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Abstract
We presented a crosstalk interference synthesis and polarization switching (CIS-PS) hybrid interrogating method designed for inline interferometric fiber Bragg grating (FBG) sensor arrays, targeting the multi-reflection (MR)-induced time division multiplexing (TDM) crosstalk and polarization-induced signal fading simultaneously. The inline interferometric FBG sensor array, which has found wide applications in underwater sensing, generally consists of a series of FBGs written on a commercial single mode fiber (SMF), where the coupling of TDM crosstalk and polarization-induced signal fading often makes signal extraction difficult. In this paper, this coupling was modeled, and the principle of the CIS-PS hybrid method was demonstrated. Experiments showed that even though the FBG reflectivities were all larger than 5%, the measured MR-induced TDM crosstalk reached −50 dB, which was the lowest to the best of our knowledge. The background phase noises were lowered and polarization-independent due to efficient control of polarization-induced signal fading. The demodulation stability of the sensing signal was enhanced from ±2.25 dB to ±0.15 dB.
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1. Introduction
The inline interferometric sensor array based on fiber Bragg gratings (FBGs) has found important applications in acoustic detection, seismic sensing, and so on [1–3], providing high sensitivity, simple and compact structure, and potential low cost [1]. In such inline interferometric sensor arrays, a series of FBGs are typically written on a single mode fiber (SMF). Therefore, optical structures of time division multiplexing (TDM) and wavelength division multiplexing (WDM) can be formed without any fusion points or other optical fiber devices, which can be highly reliable and especially attractive for underwater sensing applications.
The simple sensing structure which contains only FBGs and fibers, however, poses technical challenges to achieving excellent sensing performance. The multi-reflection (MR)-induced TDM crosstalk and polarization-induced signal fading are two serious problems limiting further applications [4]. References [5] and [6] pointed out that the TDM crosstalk could be ignored when the FBG reflectivity was less than 1% while the system signal-noise-ratio (SNR) would be deteriorated due to the ultra-weak reflected laser intensity. Reference [7] proposed the layer peeling method, achieving a crosstalk of −40 dB in a 5-TDM sensor array with an FBG reflectivity of 5%. Reference [8] reported an interference synthesis method to reduce the crosstalk for a 2-TDM inline all-polarization-maintaining FBG sensor array and the measured crosstalk was −40 dB when the FBG reflectivity was 5%. The other problem limiting the application of inline interferometric fiber sensor arrays is the polarization-induced signal fading, which is related to fiber birefringence. The all-polarization-maintaining fiber structure can provide useful solutions, though it costs highly and is only suitable for small-scale arrays. Because the reflectors in the array are intrinsic mirrors, the Faraday rotator mirrors (FRMs) are not suitable for inline interferometric sensor arrays. Though the polarization diversity receiver [9] and the polarization scanning method [10] are suitable for the inline structure and can eliminate the polarization-induced signal fading, they cannot eliminate the polarization-induced input phase noise. References [4] and [10] demonstrated a polarization switching method, which is one of the most successful solutions up to now. The solutions addressing the problems of MR-induced TDM crosstalk and polarization-induced signal fading are mostly based on signal processing. Typically, one of them was solved while the other was ignored [4,5,8]. Combining the signal processing methods to solve the two problems simultaneously remains a challenge.
In the present study we presented an interferometric FBG sensor array written on a commercial SMF fiber, in which the FBG reflectivities were all larger than 5%. The designed optical structure realized low cost and large returned light intensity. However, the MR-induced TDM crosstalk and polarization-induced signal fading problems existed at the same time, making it difficult to demodulate the phase noise. Aiming at this issue, a crosstalk interference synthesis and polarization switching (CIS-PS) hybrid interrogating method was theoretically and experimentally demonstrated. The measured crosstalk reached −50 dB even though the FBG reflectivities were all larger than 5%. The background phase noises were lowered and polarization independent due to efficient control of polarization-induced signal fading, and the demodulation stability was increased from ±2.25 dB to ±0.15 dB.
This paper is arranged as follows. Section 2 demonstrates the principles of the CIS-PS hybrid interrogating method. Section 3 includes the experimental application of the proposed method in a 2-TDM inline interferometric FBG sensor array, where the background phase noise, crosstalk, and demodulation stability were all measured and discussed in detail. Section 4 is a brief summary of this work.
2. Principles of the CIS-PS interrogating method
2.1 Coupling of polarization-induced signal fading and TDM crosstalk
A typical structure of an interferometric TDM FBG sensor array is shown in Fig. 1. Three inline FBGs are written on a SMF with a uniform reflection spectrum. Two sensor units, named S1 and S2, can thus be formed, each containing two adjacent FBGs and a fiber section between the two FBGs.
If interrogated using a pair of laser pulses, the interference occurs when the second pulse reflected by the $n\textrm{th}$ FBG overlaps with the first pulse reflected by the $({n + 1} )\textrm{th}$ FBG$({n = 0,\textrm{ }1} )$, as shown in Fig. 1. Therefore, S1 and S2 are time division multiplexed.
For each sensor, the two laser beams to be interfered can be written as
In Eq. (1), ${E_{inn}} = {[{{E_{xn}}\; {E_{yn}}} ]^T}({n = 0,1} )$ is the Jones matrix of the two injected pulses;${t_n}({n = 0,1} )$ is the amplitude transmission of the first or second FBG; ${\rho _0}$, ${\rho _\textrm{1}}$, and ${\rho _\textrm{2}}$ are FBG amplitude reflectivities; $r = \left( {\begin{array}{cc} { - 1}&0\\ 0&1 \end{array}} \right)$ is the FBG reflection matrix; ${B_j}({j = 1,\textrm{ }2} )$ is the transmission matrix of the two sensing elements, and the superscripts $\overleftarrow {}$ and $\overrightarrow {}$ indicate the backward and forward transmissions. Given that the fiber transmission loss can be ignored, ${B_j}({j = 1,\textrm{ }2} )$ can be written as ${B_j} = exp({ - i{\varphi_j}} ){U_j}$, where $\; {\varphi _j}$ refers to the phase delay and ${U_j}$ is an unitary matrix relating to the fiber birefringence transmission matrix. For an SMF, the following equation describes the properties of $\; {B_j}$ [4].
The superscript $^\ast $ and $^T$ refer to the matrix transposition and conjugate convertor, respectively, and $^\dagger$ refers to the matrix transform and conjugate convertor. Equation (1) can then be expressed as
The two interferences, corresponding to the 1τ and 2τ timeslots, can be written as
As shown in Eq. (5), ${\widetilde I_{1\tau }}$ is a primary interference generated by two primary pulses, indicating the phase information of S1. ${\widetilde I_{\textrm{2}\tau }}$ contains two parts. One is a primary interference indicating the phase information of S2. The other is the interference of one primary pulse with a crosstalk pulse, indicating the phase information of S1, which causes crosstalk from S1 to S2 and thus can be named as the crosstalk interference. Because ${U_j}({j = 1,2} )$ is determined by fiber birefringence, both sensors are polarization sensitive, which is just the phenomenon of fiber-birefringence-induced polarization signal fading. ${\widetilde I_{\textrm{2}\tau }}$ is a coupling result of polarization-induced signal fading and TDM crosstalk.
2.2 Principles of the CIS-PS method
To demodulate ${\varphi _\textrm{2}}$ from ${\tilde{I}_{2\tau }}$ by eliminating polarization-induced signal fading and TDM crosstalk simultaneously, the proposed CIS-PS hybrid processing method has two unchangeable steps.
The first step is interference synthesis (CIS), aiming to eliminate the crosstalk. Equation (5) indicates that the crosstalk interference of S2 is expressed similarly to the primary interference of S1 except for the coefficient relating to the known parameters, ${\rho _0}$ and ${\rho _1}$. The following operation can be conducted.
Equation (6) yields two new interferences indicating the phase information of S1 and S2, respectively, and the crosstalk interference of S2 can be eliminated.
The second step of the CIS-PS hybrid processing method is to eliminate the polarization-induced signal fading. The sensor impulse matrices are defined as
As mentioned above, ${U_j}\textrm{ }({j = 1,\textrm{ }2} )$ is a unitary matrix related to fiber birefringence. The multiplexing results of ${U_1}^\prime$ and ${U_2}^\prime$ are unitary matrices. Therefore, the determinants of ${\Re _\textrm{j}}({j = 1,\textrm{ }2} )$ is only determined by $\; {\varphi _j}\textrm{ }({j = 1,\textrm{ }2} )$ given that the reflectivities of the former two FBGs are constants. This provides a possible way to obtain the sensor phase and eliminate the polarization fading.
The phase can be derived using the following Eq. (8), where $\; {\varphi _j}({j = 1,\textrm{ }2} )$ is the angle of $\sqrt {\det {\Re _j}}$, and all the polarization-related factors can be eliminated.
2.3 Realization of the CIS-PS method combing PGC demodulation
The principles of the CIS-PS hybrid processing method discussed in Section 2.2 are based on matrices and complex expressions of interferences, which cannot be obtained directly in practice. To apply the CIS-PS method, four pairs of laser pulses with different polarizations can be injected into the array in sequence, as shown in Fig. 2.
Here the phase generated carrier (PGC) method, which has been demonstrated widely [11,12], is used. An artificial modulation ${\varphi _0} = C\cos (2\pi {f_0}t)$ can be found in the second pulse, in which ${f_0}$ and C are the PGC modulation frequency and amplitude, respectively. For each sensor, four interferences indicating four polarization channels, ${\widetilde I_{_{XXj}}}$, ${\widetilde I_{_{XYj}}}$, ${\widetilde I_{_{YYj}}}$, and ${\widetilde I_{_{YXj}}}$ $(j = 1,2)$, can be obtained, which can be expressed as
In Eqs. (9) and (10), the four elements of unitary matrix ${U_j}^\prime$ are denoted as ${U_{11j}}^\prime$, ${U_{12j}}^\prime$, ${U_{21j}}^\prime$, and ${U_{22j}}^\prime$, respectively; the amplitudes of laser pairs are normalized to be 1; ${t_j}^\prime$ refers to the coefficient determined by ${\rho _0}$ and ${\rho _\textrm{1}}$; $\varphi _1^{\prime} = 2{\varphi _1} + {\varphi _0}$, and $\varphi _2^{\prime} = 2{\varphi _2} + {\varphi _0}$.
First, the CIS method can be applied to all four polarization channels, and the following eight interferences can be obtained.
For each sensing unit, the sampled interferences of the four polarization channels are multiplied with $\cos (2\pi {f_0}t)$ and $\cos (4\pi {f_0}t)$, respectively, and then a low-pass filtering can be used to eliminate the carrier harmonics at ${f_0}$ and above, which is the same as in the PGC processing method. The following two items can be obtained.
Here, $U{_{mn}^\mathrm{{^{\prime}}_j}} = U{r_{mnj}}\textrm{exp} ( - iU{a_{mnj}})$. So, the complex synthesis can be completed as
Equation (14) yields the complex impulse expressions of the four polarization channels. The sensor phase can be derived using Eq. (15) and all the polarization-related factors can be eliminated.
3. Experiments and discussions
3.1 Experimental setup
The schematic diagram of the experimental system is shown in Fig. 3. Three FBGs were written inline on a commercial SMF from YOFC with Bragg wavelengths of 1539.85, 1539.88, and 1538.85 nm, respectively. The measured intensity reflectivities were 5.2%, 5.3%, and 5.6%, respectively. The fiber length between any two adjacent FBGs was 38.55 m, and for each sensor element, parts of the sensing fiber were wounded on PZT rings to introduce the simulated signals to be sensed.
To interrogate the array effectively with low noise, a narrow line-width laser from RIO was used, and the relative intensity noise was −120 dB/√Hz @ 1 kHz. The laser wavelength was 1539.85 nm, in accordance with the FBG Bragg wavelengths. The light was modulated into pulses utilizing an acoustic-optical modulator (AOM) from GOOCH&HOUSEG. An M-Z fiber interferometer was used as the compensation interferometer (CIF) providing two light pulses with a time delay decided by the interferometer path imbalance, which had a length of 79.1 m in our experiments. Part of the short arm of the CIF was wounded on a PZT to introduce the modulation signal for PGC demodulation, which had a frequency of 10 kHz. The pulse pairs were then injected to a polarization switching (PS) module from Photline where the polarization of each pulse was modulated individually, and the polarizations of the PS module output were set to be in the order of YX, XX, XY, and YY, as shown in Fig. 2.
For each sensor, five results were obtained. The four polarization channels were sampled respectively, and the results in frequency domain were shown in Fig. 4, which could be demodulated utilizing the PGC method to obtain the phase information directly. The original background phase noise, crosstalk, and demodulated signal stability could be analyzed. Then the four polarization channels were processed using the CIS-PS method, which generated a new demodulation result, indicating the final phase noise, crosstalk, and demodulated signal stability.
3.2 Background phase noise analysis
The background phase noises of S1 and S2 were measured, which were the demodulated phases without any signal acting on the sensor. For S1, five experimental results were obtained, as shown in Fig. 5. Four of which were the polarization channels, colored in black, brown, blue, and green, respectively. The last one colored in red was the PS processed result. The result implied that the background noise using the PS method was lower than those of the four polarization channels, which was about −94dB@1kHz
Figure 6 shows the measured background phase noises of S2, where (a) was a comparison between the directly demodulated results of four polarization channels and the CIS-PS processed results, (b) was a comparison between the four CIS processed polarization channels and the CIS-PS processed results. Due to the coupling of polarization-induced signal fading and TDM crosstalk, the original polarization channels of S2 exhibited relatively higher noise level. After the CIS processing procedure, where the crosstalk noise from S1 was eliminated, the background phase noise of four polarization channels were obviously lowered. The CIS-PS finally provided a lowest and stable phase noise level, as shown in Fig. 6(b), which was −92dB@1kHz
Fig. 6. Phase noise of S2. (a) Original polarization channels and CIS-PS processed results ; (b) CIS Processed polarization channels and CIS-PS processed results (Color online)
3.3. Crosstalk analysis
As mentioned above, for each sensor element, parts of the sensing fiber were wounded on PZT rings to introduce the simulated signals to be sensed. Then, 125 Hz and 630 Hz signals were applied to S1 and S2, respectively, obtaining the demodulated results as shown in Fig. 7.
Figure 7(a) displays the demodulated 125 Hz signal for S1. The amplitudes of four polarization channels and the PS processed result were −19.5 dB, −19.62 dB, −19.67 dB, −19.53 dB, and−19.58 dB ($0dB = 1rad/\sqrt {Hz}$), respectively, indicating that the CIS-PS hybrid method could exactly demodulate the interference with PGC modulation.
Figure 7(b) shows both the crosstalk signal of 125 Hz and the real signal of 630 Hz demodulated from S2. The amplitudes at 125 Hz were −51.1 dB, −57.6 dB, −44.8 dB, −47.6 dB, and −72 dB for the four polarization channels and the CIS-PS processed result, indicating that the crosstalk was −31.6 dB, −38 dB, −25.2 dB, −41.4 dB, and −52.42 dB, respectively. Evidently, the CIS-PS method provided crosstalk suppression larger than 11 dB. The amplitudes at 630 Hz were −34.3 dB, −37.7 dB,−37.2 dB,−37.1 dB and −37.6 dB respectively.
As mentioned in Eq. (4), the interference of S2 is the combination of the primary and crosstalk interferences. When processed directly with the PGC method, the demodulation result is unstable, which has been demonstrated in detail by our earlier research in Ref. [5]. Therefore, the crosstalk always fluctuates and cannot be measured exactly. In response to this, we measured the crosstalk for 150 times, and the results are shown in Fig. 8. The crosstalk of the four polarization channels and the CIS-PS processed result were colored in red, blue, yellow, green, and black, respectively. The largest number in the CIS-PS result was smaller than −50 dB, indicating that the crosstalk was well suppressed.
Fig. 8. Measured crosstalk for 150 times. (a) Demodulated results. (b) Accumulated probability (Color online)
3.4 Demodulation stability analysis
Figure 7 shows that the amplitudes of S2 at 630 Hz were −34.3 dB, −37.7 dB, −37.2 dB, −37.1 dB and −37.6 dB respectively. Due to the primary and crosstalk interferes aliasing and polarization-induced fading, as mentioned in Eq. (4), the demodulated signal amplitudes of S2 were unstable. Therefore, the demodulated signal amplitude stability was also measured. The interferences of S2 applied 630 Hz signal S2 and the interferences were sampled 150 times and demodulated, as shown in Fig. 9. All four polarization channels exhibited considerable demodulation instability and the largest fluctuation was ±2.25 dB for the YY polarization channel. The CIS-PS processed signal amplitude, however, showed a fluctuation of only ±0.15 dB. The measured results indicated that the CIS-PS hybrid method could also enhance the demodulation stability notably.
4. Conclusions
In conclusion, we demonstrated an ultra-low crosstalk and polarization-independent inline interferometric FBG sensor array. The key to achieving excellent sensing properties was the proposed CIS-PS hybrid interrogating method. Both theoretical analysis and experimental results demonstrated that CIS-PS method could significantly suppress the crosstalk, lower the background phase noise, and improve the demodulation stability. The measured crosstalk reached −50 dB even though the FBG reflectivities were all larger than 5%. The background phase noises were lowered and polarization independent due to efficient control of polarization-induced signal fading. The sensing signal demodulation stability was increased from ±2.25 dB to ±0.15 dB.
The inline interferometric FBG sensor array has found wide applications in underwater ultra-weak signal sensing, where low noise is required. The presented CIS-PS hybrid method has critical significance for facilitating the array sensing capability, especially for obtaining low and stable background noise levels, thus making it attractive for acoustic and seismic sensing applications.
Funding
National Natural Science Foundation of China (61901488).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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