December 15, 2014 / Vol. 39, No. 24 / OPTICS LETTERS
6899
Split-mode fiber Bragg grating sensor for high-resolution static strain measurements P. Malara,1,* L. Mastronardi,2 C. E. Campanella,2 A. Giorgini,1 S. Avino,1 V. M. N. Passaro,2 and G. Gagliardi1 1
2
Consiglio Nazionale delle Ricerche, Istituto Nazionale di Ottica (INO), via Campi Flegrei, 34 Comprensorio A. Olivetti, 80078 Pozzuoli (Naples), Italy
Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Via Edoardo Orabona 4, 70125 Bari, Italy *Corresponding author:
[email protected] Received September 11, 2014; revised November 2, 2014; accepted November 9, 2014; posted November 10, 2014 (Doc. ID 222881); published December 10, 2014 We demonstrate a strain sensor with very high sensitivity in the static and low frequency regime based on a fiber ring cavity that includes a π phase-shifted fiber Bragg grating. The grating acts as a partial reflector that couples the two counter-propagating cavity modes, generating a splitting of the resonant frequencies. The presence of a sharp transition within the π phase-shifted fiber Bragg grating’s spectral transmittance makes this frequency splitting extremely sensitive to length, temperature, and the refractive index of the fiber in the region where the grating is written. The splitting variations caused by small mechanical deformations of the grating are tracked in real time by interrogating a cavity resonance with a locked-carrier scanning-sideband technique. The measurable strain range and bandwidth are characterized, and a resolution of 320 pϵ∕Hz1∕2 at 0 Hz is experimentally demonstrated, the highest achieved to date with a fiber Bragg grating sensor. © 2014 Optical Society of America OCIS codes: (060.3735) Fiber Bragg gratings; (060.2370) Fiber optics sensors. http://dx.doi.org/10.1364/OL.39.006899
Fiber Bragg gratings (FBGs) possess an undisputed potential in the field of thermal and mechanical sensing thanks to their intrinsic sensitivity, immunity to electromagnetic interference and suitability of optical fibers to in-field monitoring of solid materials and large environments [1]. In recent years, sensing schemes based on π phase-shifted fiber Bragg gratings (π-FBGs) and macroscopic Fabry–Perot fiber cavities interrogated with laser-based low noise detection setups have emerged, aiming at more sophisticated applications [2–10]. The interrogation of a FBG sensor basically relies on tracking the Bragg wavelength λB , whose position shifts upon an applied strain ϵ as jΔλB j ≅ 0.79 ϵ λB ;
(1)
where 0.79 is the typical value of the gauge factor due to the elasto-optic coefficient of single-mode fibers [1]. The most straightforward way to perform this measurement is to continuously acquire the entire transmission (reflection) profile of a FBG (either by scanning a laser across it, or by using a broadband source and a spectrometer) and fitting it to instantaneously retrieve λB . However, when fitting a peak function, the uncertainty in the determination of the line center scales with the linewidth. In this case, the minimum detectable strain is limited by the spectral width of the FBG transmission, which, even in π-FBG, is typically hundreds to thousands of megahertz. A more effective interrogation method consists in locking the laser wavelength to the π-FBG resonance using the Pound–Drever–Hall (PDH) technique [11]. As the laser tracks λB , its frequency variations can be monitored through the PDH feedback signal [2–7]. With this technique, resolutions in the order of the nϵ have been achieved. The main limitation of this technique is often represented by the laser frequency noise, which is directly converted to the amplitude noise of the detected signal. 0146-9592/14/246899-04$15.00/0
In systems where this frequency jitter does not play a dominating role (e.g., when frequency-stabilized lasers are used), a further improvement of the strain resolution can be obtained using long fiber-cavity sensors, whose resonances are much narrower than those of π-FBGs [8–10]. In fact, locking the laser to a narrow resonance improves the signal-to-noise ratio of the PDH error signal, resulting in a quieter sensor output. The downsides of long cavities are the increased mechanical noise pickup and the fact that the spatial accuracy of the strain information, which represents one of the key features of a sensor, is lost. In fact, a shift of the interrogated resonance can be the result of a perturbation occurring at any point along the intracavity path. In this Letter, we demonstrate a strain sensor based on a FBG ring resonator (FBGRR), i.e., a fiber loop with a FBG integrated in the intracavity path. As already shown in [12], the split resonances exhibited by this resonator make it a good candidate as a strain sensor. In fact, because of the long fiber loop, these resonances can be extremely narrow. Yet, their frequency splitting is only sensitive to perturbations occurring within the grating region. In this way, the overall mechanical noise pickup is not increased with respect to a standalone grating, and the spatial information of the detected strain is also retained. In order to track the splitting of one FBGRR resonance, a real-time interrogation technique where the two peaks of the split mode are simultaneously probed by a carrier-sideband doublet is used. Without any laser frequency stabilization, a resolution of 320 pϵ∕Hz1∕2 is experimentally demonstrated for static deformations, which to our knowledge is the highest reported so far with a FBG sensor. While a full theoretical description of the spectral properties of FBGRRs can be found in [12,13], the general behavior of these devices is recalled in the following. At wavelengths where the FBG reflectivity R ∼ 0, the loop behaves like a conventional ring resonator, with the © 2014 Optical Society of America
6900
OPTICS LETTERS / Vol. 39, No. 24 / December 15, 2014
optical power circulating only in the direction of excitation and an output spectrum formed by equally-spaced resonances. If R ≠ 0, part of the circulating power is backscattered by the FBG and excites a resonator mode traveling in the opposite direction. The two counterpropagating modes are coupled by their continuous exchange of energy via the FBG element, resulting in a frequency splitting, S, of the cavity resonances. For a resonance at wavelength λ, in the small coupling approximation, the splitting is given by [12,13]: λ2 Sλ ≈ πnL
s Rλ; λB ; 1 − Rλ; λB
(2)
where nL is the total optical length of the fiber loop. When a strain ϵ is applied to the FBG, λB shifts, according to Eq. (1). If the observed resonance at λ is on one slope of the FBG reflection curve, the shift of λB causes a variation of R and, hence, of S. From Eq. (2), it can be seen that a mechanical perturbation of the fiber loop affects the splitting through the term L, while a perturbation on the FBG changes the reflectivity terms. Because of this, S shows a different sensitivity to variations of the fiber loop length l or of the FBG length lB . Using Eqs. (1) and (2), we can write the following: r 2 ∂S R S λ ∂l πnL2 1 − R L ;
(3a)
∂S S ∂R 0.79λB S − : ∂l 2R1 − R ∂λ l L B B B
(3b)
∂R For lB ≪ l, and considering a reflectivity slope ∂λ ≈ B 2 nm−1 (typical for the edge regions of high-reflectivity FBGs), the terms S∕L in the above equations are negligible. The resonance splitting is therefore almost insensitive to the cavity mechanical noise, and the
intracavity FBG practically behaves as an isolated, point-like sensing head. As stated by Eq. (3b), the sensitivity of the splitting measurement is the largest when the Bragg reflectivity has the largest slope. For this reason, in our experimental setup, a π-FBG (AOS GmbH, λB 1560 nm) is spliced in the fiber loop resonator and interrogated on the steep edge of its central resonance, where the reflectivity rapidly drops from 0.95 to 0 in less than 1 GHz (the width of the central π-FBG resonance is 2-GHz full width at halfmaximum). This π-FBG ring resonator has an overall optical length of 12 m, with a free spectral range (FSR) of 17.2 MHz and a finesse of ∼80, which is mainly limited by the couplers and scattering losses of the grating. Figure 1(c) shows the cavity transmission signal recorded while scanning the laser frequency across several resonances. Because in the region of interrogation the FBG reflectivity decreases with frequency, the consecutive resonances show decreasing splitting values. A shift Δν of the laser frequency by one FSR yields a variation ΔS of the observed splitting. Naturally, the same ΔS (in absolute value) can be obtained if the Bragg frequency νB shifts by the same amount. The splitting ∂S sensitivity to the Bragg frequency j ∂ν j is thus equivalent B ∂S to j ∂ν j, which can be calculated from a linear fit of the ∂S j ≈ 0.01 can be then data in Fig. 1(c). The value found j ∂ν B converted to a strain sensitivity by using Eq. (1) in the frequency domain ΔνB 0.79ϵνB : ∂S ∂S kHz : 0.79νB 1.44 ∂ϵ ∂νB nϵ
(4)
The technique for real-time tracking of the resonance splitting is illustrated in Fig. 2. The π-FBGRR is interrogated with radiation from a narrow-linewidth fiber laser (Koheras Adjustik, 1560 nm) injected in port 1 of the resonator. The cavity back-reflection is collected by a photodiode at port 2. When a couple of modulation sidebands are applied to the laser by means of an electro-optical modulator (EOM), the demodulated
Fig. 1. (a) Scheme of the π-FBG ring resonator; (b) region of interrogation; (c) cavity output recorded during a wavelength scan. It shows the different splitting of consecutive resonances in the region of interrogation.
December 15, 2014 / Vol. 39, No. 24 / OPTICS LETTERS
Fig. 2.
6901
Experimental apparatus for the monitoring of S. Upper-right: sketch of the measurement principle.
output of this detector gives an error signal for a PDH stabilization loop. From this error signal, a feedback is generated that actively controls the length of the loop through a fiber stretcher, and that keeps one of the peaks of the interrogated split resonance locked to the laser frequency. The bandwidth of the PDH stabilization loop is a few hundred hertz. Then, a second modulation (labeled “chirp”) is added to the EOM to create a fast-scanning sideband (see the upper-right sketch in Fig. 2). As the sideband scans across the second peak of the split resonance, a Lorentzian profile shapes up in the cavity transmission, which is detected at port Fig. 3(b). The position of the peak within the recorded waveform is directly related to the amount of splitting, S. The sideband scans at rate ωscan , and the signal obtained by averaging over N scans is sent to a Lorentzian fitting routine that retrieves the splitting in hertz and converts it in strain units, using the calibration given by Eq. (4). The time resolution of the measurement is set by ωscan and N. The scan rate has to be faster than the PDH bandwidth (so that the feedback signal is not perturbed by the passage in resonance of the sideband), but slow enough to avoid ringing effects and distortions of the
transmission, which are typical of a resonance crossing that is too rapid. In our experiment, a 1-kHz scan rate and N 30 were used. The final signal thus consists of a stream of data points with a 30 ms time resolution, that correspond, in the hypothesis of Gaussian noise, to a signal-effective bandwidth of 33 Hz. In Fig. 3(a), the strain applied to the intracavity FBG is monitored for a few minutes. During the observation time, a few voltage steps are applied to a piezoelectric transducer (PZT) actuator that bends a cantilever, on which the FBG is glued. In the long run, the measurement is clearly affected by a slow drift, which can be suppressed by using either a better thermal insulation of the FBG in the setup, or compensated for by using a reference grating, as is common in static strain sensing applications [5,6,8]. However, on a time scale where the drift is negligible, the distribution of the measured strain values, which is displayed in Fig. 3(c), shows a typical root mean square (RMS) value of 1.8 nε. This corq responds to a strain resolution ϵmin RMS −12
N BW
≈
330 pϵ · Hz at 0 Hz. In absolute numbers, the minimum measurable splitting depends on the width of the cavity resonances,
Fig. 3. (a) FBG strain measurement over 2 min; (b) typical signal recorded while scanning the sideband across the right peak of the split resonance; (c) close-up of a 10 s continuous measurement.
6902
OPTICS LETTERS / Vol. 39, No. 24 / December 15, 2014
according to the Rayleigh criterion. The largest possible splitting was instead measured to be S ∼ FSR∕2, which is consistent with the notion that for R ∼ 1 the FBGRR becomes a Fabry–Perot resonator. In the latter situation, the left and right peaks of the split resonances correspond to the consecutive modes of the Fabry–Perot. A total dynamic range of ∼6 μϵ is evaluated for the presented sensor. This range can be of course extended by using a π-FBG with a broader central reflectivity dip, but at the cost of a lower sensitivity. The sensing method here demonstrated can be extended to any observable method that generates a variation of the grating optical length. From this perspective, we envisage an evanescent-field coupling configuration of the FBG for refractive index sensing or nanoparticle detection applications. From the performance point of view, the technique leaves significant room for improvement. The distribution of the measured values of Fig. 3(c) is in fact dominated by a fluctuation around 1 Hz, which we attribute to a laser frequency instability. Once this is suppressed (e.g., by locking the laser to a stable frequency reference), the RMS of this distribution is expected to approach the uncertainty level of the single-fit, which is around 20 pε. To push the resolution even further below this level, a more sophisticated interrogation method has to be implemented, for example, by independently locking a laser carrier and a sideband on the two peaks of a split resonance, or by designing an active FBG-resonator that gives laser emission on a split resonance [14]. With these schemes, which are currently under investigation, the fitting routine can be circumvented in favor of a
direct readout of S based on a beat-note frequency measurement. This work was funded by the Italian Ministry of Education and Research (MIUR) under the framework of the PON01_01209 “BACKOP” project. References 1. Y. J. Rao, Meas. Sci. Technol. 8, 355 (1997). 2. D. Gatti, G. Galzerano, D. Jannner, S. Longhi, and P. Laporta, Opt. Express 16, 1945 (2008). 3. T. T.-Y. Lam, M. Salza, G. Gagliardi, J. H. Chow, and P. De Natale, Meas. Sci. Technol. 21, 094010 (2010). 4. S. Avino, V. D’Avino, A. Giorgini, R. Pacelli, R. Liuzzi, L. Cella, P. De Natale, and G. Gagliardi, Appl. Phys. Lett. 103, 184102 (2013). 5. W. Huang, W. Zhang, T. Zhen, F. Zhang, and F. Li, J. Lightwave Technol. 32, 3692 (2014). 6. Z. He, Q. Liu, and T. Tokunaga, Photon. Sens. 3, 295 (2013). 7. A. Arie, B. Lissak, and M. Tur, J. Lightwave Technol. 17, 1849 (1999). 8. Q. Liu, T. Tokunaga, and Z. He, Opt. Lett. 36, 4044 (2011). 9. J. H. Chow, D. E. McClelland, M. B. Gray, and I. C. M. Littler, Opt. Lett. 30, 1923 (2005). 10. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, Science 330, 1081 (2010). 11. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31 97 (1983). 12. C. E. Campanella, A. Giorgini, S. Avino, P. Malara, R. Zullo, G. Gagliardi, and P. De Natale, Opt. Express 21, 29435 (2013). 13. C. Campanella, L. Mastronardi, F. De Leonardis, P. Malara, G. Gagliardi, and V. Passaro, Opt. Express 22, 25371 (2014). 14. L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, Nat. Nanotechnol. 6, 428 (2011).
