlike most B-OCDA setups, the intensity of the output signal wave is inherently fluctuating due to the stochastic nature of ASE [20]. Lastly, when the bandwidth of the source exceeds ${\nu }_B$, the dual modulation side-bands in the signal wave are in spectral overlap. While one of these sidebands serves as a Brillouin Stokes wave, the other represents an anti-Stokes wave. The separation between Brillouin gain and loss at the signal output requires careful considerations. These issues are addressed in detail in the following sections.

Despite the inherent difficulties, we demonstrate below the reconstruction of the Brillouin gain spectra as a function of position along 5 cm of a silica single-mode fiber with a spatial resolution of 4 mm, using ASE-based B-OCDA. The scanning range was limited by the delay line available to us, and the restriction is not fundamental. The experimental uncertainty in the reconstruction of the local ${\nu }_B$ value is ± 1.5 MHz. A 4 mm-long hot spot is properly identified in the measurements. Preliminary results of this work have been briefly presented in [21]. The results establish a new potential approach to high-resolution Brillouin analysis, which might be particularly applicable to distributed Brillouin measurements along photonic devices [22–24].

2. Principle of operation

2.1. Brillouin correlation domain analysis using broadband amplified spontaneous emission

The complex magnitude of the acoustic density variations in fiber position $z$ and at time $t$is given by [11]:

In Eq. (1), $g_1$ is an electro-strictive parameter, $v_g$ is the group velocity of light in the fiber, $A_p\left(t\right)$ denotes the instantaneous complex envelope of the SBS pump entering the fiber at $z=0$and propagating in the positive $z$ direction, and $A_s\left(t\right)$ denotes the complex envelope of the counter-propagating signal wave which enters the fiber at $z=L$. The position-dependent temporal offset $\theta \left(z\right)$ is defined as: $\theta \left(z\right)\equiv \left(2z-L\right)/v_g$. Lastly, the bandwidth ${\Gamma }_A$ is given by the angular frequency offset $\Omega =2\pi \nu$ between the central optical frequencies of pump and signal, and the local value of the Brillouin shift ${\Omega }_B\left(z\right)=2\pi {\nu }_B\left(z\right)$: ${\Gamma }_A\left(\nu ,z\right)\equiv j\left[\left({\Omega }_B^2(z)-{\Omega }^2-j\Omega {\Gamma }_B\right)/2\Omega \right]$. It reduces to half the Brillouin linewidth ${\Gamma }_A=\frac{1}{2}{\Gamma }_B=1/\left(2\tau \right)$ when $\nu ={\nu }_B\left(z\right)$.

In B-OCDA setups, the pump and signal waves are drawn from a single source and subsequently offset in frequency, so that $A_p\left(t\right)=A_{p0}u\left(t\right)$ and $A_s\left(t\right)=A_{s0}u\left(t\right)$. Here $u\left(t\right)$ is a common, normalized envelope function with an average magnitude of unity, and $A_{p0}$ and $A_{s0}$ are constants representing the average magnitudes of the pump and signal, respectively. In most measurement configurations reported to-date, $u\left(t\right)$ represents the deterministic frequency or phase modulation of a narrowband optical carrier. In contrast, herein $u\left(t\right)$ denotes the complex envelope of polarized thermal light from an ASE source of bandwidth $\Delta {\nu }^{in}$ and coherence time ${\tau }_c^{in}\approx 1/\Delta {\nu }^{in}$ [20].

The expectation value of the acoustic field magnitude at position$z$, for $t>>\tau$, is given by:

In Eq. (2),${\gamma }_u\left(\theta \right)$ denotes the auto-correlation of $u\left(t\right)$, an overhanging bar sign represents the ensemble average, and it has been assumed that the output of the ASE source can be described in terms of an ergodic random process [20]. We may therefore expect that the acoustic field would be confined to a single short segment, whose extent $\Delta z\approx \frac{1}{2}{v}_g{\tau }_c^{in}$ is given by half the correlation length of the source, located at the center of the fiber where $\theta \left(\frac{1}{2}L\right)=0$ [11,16]. The position of the correlation peak can be scanned through a variable delay in the paths leading either the pump or the signal waves into the fiber under test [11,16].

Figure 1 shows an example of the numerical integration of Eq. (1), with both pump and signal drawn from a specific realization of polarized thermal light with a bandwidth of 25 GHz. The Brillouin frequency shift ${\nu }_B$ was constant along the simulated fiber section, and the frequency offset $\nu$ was chosen to match that value. The acoustic field is confined to a single and narrow correlation peak of 4 mm width, as anticipated. The results are analogous to those obtained with phase-coded B-OCDA [11,16], in which the spatial resolution $\Delta z$is determined by the spatial extent of a single coding symbol. The realization of shorter coherence times is technically much simpler than that of ultra-high-rate modulation by carefully designed sequences, as in [12,18].

 

Fig. 1 Simulated magnitude of the acoustic wave density fluctuations (in normalized units), as a function of position and time along a 8 cm-long fiber section. Both pump and signal waves are drawn from a polarized amplified spontaneous emission source, filtered to a bandwidth of 25 GHz. The acoustic field, and hence the SBS interaction between pump and signal, is confined to a single correlation peak, whose spatial extent of 4 mm corresponds to half the coherence length of the filtered source.

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In our experiments, the signal wave is generated through the suppressed-carrier, double-sideband modulation of the ASE source by a sine-wave of radio-frequency $\nu$. Since $\Delta {\nu }^{in}>>\nu$, the two modulation sidebands are in spectral overlap. Most spectral components of the signal wave are therefore subject to both SBS amplification and attenuation. The problem could be alleviated using a single-sideband modulator; however one is not available to us. In order to overcome this inherent difficulty, an optical bandpass filter of bandwidth $\Delta {\nu }^{out}<\Delta {\nu }^{in}$ is placed at the output signal path, prior to detection. The central transmission frequency of the filter is tuned to the lower-frequency extremity of the signal spectrum. Hence the selected signal components are those that predominantly undergo SBS amplification along the fiber under test.

Note that the generation of a stationary acoustic field is stimulated by the unfiltered input signal wave, and hence governed by ${\tau }_c^{in}$ (see the simulated Fig. 1). Therefore, the SBS amplification of the entire signal wave can only take place when $\nu$ matches ${\nu }_B$ within that short segment. The filtering of the signal at the output, after the Brillouin interaction had already taken place, does not affect the spatial resolution. To further illustrate this point, we simulated the signal gain as a function of frequency offset and path imbalance between pump and signal, using direct integration of Eq. (1). The value of ${\nu }_B$ was locally offset by 40 MHz from its reference value within a 4 mm-long segment only. At the output of the fiber under test, the 25 GHz-wide signal wave was filtered to a bandwidth $\Delta {\nu }^{out}$ of 9 GHz. The gain map shown in Fig. 2 illustrates a spatial resolution of 4 mm, which corresponds to ${\tau }_c^{in}$as discussed above. The map is practically indistinguishable from that obtained without an output filter.

 

Fig. 2 Simulated stimulated Brillouin scattering power amplification of a signal wave, as a function of the frequency offset between the central frequencies of the pump and signal waves and the position of their correlation peak along 20 millimeters of a fiber under test. The Brillouin shift of the fiber at room temperature is taken as zero frequency. The Brillouin shift within a 4 millimeter-long segment at the center of the fiber under test was raised by 40 MHz. Both pump and signal waves are drawn from a 25 GHz-wide polarized amplified spontaneous emission source. The signal wave at the output of the fiber under test was filtered to a bandwidth of 9 GHz prior to detection. The simulation indicates a spatial resolution of 4 mm, which corresponds to half the coherence length of the input, 25 GHz-wide signal.

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2.2. Signal-to-noise ratio analysis

Consider first the measurement of an output signal wave that is unaffected by SBS, using a photo-detector with an integration time $T$. The detector output is proportional to the quantity:

As the signal wave is drawn from an ASE source, $W\left(t\right)$ is a random process. The expectation value of the photo-detector output is $\overline{W}={\left|A_{s0}\right|}^{2}T$ [20]. Since the process is assumed to be ergodic, the time dependence in $\overline{W}$ is dropped. Assuming that $T$ is much longer than the coherence time of the filtered output signal wave ${\tau }_c^{out}\approx 1/\Delta {\nu }^{out}$, the standard deviation of the detector reading can be approximated as ${\sigma }_W\approx \overline{W}\sqrt{{\tau }_c^{out}/T}$ [20]. The expected increment in $\overline{W}$ due to SBS amplification with $\nu ={\nu }_B$ is given by: $\Delta W=\overline{W}\left[\exp \left(g_0{\left|A_{p0}\right|}^2\cdot \Delta z\right)-1\right]\approx \overline{W}\cdot g_0{\left|A_{p0}\right|}^2\cdot \Delta z$, where $g_0$ (in units of [W⋅m]⁻¹) is the SBS gain coefficient of the fiber under test. The SNR of the SBS amplification measurement can therefore be estimated as:

Here $B\approx 1/T$ is the integration bandwidth of the photo-detector, and the output signal power is assumed to be sufficiently high to overcome the detector thermal noise. The SNR scales with the power spectral density of the pump wave, and with the square root of the ratio between the output signal bandwidth and the detector bandwidth. In our experiments $\Delta {\nu }^{in}$ is approximately 25 GHz, $\Delta {\nu }^{out}$ is about 9 GHz, $B$ equals 200 MHz, ${\left|A_{p0}\right|}^2$ is on the order of 10 W, and is estimated as 0.2 [W⋅m]⁻¹. The expected SNR of a single acquisition trace is very low, on the order of 0.05. Averaging over a large number of repeating measurements is therefore necessary. The SNR estimate of Eq. (4) is supported by numerical simulations of SBS interactions driven by ASE sources, such as that leading to Fig. 1, using a range of $\Delta {\nu }^{in}$ and $\Delta {\nu }^{out}$ values. The calculated SNRs are within 1 dB of the corresponding predictions. The simulations also verify the functional dependence of the SNR on $\Delta {\nu }^{in}$, $\Delta {\nu }^{out}$ and $B$.

3. Experimental setup and results

Figure 3 shows the experimental setup used in high resolution B-OCDA measurements based on an ASE source [21]. Light from an erbium-doped fiber amplifier (EDFA), operating with its input disconnected, passed through a fiber-optic polarization beam splitter and a tunable optical band-pass filter of 25 GHz bandwidth. The source bandwidth corresponds to an expected spatial resolution $\Delta z$ of 4 mm. The filtered, polarized ASE source was split in two paths by a fiber-optic coupler. Light in the pump branch was amplitude-modulated by pulses of 25 ns duration and 2 μs period, amplified to an average power of 200 mW (peak power of approximately 10 W), and launched into one end of a 2 m-long fiber under test via a circulator. The fiber under test was a silica single-mode fiber with a relatively small mode field diameter of 6.7 μm.

 

Fig. 3 Experimental setup for Brillouin optical correlation domain analysis using a broadband amplified spontaneous emission (ASE) source. EDFA: erbium-doped fiber amplifier. Amp. Mod.: amplitude modulator [21].

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Light in the signal path was modulated in suppress-carrier, double-sideband format by an electro-optic amplitude modulator, driven by a sine wave of radio frequency $\nu$. The signal wave was transmitted through a manually-variable optical delay line, amplified to an average power of 10 mW, and launched into the opposite end of the fiber under test. The signal wave at the fiber under test output passed through the fiber-optic circulator and a 9 GHz-wide optical band-pass filter, which retained only part of the low-frequency spectral contents of the dual-sideband signal wave. Figure 4 shows the optical power spectra of the pump wave, the input signal wave and the output signal wave. The filtered output signal was detected by a photo-receiver of 200 MHz bandwidth, and sampled by a real-time digitizing oscilloscope.

 

Fig. 4 Normalized optical power spectral densities of the pump wave (blue, dash-dotted), input signal wave (red, dashed), and filtered output signal wave (black, solid).

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The lengths of fibers in the signal and pump branches were matched so that the single correlation peak between the two waves fell within the fiber under test. The position of the correlation peak could be scanned over a range of 5 cm by the manual variable delay line. The output signal was recorded for a range of modulation frequencies $\nu$ in the vicinity of the Brillouin shift ${\nu }_B$ of the fiber under test, and for a range of manual position variations in 2.5 mm increments. The SNR of a single acquisition trace was as low as 0.1, in general agreement with the predictions of section 2.2. Hence each trace was averaged over 4,096 repetitions. A 4 mm-long section of the fiber under test, located within the scanning range, was heated locally to 55 °C.

Figure 5(a) presents the relative measured SBS amplification of the signal $\Delta W\left(\nu ,z\right)$. The local SBS gain spectra are centered at ${\nu }_B$ ~10.2 GHz at room temperature, and characterized by a full width at half maximum of approximately 30 MHz, in agreement with expectations. Figure 5(b) shows ${\nu }_B\left(z\right)$, estimated by Lorentzian fitting of the experimental gain spectra. The local hot spot is properly identified. For comparison, ${\nu }_B\left(z\right)$ is also shown for a measurement in which the hot spot was removed. The standard deviation in the reconstructed ${\nu }_B\left(z\right)$ is ± 1.5 MHz.

 

Fig. 5 (a) Measured peak voltage of the output signal wave, as a function of the frequency offset between pump and signal and the manual position offset of the correlation peak location. A 4 mm-long hot spot was introduced near the center of the scanning range. (b) Reconstructed local Brillouin frequency shift as a function of position, with the hot spot turned on (blue, solid) and off (red, dashed).

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4. Summary

A novel B-OCDA technique was proposed and demonstrated based on the ASE of an EDFA. The method employs for the first time a source of physical noise, rather than modulated carriers, in the generation of broadband Brillouin pump and signal waves. In a proof-of-concept experiment, measurements were performed over 5 cm of fiber with a spatial resolution of 4 mm. A 4 mm-long localized hot spot within the measurement range was properly recognized. This new approach takes advantage of simple optical noise, instead of high-end electronic devices, to obtain high resolution. A stable localized SBS interaction could be achieved using fluctuating optical fields. The spatial resolution of the proposed method is scalable towards 1 mm and less, beyond those of phase-coded B-OCDA schemes. Sections of highly-nonlinear fibers may be used to enhance the Brillouin amplification over such short segments.

The measurement SNR is fundamentally restricted by fluctuations due to the stochastic nature of ASE [20]. The experimental SNR of a single acquisition trace was as low as 0.1, in general agreement with predictions. Averaging over 4,096 repeating measurements was therefore employed. The SNR is inferior to those of other high-resolution Brillouin analysis schemes, such as phase-coded and frequency-coded B-OCDA [17–19] or high-resolution B-OTDA [9,10], in which the magnitude of the signal wave is, at least in principle, deterministic. These systems can be designed to be limited by detector thermal noise. Another difficulty associated with the reported experiment is the limited range and inconvenience of manual position scanning. Motorized delay lines providing longer scanning ranges are readily available. The number of resolution points could reach several hundreds.

In conclusion, the new form of B-OCDA could provide distributed Brillouin sensing in greater detail over short segments, for example within photonic devices [22–24].