Analysis of pulse modulation format in coded BOTDA sensors

Marcelo A. Soto; Gabriele Bolognini; Fabrizio Di Pasquale

doi:10.1364/OE.18.014878

1. Introduction

The technique of Brillouin optical time-domain analysis (BOTDA) allows for implementation of fiber-optic distributed sensors with a high accuracy in strain or temperature detection [1,2], finding a broad variety of applications in structural health monitoring, geo-technical engineering and leakage detection along pipelines. BOTDA has been the subject of intense research activities at an international level, both in industry and academia, leading to BOTDA-based schemes attaining long-range [1,2] as well as sub-meter resolution [3,4].

A recently studied topic has been the application of pulse coding techniques [5] in BOTDA sensors [6,7], providing substantial benefits in the attained signal-to-noise ratio (SNR) and keeping an unaltered spatial resolution. BOTDA systems based on such schemes have shown to be able to reach sensing distances of 50-km with a 1-m spatial resolution [6]. However, when using long coded-pulse sequences to significantly improve the SNR, additional effects need to be taken into account; in particular, the dynamics of the acoustic-wave excitation can then come into play, potentially leading to trace distortions and accuracy impairments. Actually, the acoustic wave might be pre-excited to a different extent within different codewords, thus affecting the Brillouin gain and leading to a highly code-dependent probe signal amplification. It is then necessary to carefully analyze such an effect and its impact on coded-BOTDA sensors.

In this paper, we study the impact of pulse modulation format on coded-BOTDA sensors with 1 meter spatial resolution (10 ns pulse width). Theoretical and experimental results show that, in the absence a careful optimization of the modulation format, different codeword-dependent Brillouin gain levels can be experienced by the probe signal, thus leading to distortions in the Brillouin gain spectrum (BGS) and to spurious oscillations affecting the sensors accuracy. Such detrimental effects have been found to stem from acoustic-wave pre-excitation within codeword bits, as confirmed by the theory, and can be effectively avoided by using an optimized return-to-zero (RZ) modulation format, where sufficiently small duty-cycle values effectively suppress the acoustic-wave pre-excitation to negligible levels. Although our analysis has been carried out considering Simplex coding, its validity is general and can be directly applied to other intensity-modulation coding schemes, such as linear and correlation-based codes, where the acoustic-wave pre-excitation issue is also expected to play a fundamental role.

2. Theoretical background of Simplex-coded BOTDA sensors

Stimulated Brillouin scattering (SBS) is a process in which two counter-propagating optical waves, the so-called pump and probe signals, interact with acoustic phonons along an optical fiber [1,2]. In conventional BOTDA sensors with Brillouin gain configuration, a strong pulsed pump wave at a frequency ν₀ is sent in forward direction along the sensing fiber, and interacts with a weak continuous-wave (CW) probe beam that propagates in the backward direction, at a lower frequency ν₀ – Δν. This probe-pump interaction actually produces a periodic perturbation of the refractive index of the fiber, reinforcing the acoustic wave through electrostriction effect and leading to an energy transfer among the optical waves. This gain/depletion process takes place whenever pump and probe signals spatially overlap and the frequency difference between the optical waves is within the local BGS [1]. The frequency at which the maximum Brillouin amplification occurs is called Brillouin frequency shift (BFS) and is linearly dependent on strain and temperature variations. Thus, changes in the BFS measured along the sensing fiber (ΔBFS) can be expressed as a linear combination of both temperature (ΔT) and strain (Δε) variations, as follows [8]

Δ B F S (z) = C_{ν_{B} ε} \cdot Δ ε (z) + C_{ν_{B} T} \cdot Δ T (z),

where C_νBε = 0.048 MHz/με and C_νBT = 1.07 MHz/°C are the strain and temperature coefficients for BFS in silica fibers.

In order to obtain the BFS parameter, the frequency difference between the optical waves is swept within the BGS, in a range of typically some few hundreds of MHz; and the spatial resolution is determined by the pump pulse duration. Then, the intensity variations of the CW probe signal (ΔI_CW) are measured at the near end of the fiber (z = 0) as a function of time t and the optical frequency difference (Δν), obtaining [1]

Δ I_{C W} (t, Δ ν) = I_{C W L} \exp (- α L) {G (t, Δ ν) - 1},

where I_CWL is the input probe intensity at the far end of the fiber (z = L), α is the fiber loss coefficient, L is the fiber length, and G(t, Δν) is the net Brillouin gain defined as [1]

G (t, Δ ν) = \exp [\int_{v_{g} t / 2}^{v_{g} t / 2 + Δ z} g_{B} (ξ, Δ ν) I p (ξ, Δ ν) d ξ],

where v_g is the group velocity, Δz is the spatial resolution (which is proportional to the pulse length), g_B(ξ,Δν) and I_P(ξ,Δν) are the Brillouin gain coefficient and the pump intensity at a distance ξ. Neglecting pump depletion, the expression for the pump intensity simplifies to I_P0exp(-αξ), where I_P0 is the input pump intensity (at z = 0).

From Eq. (3) we can observe that the Brillouin gain, and then the SNR of the measurements, depend on both spatial resolution and pump power [6]. So, in order to reach longer sensing distances with a given spatial resolution, the pump power could be increased, enhancing the SNR and increasing the dynamic range of BOTDA traces. However, the maximum pump power is limited by pump depletion [1,2] and modulation instability [9], resulting in the main factor limiting the sensing distance. Actually, when the pump pulse width is of the order or shorter than the acoustic-phonon lifetime (~10 ns), the SBS interaction drastically drops [3,4], leading to an ultimate spatial resolution in conventional BOTDA sensors of ~1 m, reducing then the SNR of the measurements, and limiting the maximum sensing distance. In this case, g_B(ξ,Δν) in Eq. (3) should broaden since the effective BGS, when using 10-ns pulses, is given by the convolution of the natural BGS (exhibiting a linewidth of ~20-35 MHz) and the pump pulse spectrum, changing the BGS from a Lorentzian-shaped to a more Gaussian-like profile. This is actually well-described by a pseudo-Voigt profile which is simply a linear combination of both Lorentzian and Gaussian profiles with weights c and (1-c) respectively [10]

f_{p - V} (Δ ν) = G_{\max} {c \frac{Δ ν_{B}^{2}}{Δ ν_{B}^{2} + 4 {(Δ ν - ν_{B})}^{2}} + (1 - c) \exp [- 4 \ln 2 \frac{{(Δ ν - ν_{B})}^{2}}{Δ ν_{B}^{2}}]},

where G_max is the maximum Brillouin gain, ν_B is the BFS and Δν_B is the full-width at half-maximum (FWHM) BGS linewidth. The spectral broadening taking place in BOTDA sensors with pulse duration of the order of the acoustic-photon lifetime, actually increases the rms noise of BFS measurements (δν_B) according to [8]

δ ν_{B} = \frac{Δ ν_{B}}{\sqrt{2} {(S N R)}^{1 / 4}},

leading to a reduction of both temperature and strain resolution.

In order to increase the SNR, and hence to improve both temperature and strain resolution, the use of optical pulse coding techniques has been recently proposed for long-range sensors based on BOTDA, providing an extended dynamic range in the measurements, not affecting the spatial resolution [6]. This technique is based on a linearization of Eqs. (2)-(3), assuming that the intensity contrast of the measured CW probe signal (ΔI_CW) depends linearly on the pump intensity, according to

Δ I_{C W} (t, Δ ν) \propto \int_{v_{g} t / 2}^{v_{g} t / 2 + Δ z} g_{B} (ξ, Δ ν) I p (ξ, Δ ν) d ξ .

The linearity is actually one of the fundamental requirements to apply this kind of pulse coding technique, such as Simplex coding [5], which uses a linear decoding processing, based on a linear response of the fiber. Actually, this linear behavior is valid whenever g_B(ξ,Δν) can be assumed to be the same for every pump pulse within a codeword. However, when using a pump pulse width similar to the acoustic-phonon lifetime, the transient of the acoustic wave has a relevant impact on the amplification process [11]. Thus, when 10-ns Simplex-coded pulses are used in order to obtain 1-m spatial resolution, the Brillouin gain provided by each pump pulse may depend on the presence of a pre-existing acoustic wave that might have been previously generated by preceding pulses within the same codeword, leading to a nonlinear Brillouin amplification process. In order to analyze in detail the Brillouin interaction taking place in this case, the transient of the acoustic wave should be also taken into account. This can be done considering the following three-waves SBS transient model [11]

\begin{matrix} (\frac{\partial}{\partial z} + \frac{1}{v_{g}} \frac{\partial}{\partial t}) E_{P} = i \frac{1}{2} g_{2} Q E_{S}, \\ (- \frac{\partial}{\partial z} + \frac{1}{v_{g}} \frac{\partial}{\partial t}) E_{S} = - i \frac{1}{2} g_{2} Q^{*} E_{P}, \\ (\frac{\partial}{\partial t} + Γ_{A}) Q = i g_{1} E_{P} E_{S}^{*}, \end{matrix}

where E_S, E_P and Q are the normalized amplitudes of the probe (CW Stokes beam), pump and acoustic fields; g_1,2 are the electrostrictive and electro-optic coupling coefficients, respectively; Γ_A = i(Ω_B² – Ω² – iΩΓ_B)/2Ω is the frequency detuning parameter, where Ω_B/2π and Ω/2π are the Stokes resonance frequency and the pump-probe frequency difference, respectively, at a giver fiber position [11]. The factor Γ_B is the acoustic damping constant, which is related to phonon lifetime τ_A (~10 ns in silica fibers) and the spectral width of the Brillouin gain (Δν_B) by Γ_B = 1/τ_A = 2πΔν_B.

In order to provide a general idea of the transient behavior of the acoustic wave and the corresponding Brillouin gain when using Simplex coding with 10-ns pulses, the system of Eq. (7) has been solved for simple coded-pulse sequences, as for instance, for the first codeword of a 3-bit Simplex code (corresponding to the sequence ‘101’) [5]. In Fig. 1 , we can observe that the acoustic-wave amplitude rises from the zero level with the first 10-ns pulse, however, during the following 10 ns, corresponding to a bit ‘0’, the acoustic wave does not have enough time to be completely damped, and hence it rises from an upper level when the third bit is sent. This means that the Brillouin gain resulting from the third bit is significantly larger than the one obtained from the first one, as shown Fig. 1b. From Eq. (7) we can notice that the gain of the probe signal is proportional to the product of both pump and acoustic fields (as also shown Fig. 1b) [11], explaining why a meter-scale spatial resolution can still be achieved when using Simplex coding, regardless the slower transient of the acoustic wave.

Fig. 1 Transient behavior of conventional Simplex-coded BOTDA sensors. (a) Normalized acoustic-wave amplitude. (b) Normalized Brillouin gain.

Abstract

1. Introduction

2. Theoretical background of Simplex-coded BOTDA sensors

3. Experimental setup

4. Impact of conventional NRZ pulses on BOTDA sensors

5. Impact of RZ pulses on BOTDA sensors

6. Conclusions

References and links

Cited By

Figures (18)

Equations (8)

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