1. Introduction

Fiber Bragg gratings (FBGs) are wavelength-encoded sensors that have been widely used for measurements of parameters such as strain, temperature, vibration and acoustic emission [1–4]. Compared with conventional electrical sensors, FBG sensors offer many unique advantages such as immunity to electromagnetic interference, light weight, small size and ability to be embedded in composite materials and concrete structures [5,6]. Moreover, FBG sensors are very suitable for multiplexed sensing by writing FBGs with different Bragg wavelengths in a single optical fiber. The implement of multiplexed FBG sensors has received heightened interests in scientific and industrial applications, such as structural health monitoring, where FBGs can be used for distributed monitoring of static and dynamic strains [7–9].

For multiplexed strain sensing, the interrogation of the FBG sensor array is most commonly based on broadband ASE light source or tunable continuous-wave laser source. ASE source, together with an optical spectrum analyzer (OSA) can be employed to directly acquire the reflected spectrum of the FBG array, but the strain resolution is low due to the limited spectral resolution (typically, ~0.1 nm) of the OSA and the high intensity noise of the light source. Single-longitude mode continuous-wave lasers have been frequently used for highly sensitive strain sensing, where the resolution is limited by laser frequency noise [3, 10]. In addition, the intrinsic noise of continuous-wave lasers at low frequencies is much larger than that at higher frequencies, making it more difficult in measurement of static strain (<10 Hz) than dynamic strain [11]. Optical frequency combs, which offer thousands of synchronized low-noise laser lines in a board spectrum, have been widely investigated for precise determination of displacement and molecular compounds [12, 13]. The adoption of optical frequency combs for FBG interrogation would allow high resolution and broadband spectral detection. Previously, Kuse et al. presented a static FBG strain sensing system by using dual-comb spectroscopy (DCS) technique, which enables measurements of FBG spectrum in the low-frequency radio domain with a photodetector [11]. In their research, two mode-locked fiber lasers with the same center frequency but having a slight difference in repetition rates were used. However, as the two frequency combs were generated from two independent laser sources, complex controls were needed for phase locking and stabilizing the two combs, which make them costly, complicated and bulky.

Recently, dual-comb lasing in a single laser cavity has aroused considerable interests due to its potential dual-comb applications [14–17]. The generation of dual-comb pulses with a single laser could enable the development of compact and low-complexity dual-comb systems. In DCS, two coherent combs with slight difference in repetition rates are required [18]. It has been demonstrated that DCS can be achieved by using dual-wavelength or bidirectional mode-locked fiber lasers in free-running operation [16, 19]. In those mode-locked fiber lasers, the difference in the repetition rates can be slightly tuned by the group velocity dispersion and birefringence [16, 17, 20]. Furthermore, there is no need of complex phase-locking subsystems since the needed dual-comb pulses are generated from a single cavity that enables mutual coherent properties and common noise cancellation [16, 19].

Here, we demonstrate a compact and cost-effective FBG interrogation system by dual-comb spectroscopy with a free running fiber laser. Two coherent combs with slight difference in repetition rates were generated from a single fiber laser cavity that was mode-locked in both clockwise (CW) and counter-clockwise (CCW) directions. Stable dual-comb spectroscopy was achieved without the need of complex configurations for stabilization of the two combs, as they share the same cavity and suffered from the same perturbations. We show that such a simplified dual-comb system enables interrogation of the FBG strain sensors with high resolution in the static regime. To demonstrate multiplexing ability, five cascaded FBG strain sensors were experimentally investigated with the proposed system.

2. System setup and principle of operation

Figure 1 shows the schematic diagram of the experimental setup. A bidirectional mode-locked fiber ring laser was first constructed for interrogation of FBG sensor array using dual-comb spectroscopy technique. A 1-m erbium doped fiber with dispersion parameter D of –15 ps/(nm·km) acts as the gain medium and is pumped by a 980 nm laser diode through a 1550/980 WDM coupler. To achieve mode-locking, a SWNT-PVA composite film clamped between two fiber FC/PC ferrules is employed as a saturable absorber. No isolator is inserted in the cavity so that the laser can be mode-locked in both CW and CCW directions [17, 20]. The mode-locking state is optimized by tweaking the polarization controller. A 2 × 2 50/50 fiber coupler is used to extract the counter-propagating combs out of the cavity. Then, the two combs are combined together via a 1 × 2 50/50 coupler for FBG interrogation. A small portion (10%) of the combined combs are extracted by a 10:90 fiber coupler for repetition rate measurements with a RF spectrum analyzer (RBW, 1 Hz). The total length of the cavity is about 9.5 m, by which the fundamental repetition rate is estimated to be ~21 MHz. To demonstrate multiplexing capability of the proposed system, five FBGs with different Bragg wavelengths (i.e., 1557.44 nm, 1558.42 nm, 1559.52 nm, 1560.32 nm, and 1561.43 nm) are cascaded along a single-mode fiber and the FWHM bandwidth of FBGs is about 0.2 nm. In particular, FBG1 is chosen as a reference to eliminate environmental perturbations by using differential measurement [21]. Light reflected from the cascaded FBGs is guided to a fast photodetector (Bandwidth, 200 MHz) via an optical circulator. The detected signal is then being low-pass filtered to obtain the time-domain interferogram before recorded with a digital oscilloscope. Static strains are applied to the FBGs by using a translation stage with a tuning step of 10 μm. The length of the fiber hold by the translation stage is measured to be 23.1 cm, thus an increment of each step corresponds to a strain of 43.3 με.

 

Fig. 1 Schematic diagram of the experimental setup. EDF: Er-doped Fiber; WDM: wavelength division multiplexer; SMF: single-mode fiber; PC: polarization controller; SWNT: single-wall carbon nanotubes; PVA, polyvinyl alcohol; PD, photodetector; CW, clockwise; CCW, counter-clockwise.

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The basic principle of the proposed system is based on dual-comb spectroscopy. The fiber laser, mode-locked in both CW and CCW directions, generates two trains of pulses with repetition rates differing slightly by $\Delta f$ (Fig. 2(a)). The difference in the repetition rates is attributed to the nonidentical central wavelengths of the two combs [20]. In the frequency domain, the output optical pulses correspond to broadband frequency combs that evenly spaced by the repetition rates $f_r$and $f_r+\Delta f$, respectively (Fig. 2(b)). The frequency of the nth combs can be expressed by $f_n=f_0+n{f}_r$, where $f_0$ is the offset frequency. An FBG sensor filters the combs in reflection and the beating of the two optical combs results in a third RF combs spaced by$\Delta f$. The RF combs are linearly mapped with the optical frequency spectrum with a scaling coefficient of $f_r/\Delta f$, allowing detection of the FBG spectrum in the low-frequency RF domain. To ensure the one-to-one mapping from the optical to RF domain, the spectral bandwidth of the optical combs shouldn’t be larger than $f_r{}^2/\text{2}\Delta f$, limited by the aliasing effect [18]. From the view of time domain, the pulses of one comb scan over those from the other comb at varying time delay at an interval of $\Delta T\text{=}\Delta f/f_r{}^2$, similar to a scanning interferometer. The interferences between the two combs result in an interferogram as shown in Fig. 2(c). The spectrum of the FBG sensor can be reconstructed in RF domain from Fourier transform of the time-domain interferogram detected by a photodetector. When a strain is applied to a FBG, the effective refractive index as well as grating period will be changed due to the strain-optic and geometric effects, causing spectral shift. Such a spectral shift can be detected from the RF spectrum of the FBG.

 

Fig. 2 Interrogation of FBG sensor based on dual-comb spectroscopy. (a) Dual-comb spectroscopy in time-domain. (b) Linear mapping of FBG spectrum from optical to RF domain. (c) Time-domain interferogram.

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3. Results and discussion

By increasing the pump power above the mode-locking threshold and properly adjusting the polarization controller, stable mode-locking state in both CW and CCW directions can be achieved (Fig. 3(a)). Once mode locked, the fiber laser remained stable in many hours. The average optical power at the CW and CCW outputs are 1 mW and 0.36 mW, respectively. Figure 3(b) shows the spectra from the two outputs. The spectral bandwidth at −10 dB from their peaks are measured to be 13.1 nm for the CW and 12.8 nm for the CCW directions. The central wavelength of CW and CCW pulses are respectively 1559.42 nm and 1559.64 nm, by which the difference in the repetition rates is estimated to be 12.4 Hz, as result of group-velocity mismatch. The different characteristics of the two pulses are mainly attributed to the asymmetry of the cavity and fiber birefringence [17, 20]. The CW and CCW pulses propagates through the fiber components in different orders, which thus result in slight differences in the peak power and polarization state of the counter-propagating pulses along the laser cavity. Kelly sidebands are clearly observed from the spectra, which indicate soliton mode locking [20, 22]. The spectral shift of the laser output was within ± 0.15 nm in one hour as shown in inset of Fig. 3(b). Figure 3(c) presents the RF spectrum measured by combining the CW and CCW combs into a RF spectrum analyzer. The spectrum shows two strong frequency peaks differing by $\Delta f$ = 9 Hz, which is in accordance with the estimated result. These peaks are the fundamental repetition rates associated with the CW and CCW pulses, which are 20.876466 MHz and 20.876457 MHz, respectively. The difference in the repetition rates can be tuned in the range of 0-30 Hz by adjusting the polarization controller. The FWHM bandwidths of the CW and CCW peaks are respectively 2.3 Hz and 1.5 Hz. The weaker frequency peaks, equally spaced by the difference in the repetition rates, are beat notes between the two combs. The FWHM bandwidth of beat note is about 1.6 Hz. As mentioned above, dual-comb spectroscopy has an aliasing-limited bandwidth of$f_r{}^2/\text{2}\Delta f$. If we take the values: $f_r$ = ~20.9 MHz, $\Delta f$ = 9 Hz, the aliasing-limited bandwidth of our system would be as high as 24.3 THz.

 

Fig. 3 (a) Mode-locked pulse trains from the CW and CCW outputs of fiber laser. (b) Optical spectra of the CW and CCW pulses. The inset shows the long-term spectral drift of the fiber laser (CW output). (c) RF spectrum of the CW and CCW combs. The pair of strong frequency peaks, which give the repetition rates of the CW and CCW pulses.

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We also investigate the stability of the combs’ repetition rates in free-running operation. The repetition rates are measured from the RF analyzer and averaged at a time step of 1 min, as shown in Fig. 4(a). As no active control was applied to the fiber laser, the repetition rates of both the CW and CCW combs slowly drift due to the environmental perturbations such as temperature fluctuations and acoustic noises. The maximum drift of the repetition rates in 1 hour is about 13 Hz. However, the difference in the repetition rates of the two combs exhibits negligible changes, where the standard deviation of $\Delta f$ is only 0.06 Hz (Fig. 4(b)). The high stability of $\Delta f$ is attributed to the synchronous drift of the two combs as they share the same cavity and suffer from the same perturbations.

 

Fig. 4 (a) Long-term drift of the repetition rates of the CCW and CW pulses. (b) The difference in the repetition rates over time.

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The high stability of $\Delta f$ makes it feasible to achieve dual-comb spectroscopy by using the fiber laser in free-running operation. By interfering the two frequency combs with repetition rates differing slightly by $\Delta f$, the optical spectrum of the combs would be downscaled to the low-frequency radio domain by the ratio of $f_{rep}/\Delta f$. Figure 5(a) shows the photo-detected temporal interferogram produced by interference between the two combs. The sampling rate is set at 25 MS/s. The SNR of the temporal signal defined by the ratio of the signal peak to background noise is about 114. By taking Fourier transform of the temporal interferogram, the spectrum of the combined combs in RF domain are obtained as shown in Fig. 5(b). The time window-width for the Fourier transform is set at 1 s. The obtained spectrum covers a wide range of 0.5 MHz (10-dB bandwidth), corresponding to an optical frequency bandwidth of approximately 1.2 THz.

 

Fig. 5 (a) Temporal interferogram detected by interfering the CW and CCW combs together. (b) Spectrum of the laser combs in RF domain by taking Fourier transform of the temporal interferogram. The spectra were obtained from 10-times averaged shots.

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The broadband dual-comb spectroscopy is especially attractive for spectral measurement in WDM sensing networks. We applied the laser combs to interrogate multiplexed FBGs for static strain sensing. Five FBGs fabricated with different Bragg wavelengths are cascaded along a single-mode fiber (Fig. 6(a)). The combs sampled the FBGs’ reflection spectrum and produced an interferogram as shown in Fig. 6(b). The corresponding RF spectrum is presented in Fig. 6(c). The spectrum exhibits five well-resolved frequency peaks that corresponding to the Bragg wavelength (${\lambda }_B=2n_{eff}\Lambda$) of the five FBGs, where $n_{eff}$denotes the effective refractive index and $\Lambda$ is the grating period.

 

Fig. 6 (a) Dual-comb based interrogation of multiplexed FBG array. (b) Temporal interferogram detected after reflection from the multiplexed FBG array (10-times averaged). (c) Reflection spectrum of the FBGs in RF domain.

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The detection of static strains using FBGs relies on the Bragg wavelength shift attributed to the changes of effective refractive index and the grating period. Moreover, according to the theory in Ref [23], the Bragg wavelength shift is in linear relationship with the applied strain, given by:

Strain measurement is then performed with the multiplexed FBG sensor array. Static strains are simultaneously applied to the sensor FBG3 and FBG5, while the other FBGs are kept unloading. The spectral shift of the FBG sensors can be measured from their RF-domain spectrum that linearly mapped with the optical domain by taking Fourier transform of the temporal interferogram. Figure 7(a) depicts the RF-domain spectra of the FBGs versus the applied strains. As expected, the peak frequencies of the FBG3 and FBG5 move toward the long-wave direction as the applied strains increase. The peak frequency difference between the sensing FBGs (FBG2, …, FGB5) and the referenced FBG1 are used to eliminate environmental influences (Fig. 7(b)). As is shown, the frequency shifts of the FBG3 and FBG5 exhibit good linear relationships with the applied strain in a large dynamic range of 520 με, while the unloading FBG2 and FBG4 exhibit negligible frequency shift. The slope coefficients for the FBG3 and FBG5 achieved with the proposed system are respectively 45.4 Hz/με and 46.5 Hz/με, corresponding to 0.1 GHz/με and 0.11 GHz/με in optical frequency, which are in accordance with the theoretical expectation based on Eq. (1).

 

Fig. 7 (a) Reflection spectra of the FBG sensor array versus the applied strains. The spectra were obtained by taking Fourier transform of the 10-times averaged time-domain interferograms. (b) Frequency shifts of the sensing FBGs after subtracting the peak frequency of the referenced FBG1. (c) Frequency fluctuations of peak reading for FBG3 when no strain was applied.

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To estimate the strain resolution of the proposed system, the frequency fluctuation of the peak reading for FBG3 over time is analyzed when no strain is applied (Fig. 7c). The peak frequency of the FBG sensor is obtained by taking Fourier transform of single-shot temporal interferogram and the results are recorded for 30 s at a time-step of 1 s. As shown in Fig. 7(c), the strain resolution for FBG sensor achieved with the proposed interrogation system is about 0.5 με, estimated from the standard deviation of the peak frequency fluctuation.

4. Conclusion

In this paper, we have demonstrated a FBG-based multiplexed strain sensing system with a free running fiber laser. The fiber laser was mode-locked in both CW and CCW directions that generated two coherent combs slightly differing in repetition rates. Dual-comb spectroscopy with a broad bandwidth of 1.2 THz has been achieved with the laser combs for determination of strain-induced spectral shift of the FBGs. The spectral bandwidth of the combs can be further expanded by using a highly nonlinear fiber to increase the multiplexing capacity of the proposed system. Multi-point strain measurement was performed with the FBG sensor array, where a large dynamic range of 520 με with 0.5 με resolution was achieved. The proposed system enables interrogation of multiplexed FBG arrays simply by a free running fiber laser and a photodiode, providing a compact, simple and low-cost approach for monitoring FBG-based sensing networks.