Distributed optical fiber sensors have been extensively employed as an excellent method for high-precision monitoring in diverse fields, such as geophysical,1^,2 structure safety,3^–6 and life sciences.7 Among them, various stimulated Brillouin scattering (SBS)-based schemes, including differential pulse-width pair Brillouin optical time domain analysis (BOTDA),8^,9 rising edge demodulation BOTDA,10 and high-correlated source Brillouin optical correlation domain analysis (BOCDA)11^–13 have been proposed to achieve a spatial resolution of a centimeter or even millimeter level. However, the performance of BOTDA schemes, including resolution and measurement accuracy, is significantly limited by the gain mode of temporal-spatial synchronous excitation and by the sampling predicament of the high-frequency narrowband pulse.14

Interestingly, in BOCDA schemes, the acoustic field of temporal-spatial independence is stimulated by the narrowband coherent optical fields, which could circumvent the phonon lifetime limitation and provide unique advantages in millimeter-level spatial resolution.15 The sinusoidal frequency-modulation BOCDA with the 40-cm resolution was first proposed in 2000,16 and that was improved to 1.6 mm in 2006.17 However, the feeble gain is easily overwhelmed by the accumulated noise along the fiber, or disturbed by the cross-talk signal of periodic correlation peaks (CPs), leading to a severe deterioration of the signal-to-noise ratio (SNR).18 Consequently, the sensing performance, encompassing sensing distance, spatial resolution, and measurement accuracy, is directly limited by the inferior SNR. Several enhanced BOCDA protocols have been inspired to improve the SNR. Methods for extracting pure Brillouin gain, such as intensity modulation,19 differential measurement,20^,21 and phase-shift keying,22 have been employed to enhance the spatial resolution to 0.64 mm.15 The techniques aimed at suppressing accumulated noise, such as Golomb encoding,11^,23 temporal gating,12^,24^,25 and gradient descent frequency shift estimation,26 have achieved a Brillouin frequency shift (BFS) error of <1 MHz. Concurrent interrogation of multiple CPs, employing techniques, such as time-domain data processing,12^,24 hybrid aperiodic coding,27 and injection locking combined with distributed Raman amplification,28 has significantly promoted the sensing range to 72.65 km. However, the optimal merit is barely achieved in pairs. Exploring a multimeric coupling scheme reliant on a higher SNR shows a promising future.

In addition, the chaos BOCDA29 was proposed and experimentally demonstrated as another competitive long-range high-resolution configuration. The chaotic laser features broadband in the optical spectrum and random fluctuation in the power sequence.30 This utilization ensures the excitation of a sole narrow CP along the entire fiber, primarily avoiding high-rate external modulation and periodic CP interference. The bandwidth-enhanced chaotic laser has been applied to achieve a spatial resolution of 3.1 mm,31 and then the optimized time-gated scheme combined with differential denoising configuration has been proposed to increase the sensing range to 27.54 km.32 Similar to the above schemes, the best performances of chaos BOCDA are independently implemented, e.g., the sensing range being 19 m at a 3.1-mm spatial resolution, and the measurement accuracy being 2.98 MHz at 27.54-km sensing distance. The physical mechanism reveals that the SBS gain highly depends on the relative power variation of pump and probe waves. Specifically, chaos BOCDA suffers significant deterioration due to inherent power fluctuation. Simultaneously, the residual off-peak background noise is parasitically stimulated and consistently accumulated, which cannot be nearly inhibited completely. Therefore, in the original chaos BOCDA, the performances are enormously subject to the inferior SNR and are hardly to upgrade further.32

In this paper, a novel high-correlated laser source, referred to as phase-chaos laser (PCL), is proposed and introduced in the BOCDA scheme to promote the SNR and achieve a high-accuracy measurement. The PCL and its characteristics are first presented, and the determinants of the SNR are comprehensively deduced, given the operating mechanism of chaos BOCDA. Then, the leading role of the chaos phase term in the temporal frequent excitation of the SBS acoustic field and the impact of the fluctuation and correlation characteristics of power on the pure gain extraction are investigated in the simulation. Further, the PCL is experimentally generated by an optical injection scheme, and its chaos properties are amply verified. Finally, the proposed PCL-BOCDA scheme markedly improves the accuracy of BFS and the signal-to-background noise ratio (SBR) of the Brillouin gain spectrum (BGS).

The PCL, in definition, features a stochastic variation in phase and a constant in power. The PCL remains a Lorentz-shaped broadband in the optical spectrum. In contrast, the power fluctuation is approximately equivalent to that of the general laser, whose peak-to-peak value is approaching the noise floor in the time sequence, compared to the original chaotic laser.

The light field E(t) and intensity I(t) of the PCL can be expressed as E(t)=A(t)exp{−i[ω0t−φ(t)]},(1)I(t)=|A(t)exp{−i[ω0t−φ(t)]}|2,(2)where A(t) and φ(t) are the temporal functions of a chaotic stochastic variation in the amplitude and phase, respectively. Under the ideal condition, the PCL maintains a constant amplitude, and its intensity is equivalent to the mean value I¯ correspondingly. As shown in Fig. 1(a), the power sequence of the PCL is almost the same as that of the general single-frequency laser and the intensity remains in a stable state. Its phase term presents a continuously random fluctuation in the range of −π–π. However, the intensity fluctuation is inevitable owing to the operating mechanism of a chaotic laser, and its probability density PU(I) can be described as Eq. (3). Therefore, the intensity of PCL presents a weaker fluctuation benefiting from the paltry variance σu2. This feature would also reduce the correlation degree of the intensity, and thus the quasi-periodic property, mainly resulting from the amplitude resonance in chaos generation, could be largely inhibited: PU(I)=12πσuexp[−(I−I¯)22σu2].(3)

In the BOCDA scheme, SBS interaction is stimulated by the highly correlated pump and probe waves, which are jointly modulated in phase or amplitude. Serving the PCL as the sensing signal, the beat interaction is operated between the counterpropagating pump and probe waves with the frequency detuning of ν, which is around the local BFS of the fiber. Figure 1(b) illustrates the distribution of the beat spectra along the sensing positions. A sharp strong beat field is excited at the highly correlated position, where the optical path of the pump and probe waves is equal and the phase difference remains constant. With the optical path offset, the beat spectrum gradually broadens and thereupon its intensity decreases on either side of the center position. Remarkably, the secondary beat fields, stimulated by the quasi-periodic weak CPs of the PCL, are presented in this schematic diagram, although the impact of these could be ignored.

Further, the SBS acoustic fields are excited at the beat positions due to the electrostriction effect, and then the BGS at a particular position could be obtained by scanning the detuning frequency ν, as shown in Fig. 1(c). In the gain-mechanism SBS-based sensors, the probe wave is gradually amplified along the fiber, and thus the recorded intensity at the front of the fiber is the superposition of the gain signals at each position. Assume that the gain or loss experienced by the probe wave in a brief local interaction is small (<5%); thus, the protocol is operated in a small gain condition. The intensity difference ΔI detected can be expressed as ΔI=∫IS(L−z)IP(z)g(v,z)dz,(4)where IS(L−z) and IP(z) are the intensity of probe and pump waves, respectively. The pump launched at the near end (z=0) simply experiences an exponential decay during the propagation and can be expressed as IP(z)=IPiexp(−αPz), where αP is the linear attenuation coefficient of the pump wave and IPi=IP(0) is the input power of the pump pulse at z=0. Similarly, the probe wave launched at the far end (z=L) can be expressed as IS(z)=ISiexp[−αS(L−z)], where αS is the linear attenuation coefficient of the probe wave and ISi=IS(L) is the input power of the probe wave. The g(v,z) is the actual BGS of the fiber at the position z, which can be presented as the convolution of the pump-Stokes beat spectrum, Sb, with the local BGS: g(v,z)=Sb⊗gB=∫ρb(ω,z)g0ΔvB2ΔvB2+4(v−vB−ω)2dω,(5)where gB is the intrinsic gain spectrum, ρb(ω,z) is the spectral density of the beat frequency, ω is the beat frequency range, g0 is the Brillouin gain coefficient, ΔνB is the Brillouin linewidth, and νB is the central BFS of the fiber. As shown in Fig. 1(d), when the detuning frequency is equal to νB, the power of the Stokes wave is sharply increased only at the CP position in the ideal state. By scanning ν nearby νB, the pure BGS of the central position can be reconstructed according to the measured Stokes power at the front of the fiber.

The intensity of measured gain ΔIR is systematically subject to the position and scanning frequency, which can be expressed as$$\begin{gathered} ΔIR(v)=ISiIPiexp(−αSL)∫exp(−αPz)g(v,z)dz \\ ≈ISiIPiexp(−αSL){exp(−αPzC)gC(v)ΔzC+∑n=1Nexp(−αPzSn)gSn(v)ΔzSn+1αP[1−exp(−αPL)]gF(v)}, \end{gathered}$$(6)where L, ΔzC, and ΔzSn represent the length of the fiber, the range of gain at the central position and the suborder beat positions, respectively, and N is the number of the suborder beat in the optical fiber, which is determined by the length of the fiber and the characteristics of the light source. gC(v), gSn(v), and gF(v) are the gain envelopes at the central CP, the suborder beat CPs, and the off-peak backgrounds along the fiber, respectively. In fact, the fluctuation of light intensity I has a random property and the variance of gain intensity σΔIR(v)2 is positively correlated with the variance of light intensity σu2.

The pure SBS gain ΔI0(ν)=IS¯IP¯gC(v)ΔzCexp(−αSL)exp(−αPzC) cannot be affected by the amplitude fluctuation of the chaotic laser under ideal conditions. When the probe wave is collected by the photodetector (PD), the incident energy is randomly and independently converted into photoelectric events.33 When the integral intensity W of the light intensity I passes through the surface A in time T, it is found that the probability of K photoelectric events can be given by Poisson distribution P(K)=(αW)KK!exp(−αW). According to Mandel formula, the variance can be expressed as σK2=K¯+α2σΔIR2. The variance consists of two terms. The first term represents the Poisson noise effect caused by the random interaction of photoelectron emission. The second term is proportional to the variance of the strong fluctuation of the incident light. Consequently, the SNR of the system can be expressed as $$\begin{gathered} SNR(v)=ΔI0(v)ΔIR(v)¯−ΔI0(v)•K¯K¯+α2σΔIR(v)2 \\ =ΔI0(v)ΔIR(v)¯−ΔI0(v)•K¯K¯+α2σΔIR(v)2 \\ =gC(v)ΔzCexp(−αPzC)∑n=1Nexp(−αPzSn)gSn(v)ΔzSn+1αP[1−exp(−αPL)]gF(v)•K¯K¯+α2σΔIR(v)2. \end{gathered}$$(7)

The first term of Eq. (7) on the right represents the influence of noise along the optical fiber. The second term of Eq. (7) on the right is the influence of light intensity fluctuation and the average number of times. Therefore, for the PCL system, the impact of σu2 on pure gain extraction could be ignored and the accumulated noise floor induced by gSn(v) and gF(v) would be reduced. Although the SNR could be improved by increasing the average number of measurements, the core factor impacting the quality of SNR is the intensity of σu2. PCL, with a lower and ignorable σu2, is the significant merit of promoting SNR in the context of the physical mechanism.

In BOCDA schemes, the acoustic field of temporal-spatial independence is stimulated by the narrowband coherent optical fields. However, tracing to the gain motivation mechanism, the feeble gain is easily overwhelmed by the accumulated noise along the fiber, or disturbed by the cross-talk signal of periodic CPs. According to Eq. (7), the SNR is severely deteriorated in principle. The sensing performance, including sensing distance, spatial resolution, and measurement accuracy, cannot be simultaneously improved due to the limitation of inferior SNR. Remarkably, the utilization of the PCL could achieve a higher measurement SNR by stimulating a purer gain and significantly suppressing the noise floor. In addition, this proposed model is suitable for clarifying the gain component and noise structure for the general BOCDA schemes. In the phase coding or sine frequency modulation schemes, the suborder CPs should be separate from the central CP, and the parasitic power fluctuation should be eliminated. For the amplified spontaneous emission source, the feeble gain is approximately submerged by the intensive amplitude fluctuation, resulting in a poor SNR.

To determine the dominant role of the phase term in Brillouin gain excitation, the temporal–spatial distribution of the SBS acoustic field at ν=νB is simulated in different correlation conditions of the chaos amplitude term or its phase term. When only the phase term of the chaos pump and probe waves are highly correlated, an intense and steady acoustic field is motivated at the center of the fiber, while there is scarcely any effective Brillouin gain generated at the other positions in Fig. 2(a). On the contrary, when the amplitude term of these two beams with quite separate phase terms is highly correlated, a constant gain cannot be generated and the fluctuating noise floor is continuously motivated along the fiber in Fig. 2(b). Therefore, the pure SBS gain mainly results from the correlation of the chaos phase term, and the amplitude term would introduce a large amount of noise structure along the fiber in the original scheme.

The intensity of the acoustic field is further analyzed in both the phase chaos and original chaos schemes. As shown in Fig. 3(a), although the sharp acoustic field could be excited at the center CP in both schemes, the noise intensity of the suborder field is significantly reduced, with an SBR of 12.79 dB in the PCL-BOCDA, ∼7.35dB higher than that of the traditional scheme.

SBR is defined as the ratio of gain signal to background noise, where the noise level represents the level of the second largest peak that appears at ΔνB different from the real value. The SBR is a general index for comparing the performances under different conditions, and the larger SBR indicates that it is more robust against the noise sources in the real measurement and so becomes preferable.

In addition, as the inset shows, the noise floor along the fiber presents a gentle variation in the PCL system rather than a drastic fluctuation. The gain intensity of the Stokes wave varying with the positions is further compared in Fig. 3(b). Obviously, in the PCL-BOCDA, the pure gain signal is sharply generated at the CP position, and there is negligible accumulated noise along the off-CP positions. Contrariwise, the effective gain is submerged by the noise structure in the original chaos scheme. According to Eq. (7), the SNR of the PCL-BOCDA is prominently increased to 8.05 dB, which is 5.56 dB higher than the original one.

When ν is scanned near νB, the BGS of the central position can be reconstructed by sampling the power variation at the front of the fiber. According to Eq. (6), the measured BGS is the spatial integration of Brillouin gain at each position along the fiber. The impact of σu2 on chaotic BGS in different schemes is simulated and analyzed in Figs. 4(a1) and 4(b1), where the blue lines and the red lines show the demodulated BGS under a single measurement averaging 15 times, respectively. Similar to Fig. 3(b), the sharp gain signal is concentrated near the center BFS, and the intensity slightly fluctuates in the PCL-BOCDA. In the original scheme, the obvious gain jitter is observed, resulting in the feeble peak gain of the center BFS, which is presumably submerged and can hardly be identified. In our previous works,29^,32 the average processing was usually employed to weaken the random noise of Gaussian fluctuation. In this work, the red points plot the BGSs after averaging them 15 times; their Lorentz-fitted curves are depicted in Figs. 4(a2) and 4(b2). The BGS of the PCL scheme exhibits an approximately perfect Lorentz shape with a fitting coefficient of up to 0.9999, while the original BGS remains a minor fluctuation and the fitting coefficient is 0.9951.

The influence of the cumulative noise on the BGS measurement is further considered by increasing the sensing distance and the average times. The length of the fiber under test (FUT) with a BFS of 10.73 GHz is 100 km, and a 10 cm-long event section is set as a BFS of 10.64 GHz. The red curve of Fig. 4(c) demonstrates that when the central CP and the event region are located at the front of the FUT, the central BFS of the event region could be accurately distinguished with a neglected noise background, the SBR reaching 9.21 dB in the PCL-BOCDA scheme. Conversely, in the original system, the BGS performs bimodal and the SBR decreases to 2.07 dB, although the center BFS could be extracted. Figure 4(d) depicts that when the central CP and the event region are located at the end of the FUT, the central gain of the traditional system has been submerged by the accumulated noise along the fiber, presented as the subpeak being higher than the main peak. The SBR is severely deteriorated to −2.39dB, and thus the central BFS cannot be accurately identified. Prominently, the low-noise PCL could sufficiently generate effective SBS gain; the SBR of the BGS is increased by 8.28 dB, whose residual secondary beat and off-peak background noise are hardly able to worsen the accurate BFS extraction. The SBR of the BGS at the end of the fiber is lower than that at the front of the fiber because the noise gain is stronger along the front of the fiber, whereas the gain of strain region is weaker because of the excessive transmission of the pump light power to the probe light power at the end of the fiber. It should be noted that the massive averaging (50 times in this simulation) cannot completely remove the impact of σu2 on BGS measurement, and the gain floor of the original chaos BGS still performs an intensity fluctuation. Based on these, the following verification of the proof-of-concept experiment is carried out.

The experimental setup of the PCL-BOCDA is shown in Fig. 5. The PCL is generated by an optical open-loop injection configuration. The chaotic laser as the master laser (ML) is injected into the slave laser (SL) through the polarization controller (PC1) and variable optical attenuator (VOA). Utilizing optical injection, a strong semiconductor laser is controlled by a weak broadband chaotic laser. The center wavelength between the ML and the SL is adjusted to ensure the frequency detuning is within a certain range. The optical spectral shape of the output light of the SL is changed by adjusting the detuning frequency. The injection intensity is controlled by the VOA, and the PC1 can change the polarization-matching state of the two beams. The optical spectral width of the PCL is changed by adjusting the injection power and polarization-matching state. The PCL is split into two beams by an optical coupler, where the upper branch (90%) is used as the probe light and the lower branch (10%) is used as the pump light. The probe light is modulated in a suppress-carrier, double-sideband format by the electro-optic modulator (EOM), driven by the microwave signal generator (MWG), and the sideband frequency shift is approximately equal to that of the fiber BFS. The modulated probe light is transmitted through the programmable optical delay generator (PODG), amplified by the continuous-wave erbium-doped fiber amplifier (C-EDFA), and then launched into the end of the FUT through the polarization scrambler (PS) and the optical isolator (ISO). The pump light is modulated into the pulsed laser by the semiconductor optical amplifier (SOA) and then is launched into FUT via the pulse-EDFA (P-EDFA) and optical circulator (OC). The probe light is amplified by the SBS interaction along the FUT and filtered by the optical bandpass filter (BPF) with a bandwidth of 6 GHz. Finally, the filtered Stokes light is detected by a PD, sampled, and processed by a lock-in amplifier (LIA). Remarkably, the pulse modulation in this experiment is used as a trigging and chopping signal for lock-in detection, and the time-gated configuration is unadopted.

In this work, the PCL is experimentally generated. Figure 6 shows the typical properties of the original chaos and the proposed PCL. Both optical spectra present a wideband distribution and the −3dB linewidth is about 5 GHz in the Fig. 6(a). The theoretical spatial resolution is 6.4 mm correspondingly. Figure 6(b) shows the time sequence of phase term measured by a heterodyne interferometry. That of the PCL maintains stochastic fluctuation, and its Lyapunov exponent is 2.1469, implying a convincing chaotic characteristic. Interestingly, Figs. 6(c) and 6(d) display the time sequences and the probability density functions of their power distribution. The peak-to-peak value of the PCL has been reduced to 3.97 mV, which is 0.13 times that of the original one of 29.57 mV. Further, the standard deviation of the probability distribution of the PCL is improved from 3.25 to 0.38, indicating the inherent power fluctuation has been significantly inhibited. As mentioned above, the chaotic laser generated by the optical feedback loop has a certain periodicity in the power sequence that is characterized by a series of weak peaks on both sides of the central CP. As shown in Fig. 6(e), the secondary CPs are significantly restrained for the PCL, where the intensity of the second CP is only 0.0376 and much less than that of the original chaos of 0.2661. The suborder beat CPs and the off-peak backgrounds along the fiber of the PCL scheme are so low they can be ignored. Therefore, the pulse modulation, employed for suppressing the impact of the suborder beat noise in the original schemes, is only used as a trigging and chopping signal for LIA detection and is taken out of consideration for time-gated configuration. According to Eq. (7), the utilization of the PCL could achieve a higher measurement SNR by stimulating a purer gain and significantly suppressing the noise floor, introduced by amplitude fluctuation or correlation.

Serving these two lasers as the sensing source, the measured BGSs are illustrated in Fig. 7(a). In the lock-in detection system, each BGS was obtained via a single measurement, where MWG was scanned from 10.68 to 10.88 GHz with a 1 MHz step. It only consumes 0.2 s for a single measurement, which is only determined by the sweeping speed of MWG and the sampling rate of LIA, with a sensitivity of 10μV and a maximum sampling rate of 1 kHz of the LIA. The FUT is a 1 km single-mode fiber (SMF) with a BFS of 10.805 GHz. Similar to the simulation results, the measured BGS of the original chaos scheme performs an oscillatory floor and a slightly shifted center frequency, with the Lorentz fitting coefficient of about 0.9284. The BGS of the phase-chaos scheme exhibits an approximately perfect Lorentz curve, with a fitting coefficient of up to 0.9951. Remarkably, considering the original chaos scheme, the BGSs after being averaged 30 times are presented although fewer average times, even a single measurement, are adequate in the PCL scheme. The fluctuation near the peak gain has been largely eliminated on both the BGSs. To verify the accuracy of the BFS measurement, the BFS errors of these two schemes are compared in Fig. 7(b), where independent repeating experiments are conducted 25 times at a single position. Benefiting from the pure BGS, the BFS accuracy of the phase-chaos scheme could be promoted to ±0.64MHz, which is significantly higher than that of ±3.12MHz achieved by the original chaos system.

Finally, the BGSs of the relatively long-range systems are measured to conduct the suppression of background noise in the PCL-BOCDA. Figure 8(a) shows the structure of the FUT, which consists of 1400-m SMF1 with a BFS of 10.748 GHz and a 10-m SMF2 with a BFS of 10.805 GHz. Figures 8(b) and 8(c) describe the measured BGSs at the front and end of the FUT under different schemes. When the central CP is located at the SMF1, the BGS of the original chaos scheme shows a slightly bimodal structure with a gain fluctuation, and the SBR of that is decreased to 4.36 dB. The deterioration of the original chaos BGS is aggregated, as the central CP is located at the SMF2, where a powerful subpeak induced by the secondary beat and off-peak substrate results in the SBR value is as low as 2.20 dB. Significantly, whether the central CP is placed at the front or tail of FUT, the BGSs of the phase-chaos scheme present a nearly coincident Lorenz shape, whose SBRs are promoted to 12.60 and 12.97 dB, respectively. Therefore, this proof-of-concept implementation of the PCL-BOCDA scheme presents a higher SNR and enormous development potential in high-performance sensing.

In BOCDA schemes, the acoustic field of temporal-spatial independence is stimulated by the narrowband coherent optical fields, which could circumvent the phonon lifetime limitation and provide unique advantages in high spatial resolution. However, the feeble gain is easily overwhelmed by the accumulated noise along the fiber or disturbed by the cross-talk signal of periodic CPs.

For all BOCDA schemes, two indices are mainly proposed to estimate the sensing performance.

Remarkably, the SBR of BGS is directly related to the system SNR. The SBR improvement is one of the manifestations of the higher SNR and could be constantly degraded with further improvement of the sensing performance.

A brief overview of the SBR or SNR of BOCDA is summarized in Table 1. The highest SBR of 12.97 dB has been experimentally demonstrated in this paper, the accuracy of BFS being prior. With the sensing range increasing, the SBR of the traditional scheme severely deteriorates to 0.36 dB, although the extra method of optimal temporal gating is applied. In contrast, a higher SBR of 5.35 dB with a range of 100 km is theoretically achieved, and an enormous potential for long-reach high-resolution application is presented in the PCL scheme. Remarkably, although the differential measurement and Golomb coding are employed to reduce the noise floor and promote the SBRs in sine-FM and phase modulation schemes, respectively, the PCL-BOCDA system could reduce the power fluctuation of the light source and not be limited by the bandwidth of the modulation device with the same or even higher SBR.

The SNR or SBR of the proposed PCL protocols has been promoted, although some indices should be further enhanced compared to the state-of-art methods. In addition, PCL optimizes the optical spectral shape of chaotic light, which can further provide a positive improvement in the measurement of spatial resolution. PCL BOCDA performs a significant competitiveness in multimerit coupling achievement and is expected to highlight the future avenues after revising the intrinsic drawbacks of the traditional chaos.

In summary, we propose and demonstrate a novel BOCDA scheme based on a PCL. It is understood that the SNR of SBS-based sensors is principally limited by the gain stimulation mechanism, which severely restricts the development of the SBS-based sensors. The PCL is proposed and subsequently utilized to deduce the SNR impact factors of the chaos BOCDA. Then, the SNR of the PCL-based scheme is increased by 5.56 dB, and the SBR of BGS is improved by 8.28 dB at an FUT of 100 km, which significantly promotes the theoretical optimal sensing performance. Further, the PCL is experimentally generated by the optical injection scheme for the first time. In the proof-of-concept PCL-BOCDA, the measurement accuracy of BFS is preliminarily improved from ±3.12 to ±0.64MHz, and the SBR of chaotic BGS can be increased from 2.20 to 12.97 dB on a 1.41 km fiber.

The generation and utilization of the PCL provide a new research direction for optical chaos, and an advanced exploration would be further conducted including spectral characteristics, relevant dimensions, and applications in optical coherence tomography. In addition, the SNR model, aiming at the impact factors and improvable avenues, offers some experience and instructions for the general BOCDA schemes. The PCL-BOCDA provides a competitively novel solution for high-SNR measurement, and the multimeric coupling sensing promises to be achieved by combining broadband enhancement, differential measurement, and temporal gating in the future.

Lintao Niu received her BS degree in 2021 in photoelectric information science and technology from the College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China, where she is currently working toward the PhD in optics engineering. Her current research interests include chaotic laser and optical fiber sensing.

Yahui Wang is an assistant research fellow at Taiyuan University of Technology, Taiyuan, China. He received his PhD in optics engineering from Taiyuan University of Technology, Taiyuan, China, in 2021. His research interests include chaotic laser and its Brillouin distributed fiber sensing.

Jing Chen received her BS degree in applied physics from the College of Physics and Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan, China, in 2022, where she is currently working toward a master’s degree in optics engineering. Her current research interests include chaotic laser and optical fiber sensing.

Haochen Huang received his BS degree in optoelectronic information science and Engineering from the College of Physics and Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan, China, in 2022, where he is currently working toward the master’s degree in optics engineering. His current research interests include chaotic laser and optical fiber sensing.

Lijun Qiao received her PhD in microelectronics and solid electronics from the Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China, in 2017. She is currently an associate professor at the College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China. Her research interests include nonlinear dynamics of laser diodes and photonic integrated broadband chaotic semiconductor lasers.

Mingjiang Zhang is a professor and PhD supervisor at Taiyuan University of Technology, Taiyuan, China. He received his PhD in optics engineering from Tianjin University in 2011. He was a visiting scholar at the University of Ottawa, Canada, in 2016. His current research interests include photonic integrated chaotic lasers and distributed optical fiber sensing. He also serves as a reviewer for IEEE, OSA, and Elsevier journals.