1. Introduction

Fiber-based lasers exhibit various noises such as intensity noise, frequency noise and phase noise. The frequency and phase noises can be minimized using various techniques such as a Pound-Drever-Hall scheme, a scattering-based scheme or with semiconductor optical amplifier [1–3]. The intensity noise is often minimized using an optoelectronic-based feedback loop which adjusts the pump current or the internal temperature of the laser, or using other techniques such as an external feedforward compensation system [4,5]. However, using a control loop to reduce one noise parameter usually comes at the expense of increasing other noise parameters, especially phase noise. When performing phase-sensitive optical time domain reflectometry ($\Phi$-OTDR), both low laser frequency drift and low power fluctuation are required [6,7]. $\Phi$-OTDR allows for distributed vibration sensing with high sensitivity and is widely applied in seismic sensing, perimeter monitoring and structural health monitoring [8–10]. As nanosecond pulses from a highly coherent laser source are sent into a sensing fiber, Rayleigh scattering occurs at every point along the fiber and a fraction of the scattered light propagates backward towards the interrogating system. By monitoring the evolution of the backscattered light amplitude, vibrations occurring on the sensing fiber can be located and characterized [11,12]. To improve the detection of events in $\Phi$-OTDR, the signal-to-noise ratio (SNR) of the system must be increased. This can be achieved through various techniques such as coding-schemes or algorithm-based methods generating up to 14 dB of SNR enhancement, or using a coherent detection technique leading to a 10 dB SNR improvement [13–15]. Another technique uses chirped pulse amplification and an SNR improvement of 20 dB was reported when detecting strain [16]. $\Phi$-OTDR performances can also be enhanced when focusing on the pulse source and it has been demonstrated that a high pulse extinction ratio ($\varepsilon$), defined as the pulse peak power divided by the power at the pedestal of the pulse, leads to longer detection ranges and improves sensitivity [17,18]. To ensure reliable measurements, $\Phi$-OTDR requires a stable pulse peak power. Stabilization of pulses in the femtosecond regime has been demonstrated in free-space optics using self-phase modulation (SPM) and parametric chirped-pulse amplification [19,20].

In this paper, we present an all-optical pulse peak power stabilization technique using SPM and demonstrate its interest in $\Phi$-OTDR vibration detection. First, we illustrate how to achieve a power fluctuation reduction using the nonlinear Kerr effect. Second, we present a theoretical model for the principle of power fluctuation reduction. Third, we experimentally demonstrate pulse peak power stabilization with a pulse duration in the nanosecond regime. We apply the stabilized pulses to a $\Phi$-OTDR direct-detection scheme and demonstrate a vibration detection improvement. This all-optical process replaces intensity stabilization feedback loops on the laser and thus allows for higher laser phase stability. Moreover, this SPM-based method can be combined with other modulation-based or all-optical SNR-enhancement techniques as well as with all-optical laser stabilization techniques to further improve the performances of $\Phi$-OTDR systems.

2. Stabilization of pulsed optical signals

The behaviour of sinusoidally modulated optical signals undergoing the nonlinear Kerr effect allows for all-optical small signals magnification and high-$\varepsilon$ pulse generation both by generating and extracting a specific SPM-generated optical sideband [17,21]. Figure 1 presents the evolution of the relative output power of the first SPM-generated sideband with respect to the nonlinear phase shift $\phi _{\textrm {SPM}}$, calculated using $P^{(1)}(\phi _{\textrm {SPM}})/P_0 = \left [ J_1^2(0.5\phi _{\textrm {SPM}}) + J^2_{2}(0.5\phi _{\textrm {SPM}})\right ]$ where $P^{(1)}$ is the first order sideband output power, $P_0 = P_p/4$ with $P_p$ the input peak power and $\phi _{\textrm {SPM}}=\gamma P_pL$ where $\gamma$ and $L$ are respectively the waveguide nonlinearity parameter and the length of the Kerr medium [17]. The relative first-order output power exhibits a flat region around $\phi _{\textrm {SPM}}/1\textrm {rad}=6.4 $ dB, which can be utilized to reduce the peak power fluctuations of an incoming optical signal, $F_{in}$, defined as $F_{in}=\sigma _{P}/P_p$ where $\sigma _P$ is the standard deviation of the peak power varying over time. By fixing the length of the Kerr medium, $\gamma$ and $L$ are determined and the signal peak power at the entrance of the Kerr medium can be adjusted to match the $\phi _{\textrm {SPM}}$ condition that minimizes power fluctuations. When the fluctuation minimization condition is satisfied, the power fluctuations of the signal at the first SPM-generated sideband, $F_{out}$, is reduced as illustrated in Fig. 1. The amount of fluctuation reduction provided by this technique is presented in Fig. 2. Figure 2 shows that, for example, a peak power fluctuation of 0.7 % at the input signal is reduced to 0.012 % at the output of the first SPM-generated sideband, as illustrated by the dashed yellow lines in Fig. 2. The relationship between $F_{out}$ and $F_{in}$ is fitted by a second order polynomial to obtain a simple analytical formula describing the theoretical power fluctuation reduction provided by the proposed technique.

 

Fig. 1. Relative output intensity of the first sideband as a function of the nonlinear phase shift, $\phi _{\textrm {SPM}}$. Also illustrated is the reduction of the input signal power variation.

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Fig. 2. Reduction of input peak power fluctuation provided by the first SPM-generated sideband around $\phi _{\textrm {SPM}}= {6.4} $ dB/1rad.

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3. Experimental setup and results

The advantage of the proposed power fluctuation reduction approach is experimentally demonstrated by comparing the vibrations detected using stabilized and non-stabilized pulses in the direct-detection $\Phi$-OTDR setup presented in Fig. 3. A coherent continuous light at 1550.196 nm is generated by a low phase-noise laser (NP Photonics FLS-25-3-1550-12) and is amplified using an erbium-doped fiber amplifier (EDFA, Amonics AEDFA-C-30B). A polarization controller (PC) then ensures the alignment of the light polarization with the main polarization axis of the following electro-optic modulators (EOMs). A non-stabilized optical pulse is generated by following the dashed line from point $a$ to point $b$ in Fig. 3. In this case, two cascaded EOMs (EOM3 and EOM4, Photoline S/N: 3604-14) generate a 10 ns pulse with an extinction ratio equal to 60 dB$\pm {2} $ dB [22] at a 20-kHz repetition rate. The non-stabilized pulse is amplified by an EDFA (Amonics AEDFA-PA-25-B-FA) and filtered using a band-pass filter (BPF, TFC-C-Band), with a 3 dB bandwidth of 3 GHz, to reduce the amplified spontaneous emission noise. The generation of pulses with stabilized peak power is presented in Fig. 3 following the solid line between points $a$ and $b$. The light at point $a$ passes through a first EOM (EOM1, OC-192) applying an 8.825 GHz sinusoidal modulation, then through a second EOM (EOM2, OC-192) applying a 10 ns pulse originating from the same function generator (Tektronix AFG3252) using the same pulse duration and repetition rate as the non-stabilized case. The light is then amplified using an EDFA (Amonics AEDFA-PA-25-B-FA) and filtered using a dual-grating filter ($\lambda _{1}= {1550.110} $ nm and $\lambda _{2}= {1550.268}$ nm). The pulse power is then increased by a high-power EDFA (HP-EDFA, Amonics AEDFA-33) and the light is re-filtered by an inverted version of the dual-grating filter before entering the Kerr medium (KM) composed of a 2-km dispersion-shifted fiber. The pulse experiences SPM in the KM leading to the generation of sidebands and the first order sideband is extracted using a BPF (TFC-C-Band). The amount of amplification is adjusted to match the $\phi _{\textrm {SPM}}$ condition presented in Fig. 1. The extinction ratio of the stabilized pulse is 54 dB. The difference in $\varepsilon$ between stabilized and non-stabilized pulses has no impact on our measurements. The amount of amplification provided to the non-stabilized pulse is also adjusted so that at point $b$ in Fig. 3 both stabilized and non-stabilized pulses exhibits a 14 dBm peak power. After point $b$, pulses are amplified by an EDFA (Amonics AEDFA-PA-25-B-FA) operated away from the saturation regime and sent to a 4-km FUT through a circulator. A piezoelectric transducer (PZT) located at the end of the FUT produces a 2-kHz vibration on 2 m of fiber wrapped around it. A fraction of the pulse power propagates backwards due to Rayleigh scattering and is amplified by a high-gain EDFA (HG-EDFA, Amonics APEDFA-C-10-B-FA). The backscattered light is then filtered by a band-pass filter (TFC-C-Band) before being detected by a low-noise photodetector (New Focus 1811- IR DC 125MHz) and captured by an oscilloscope (LeCroy 64Xi-A).

 

Fig. 3. Schematic of the setup to measure optical pulse’s peak power fluctuation reduction. ATT: Variable, Attenuator, BPF: Band-Pass Filter, EDFA: Erbium-Doped Fiber Amplifier, EOM: Electro-Optical Modulator, HG-EDFA: High-gain EDFA, HP-EDFA: High-power EDFA, KM: Kerr Medium, OSC: Oscilloscope, PD: Photodiode.

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To demonstrate the peak power fluctuation reduction provided by the proposed approach, stabilized and non-stabilized pulses with a duration of 100 ns are generated and measured at point $b$ in Fig. 3. A set of 400 traces is recorded in both cases and the measured fluctuations of the pulses peak power are presented in Fig. 4 where the original non-stabilized pulse is presented in dashed blue line and the stabilized first-order pulse is in solid blue line. The percentage of fluctuation is measured on the flatter part of the pulse to avoid transient power variations imposed by the function generator at the pulse edges. Figure 4 shows a clear reduction of the peak power fluctuation when stabilizing using the proposed approach. The amount of fluctuation reduction presented in Fig. 4 is consistent with the amount predicted by the example in Fig. 2 after taking the 8 mV measurement resolution of the oscilloscope into consideration, corresponding to 0.26 % of the peak voltage. A laser exhibiting large intensity noise is utilized to better demonstrate the peak power fluctuation reduction provided by the proposed approach.

 

Fig. 4. Measured original non-stabilized and stabilized 100 ns pulses. The black circles and their associated arrows indicate the axis of reference for the corresponding traces.

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Figure 5 presents experimental vibration detection results from direct-detection $\Phi$-OTDR systems with and without stabilization, respectively shown in red and blue. Figures 5(a) and (e) respectively show overlapped backscattering traces from 10-ns pulses for the non-stabilized and stabilized intensity cases. A sliding window average is applied on each backscattering trace to improve locating the vibration [11]. Figures 5(b) and (f) present the conventional trace-to-trace difference [11] for the non-stabilized and stabilized backscattering traces, respectively. The intensity fluctuations of the non-stabilized pulse prevent locating the vibration as observed in Fig. 5(b). When stabilizing the pulse, the amplitude fluctuations in the backscattering traces are reduced by a factor of 1.95, in close agreement with the results from Fig. 4, which allows for detecting the vibration location, as shown in Fig. 5(f). To reliably locate the vibration, the difference between each trace and the average of all traces is calculated and the results for the non-stabilized and stabilized cases are presented in Fig. 5(c) and (g), respectively, showing that the vibration is located at 4.09 km. The detected vibration and scaled version of the signal driving the PZT are presented in Fig. 5(d) and (h) for the non-stabilized and stabilized cases respectively, and show 11 cycles over 5.5 ms, corresponding to the 2-kHz vibration applied by the PZT. The vibration location cannot be identified in Fig. 5(c) corresponding to the case of non-stabilized pulses but can be identified in Fig. 5(g) corresponding to the case of stabilized pulses, which demonstrates the practicality of this stabilization technique.

 

Fig. 5. Comparison of $\Phi$-OTDR vibration detection in the non-stabilized and stabilized scenarios, respectively in blue and red: a) Non-stabilized overlapped backscattering traces, b) Overlap of trace-to-trace difference in the non-stabilized scenario, c) Overlap of the difference to the average trace in the non-stabilized scenario, d) Detected vibration from the non-stabilized scenario and scaled PZT driving signal, e) Stabilized overlapped backscattering traces, f) Overlap of trace-to-trace difference in the stabilized scenario, g) Overlap of the difference to the average trace in the stabilized scenario, h) Detected vibration from the stabilized scenario and scaled PZT driving signal.

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4. Discussion

The proposed all-optical power fluctuation reduction approach is not limited to pulse peak powers and can also be applied to sinusoidally modulated continuous wave lasers. We utilize optical pulses to mitigate the generation of Brillouin scattering in the Kerr medium which would drain the signal power and limit the achievable nonlinear phase shift. Optical pulses also allow for achieving higher peak power and ease achieving the optimal $\phi _{\textrm {SPM}}$ value to satisfy the power fluctuation reduction condition. For initial power fluctuations below 1 % of their reference power, this technique allows for a reduction of power fluctuations by a factor of at least 40 as can be observed in Fig. 2. The proposed all-optical technique replaces optoelectronic feedback loops on the laser and thereby eliminates their impact on phase noise and improves $\Phi$-OTDR performance.

A photodetector with low detection threshold is required to reduce the intensity noise observed in the backscattering traces from Fig. 5(a) and (e). Such photodetector allows for the reduction of signal amplification provided by the HG-EDFA in Fig. 3 and therefore minimizes the intensity noise added by this amplification stage [23]. The amplifier present before the FUT in Fig. 3 can be bypassed if the length or the $\gamma$ parameter of the Kerr medium are tuned to match a required output peak power. For example, a shorter Kerr medium requires a higher input peak power to achieve the optimal $\phi _{\textrm {SPM}}$ value and therefore induces a higher peak power at the first order sideband, as shown in Fig. 1.

5. Conclusion

We present a new all-optical technique for stabilizing the peak power of an optical signal by tuning the amount of SPM experienced by a sinusoidally modulated optical signal entering a Kerr medium and extracting the first order sideband that is generated by SPM. The advantage of this technique is demonstrated using a $\Phi$-OTDR direct-detection scheme to detect vibrations applied on a fiber at a 4-km distance. We experimentally demonstrated a trace-to-trace amplitude fluctuation reduction using our stabilization technique, which allows for locating vibrations that could not be located in the case of non-stabilized laser power. This all-optical technique can also be combined with other $\Phi$-OTDR performance enhancing techniques for broader sensing capabilities.