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Abstract
A microwave photonics interrogation system for multiplexing fiber Fabry–Perot (FP) sensors is demonstrated in this paper. Different from previous FP demodulation schemes, this system aims at quasi-distributed sensing networks composed of FP sensors with a short effective cavity length less than 1 mm. With the help of a dispersion element, the superimposed reflected spectrum from FP sensors based on a hollow core fiber (HCF) can be converted into separate response passbands in the frequency domain simultaneously, whose center frequency will shift linearly with the variations of environment. The experimental results exhibit high linearity and interrogation ability for both the all-FP multiplexing system and hybrid multiplexing system. A strain interrogation sensitivity of 0.938 kHz/µɛ and temperature sensitivity of −0.699 MHz/°C have been realized, corresponding to a FP cavity length demodulation sensitivity of 1.563 MHz/µm. Furthermore, numerical studies about the impacts of the HCF-FP spectrum envelope on the RF response passband, as well as the theoretical minimum detectable cavity length and multiplexing capacity of the system, are also carried out.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber Fabry–Perot (FP) sensors have been widely used in the measurement of strain [1,2], temperature [3,4], vibration [5], pressure [6], liquid level [7,8], acoustic [5,9], humidity [10] and so on. The environment parameters will change the details of optical spectrum by affecting the effective cavity length of FP sensors. In order to obtain the information of the target physical quantity, many interrogation schemes for FPs are proposed, for example, common-path dual-wavelength quadrature phase demodulation [11], high-order harmonic-frequency cross-correlation [12], instantaneous frequency definition [13] and so on. But there exists some problems in these proposals. On the one hand, the methods of wavelength scanning are not conducive to enhancing the demodulation rate of the system [14–16]. On the other hand, there usually requires more than one FP sensing element in the actual on-line environment monitoring system, that is, a quasi-distributed FP sensing network. The reflected spectra with different free spectral ranges (FSRs) are superimposed together, which would be difficult to be distinguished directly by conventional wavelength demodulation, or intensity-based schemes such as dual-wavelength intensity modulation [17] for a single FP. Machine learning or image recognition algorithm may be able to solve this problem, but it needs a lot of advance learning, and puts forward high requirements for the spectrum quality of input samples. Other demodulation method, like self-calibrating wavelength shifting interferometry [18], needs as many detection channels as the number of sensor channels, which will undoubtedly increase the complexity and maintenance difficulty of the system. Therefore, it is necessary to study a more convenient scheme for the simultaneous demodulation of multiplexing FP arrays.
In recent years, with the rapid development of microwave photonics technology, more interrogation systems with high interrogation speed for multiplexing FP sensors are proposed. By optical carrier based microwave interferometry (OCMI) [19] and coherent microwave-photonics interferometry (CMPI) [20], the demodulation of spatially-continuous cascaded FP sensing system can be realized easily. However, since these methods can be seen as the derivations of incoherent optical frequency-domain reflectometry (I-OFDR), they are only suitable for the FPs with the long cavity length over a few centimeters [21,22], while fail to satisfy the conditions when the FP sensor is more compact with cavity length less than one millimeter. On the other hand, various single-passband microwave photonic filters (MPFs) have been widely applied in signal process and fiber sensing as one of the most important branches in microwave photonics, for their advantages of high bandwidth, low loss, fast response speed, high resolution and flexible reconfigurability [23–27]. Inspired by the single-passband MPF based on broadband light source slicing through fiber interferometer [28], which could convert continuous broadband interference spectrum into single RF response, we find the possibility of demodulating short-cavity FP sensors simultaneously for the tunability and wideband ability of MPF.
In this paper, we demonstrate a microwave photonics interrogation system for multiplexing optical fiber FP sensors. Aiming at the extrinsic FP interferometer sensors based on the SMF-HCF-SMF sandwich structure, which is one of the most popular FP schemes for its simplicity, compactness and flexibility, we establish an FP sensing network utilizing spatial-frequency-division-multiplexing and verify this demodulation scheme by both mathematical analysis and experiment results. Through a microwave photonics filter with dispersion element as the core, different reflected optical spectra from different FPs are converted into separate radio-frequency (RF) response passbands, whose center frequency is closely related with the effective cavity length of FP, that is, the total length of HCF fused between two SMFs. Besides the all-FP multiplexing array, this system shows good interrogation ability for hybrid multiplexing array as well. In the sensing experiment, this system is able to realize a strain interrogation sensitivity of 0.938 kHz/µɛ and a temperature sensitivity of −0.699 MHz/°C, whose sensing sensitivity can be further improved by system parameter or sensing structure design. What’s more, numerical studies about the impacts of HCF-FPs’ spectrum envelope on the frequency, 3-dB bandwidth and intensity of RF response passbands are carried out, which are discussed in the microwave photonics interrogation system for the first time to the best of our known. Apart from that, the theoretical minimum detectable cavity length and multiplexing capacity are also analyzed.
2. Principle
The schematic of microwave photonic interrogation for multiplexing fiber FP arrays is as Fig. 1 shown. The output broadband light from an amplified spontaneous emission (ASE) source is sent to four parallel fiber FPs first, which are connected by 50:50 1×2 optical couplers. Travelling through an optical circulator (OC), the reflected spectrum enters the 3 GHz electro-optic modulator (EOM, AVANEX) after amplified by the erbium-doped optical fiber amplifier (EDFA, Amonics AEDFA-C-DWDM-23-B-FA), and then is modulated by the radio frequency (RF) signal emitted from the vector network analyzer (VNA, Rohde & Schwarz ZVL6). Since the measurement speed of the VNA with normalization calibration is less than 50 ms, the high-speed interrogation for the system can be guaranteed. The modulated light passes through a dispersion module (DM), which is a 25-km SMF in this experiment, and is finally captured by a 10 GHz photodetector (PD). By sending the electrical signal from the PD back to the VNA, the frequency response of the whole system can be obtained. In order to guarantee the reliability of the interrogation results, the dispersion module should be kept in a stable experiment environment or be packaged well, in case the dispersion property of the whole system changes with the external interferences.
Fig. 1. Schematic of microwave photonic interrogation system for multiplexing fiber FP arrays. The inset gives the illustration of FP sensors based on SMF-HCF-SMF structure. ASE: amplified spontaneous emission; EDFA: erbium-doped optical fiber amplifier; EOM: electronic optic modulator; OC: optical circulator; DM: dispersion module; SMF: single mode fiber; HCF: hollow core fiber; VNA: vector network analyzer; PD: photodetector
The structure of these fiber FPs is illustrated in the inset. They are made by the fusion of SMF and HCF. Assume that the length of the HCF is L, the reflection coefficients of two interfaces of FP are r1 and r2, the refractive index of the air is n0 and the speed of light is c. If the optical frequency is ω, then the phase shift φ satisfies $\varphi = {{nL\omega } / c}$. The output of the parallel FP sensors can be depicted as [29]:
Based on Eqs. (1) and (2), we can simulate the optical spectra of various HCF-FPs with different HCF length, that is, different FSRs. Here we select four FPs with FSR of 5.26 nm, 4.02 nm, 2.41 nm, and 1.34 nm around the wavelength of 1550 nm, which are as Figs. 2(a)–2(d) shown.
Fig. 2. Simulated spectra of four HCF-FPs with different FSR: (a) 5.26 nm, (b) 4.02 nm, (c) 2.41 nm, (d) 1.34 nm, and (e) their RF response when 25- km SMF is used as the dispersion module.
When the optical signal from parallel FP array is modulated by the EOM and sent into the system given in Fig. 1, the overall frequency response is [28]:
Considering Eqs. (3) and (4), the RF response of this system can be calculated. As the red dashed areas in Fig. 2(e) shown, there exists four separate peaks with different center frequency of 341.57 MHz, 624.62 MHz, 1067.71 MHz, and 1871.37 MHz, which are corresponding to four HCF-FPs. Therefore, by tracking the frequency shift of these RF peaks, we can demodulate the FSRs of FP sensors, further, the cavity length of FP interferometers and variations of the parameters applied to the sensors. The response frequency of FPs satisfies Eq. (5), showing a good linearity with 1/FSR, where DDM is the dispersion coefficient (ps/nm) of the dispersion element [30].
In addition, it can be also found in Fig. 2(e) that the line-shapes of RF responses will experience distortion due to the quadratic phase response induced by non-zero third order dispersion in optical fibers [31], especially for the FP structures with smaller FSRs. This phenomenon will set draw backs to measurement resolution and limit distinguishable cavity length of the interrogation system, which could be resolved by third order dispersion compensation [32,33], but the linearity of response frequency is not affected by the presence of high-order dispersion [34].
3. Experiment results
The experiment of this microwave photonics interrogation system for multiplexing fiber FP sensors mainly includes two parts. We first demonstrate the demodulation ability for all-FP multiplexing system, whose sensing region only contains parallel HCF-FPs. Then we test the demodulation ability for hybrid multiplexing system, which consists of two different kinds of fiber sensors simultaneously, short-cavity FP and polarization maintaining fiber interferometer (PMFI), to verify the potential of this scheme in a wider range of sensing systems.
3.1 Interrogation for an all-FP multiplexing system
In order to realize an all-FP sensing multiplexing system depicted in Fig. 1, we splice four fiber FP structures with different HCF length. Their FSRs are designed to be 5.52 nm, 3.76 nm, 2.00 nm and 1.28 nm around 1550 nm, equal to the cavity length of 217 µm, 319 µm, 600 µm, 938 µm respectively, so that their response peaks can be accurately distinguished in the RF spectrum. The measured optical spectra of them obtained from the spectrometer (YOKOGAWA, AQ6370C) are as Figs. 3(a)–3(d) shown. It can be found in Figs. 3(c) and 3(d) that there exists obvious envelope with the increase of HCF length, which is caused by the inevitable anti-resonant effect in SMF-HCF-SMF structures [35]. In the following part, we are able to see that this effect will influence RF response peaks.
Fig. 3. Measured spectra of four HCF-FPs with different FSR: (a) 5.52 nm, (b) 3.76 nm, (c) 2.00 nm and (d) 1.28 nm. (e) Measured RF response of the FP arrays. The red dashed boxes denote the RF peaks corresponding to four different FPs. (f) Measured RF response after FP2 is removed from the multiplexing array. The corresponding RF peak disappears while other peaks remain unchanged.
In order to obtain sufficient dispersion, we choose a 25-km SMF to carry out the experiment. The frequency response of the all-FP interrogation system is as Fig. 3(e) shows. There are four separate RF peaks at the frequency of 380.10 MHz, 643.91 MHz, 1125.90 MHz and 1890.47 MHz, which correspond to cavity length of 228 µm, 328 µm, 575 µm and 964 µm respectively. Compared with the results obtained from the spectrometer, the demodulation errors of effective cavity lengths are less than 5.06%. The errors may come from the equations used to calculate FSR and effective cavity length of FPs, which have some approximate treatments. For example, Eq. (5) does not take the impacts of high-order dispersion effect on response frequency into the consideration. When we remove the second FP sensor FP2 from the sensing region, as Fig. 3(f) depicted, the corresponding RF peak disappears without any impacts on the center frequency of other response passbands. It shows that the interrogation for the sensors in the parallel multiplexing FP system is independent of each other. The damage or performance decrease of one sensing element wouldn’t have negative impact on the demodulation of other sensors. On the other hand, by observing the change of the RF response, it is convenient to identify which sensor is abnormal, which would be helpful for the maintaining of sensing system.
Consistent with the simulation results in Fig. 2(e), we can find in the experiment results that all the RF response passbands will experience distortion and broadening because of the quadratic phase response caused by high-order dispersion in SMF, especially for the FPs with longer HCF cavity and shorter FSR. Although it will affect the multiplexing capacity of the sensing system and measurement resolution, the linearity of interrogation will not be influenced. With the help of third order dispersion compensation scheme, the broadening effect could be suppressed and the resolution could be improved, but the complexity of the experiment system will be increased significantly. Moreover, this phenomenon also indicates that for HCF-FPs with longer cavity length over 1 mm, the interrogation effects may be reduced for the negative influences caused by increase of structure loss, decrease of optical spectrum contrast ratio and passband broadening from high-order dispersion, and it would be more difficult to distinguish the RF response passbands from the background signal. On the other hand, another thing shouldn’t be ignored is that there exists baseband response with high intensity at low frequency region. When it comes to the HCF-FPs with shorter cavity length, their RF responses would be partially overlapped or even completely covered by the baseband response caused by double-sideband modulation, which limits the shortest measurable cavity length of HCF-FP.
Then we demonstrate strain sensing experiment, and the demodulation results are as below. Figure 4(a) shows the shift of the whole RF response when only FP2 is placed and fixed on the micro-displacement platform. From the local enlarged figures in Figs. 4(b) and 4(c), it is clear that only FP2 experiences red-shift while the frequency of FP1 stay unchanged during the process of strain increasing. Figures 5(a)–5(d) compare the RF response frequency of these FPs when the strain applied to FP2 ranges from 0 µɛ to 1400 µɛ with a step of 100 µɛ, indicating that the interrogation for each FP has good independence to other sensors, that is, low cross-sensitivity. This feature guarantees its application in multiplexing network. The demodulation sensing results of FP2 enjoy good linearity and its sensitivity is 0.563 kHz/µɛ at the frequency around 649 MHz. It means that this demodulation system can obtain a strain resolution at least 100 µɛ.
Fig. 4. (a) The whole RF responses when different strain applied to FP2, and local enlarged figures of (b) FP1 and (c) FP2 after de-noise and fitting process.
Fig. 5. (a)-(d) RF frequency of FP1-FP4 when different strain applied to FP2. (e)-(h) RF frequency of FP1-FP4 when different strain applied to FP3.
It should be pointed out that the sensitivity depends on both the systematic dispersion and the performance of the sensors itself. In this experiment, since HCF-FPs has no special advantages in strain sensing, the sensing sensitivity we could obtain is quite limited. It can be much enhanced when RF response passbands are located at higher frequency, or other sensitivity-improved FP structures are used as strain sensors. Take the condition when RF passband locates at higher frequency as an example. When similar experiment carried out on FP3, as Figs. 5(e)–5(h) show, the strain sensitivity will be improved to be 0.938 kHz/µɛ at the frequency around 1127 MHz, without any additional sensitization performing on the sensor. Combining with the cavity length of FP3, the demodulation sensitivity for the cavity length of HCF-FP sensor is 1.563 MHz/µm.
3.2 Interrogation for a hybrid multiplexing system
Since traditional HCF-FPs are insensitive to environment temperature variations, for a certain sensing application, it may be necessary to use a combination of HCF-FPs and other types of temperature-sensitive optical fiber sensors to monitor the environment more comprehensively, that is, utilizing a hybrid multiplexing sensing system. Therefore, after the experiment for all-FP sensing system, we also demonstrate the demodulation of hybrid multiplexing system to verify its interrogation application in a wider range of fields.
The system schematic is shown as Fig. 6. Here we choose PMFI as another fiber sensor in parallel with FP2, because it can realize a smaller FSR <1 nm easily, which is difficult for HCF-FPs due to anti-resonant effect and high transmission loss, and more sensitive to environment temperature variation as well. The interferometer is composed of two polarizers, one polarization controller (PC) and a SMF-PMF-SMF structure. Here we use a dispersion compensation module (DCM) with dispersion coefficient about −1700 ps/nm at 1550nm to provide more dispersion. The optical spectrum of PMFI is depicted in Fig. 7(a). The length of PMF is 8.23 m and its FSR is 0.70 nm, while the cavity length of FP5 is 220 µm and its FSR is 5.47 nm, corresponding to the RF response peak at 804.45 MHz and 107.88 MHz respectively in Fig. 7(e).
Fig. 6. Schematic of microwave photonic interrogation system for hybrid multiplexing system composed of FP and PMFI. The inset gives the illustration of PMFI sensor based on SMF-PMF-SMF structure. PC: polarization controller; DCM: dispersion compensation module; PMF: polarization maintaining fiber.
Fig. 7. Measured optical spectrum of (a) PMFI with FSR of 0.70 nm and (b) FP5 with FSR of 5.48 nm. The frequency shifts of (c) FP5 and (d) PMFI when temperature changes applied to the PMFI, and (e) the RF response variations of the whole system with the dispersion coefficient of −1700 ps/nm.
In the temperature sensing experiment, we heat the SMF-PMF-SMF structure and record the frequency spectrum variations from 55 °C to 85 °C with a step of 5 °C. It can be seen in Figs. 7(c) and 7(d) that the RF response peak of PMFI experiences obvious shift and the frequency changes show good linearity. The temperature sensing sensitivity of PMFI is −0.699 MHz/°C. In the meanwhile, the RF peak frequency of HCF-FP remains stable, promising the interrogation ability for hybrid multiplexing sensor arrays without any restriction on reflection-type or transmission-type sensors.
From the above experiment results, it is clear that this interrogation scheme exhibits good demodulation ability for multiplexing FP sensor system. Compared with the detection scheme based on the spectrometer, this system can intuitively distinguish the overlapping optical spectra of cascaded FPs without subsequent algorithm processing by only one sweep measurement, which would be hard to be distinguished by the spectrometer scheme directly. Therefore, it can meet the needs of FP multiplexing system better. On the other hand, there also exists some disadvantages of this system. The interrogation scheme based on signal modulation and dispersion will increase the complexity of the experiment system. In particular, it also requires sufficient dispersion coefficient and stable performance of the dispersion module, making the system maintenance requirements more stringent. These problems might be solved with the development of integrated microwave photonic technology, which can not only meet the experiment conditions but also obtain stability and compactness.
4. Performance analysis
In this part, we will study the impacts of optical spectrum envelopes of FP sensors on the features of RF response peaks, which are discussed for the first time as far as we know. Besides, the minimum detectable FP cavity length and multiplexing cavity of this demodulation system will be analyzed as well.
As we can see in Figs. 3(a)–3(d), with the increase of HCF length, not only the FSR of FP structures decreases, but also the reflection spectrum presents more and more obvious envelope. Actually, due to the existence of anti-resonance effect, when the length of HCF is longer than the threshold, the spectrum of FP will appear outer envelope. The value of this threshold is determined by the inner diameter of HCF [35], such as only 203 µm for the HCF we use in the experiment. So the existence of spectrum envelope is a very common phenomenon for HCF-FP multiplexing sensors, and it is necessary to discuss the impacts of FP spectrum envelope on RF response passband for the accuracy of this demodulation method. In order to facilitate the calculation, here we simplify the envelope of HCF-FP to cosine-shape, as Fig. 8(a) depicted, and discuss the influences of envelope FSR and contrast ratio respectively.
Fig. 8. (a) The HCF-FP spectrum with simplified cosine-shape envelope in our discussion. (b) RF response spectra when envelope FSR changes and (c) the impacts on frequency and response intensity. (d) RF response spectra when envelope contrast ratio changes and (e) the impacts on frequency and response intensity.
In this simulation part, we fix the spectrum FSR to be 2.00 nm around 1550 nm and optical bandwidth to be 35 nm. The definition of envelope contrast ratio and envelope FSR we mention here is as Fig. 8(a) given. We first calculate the RF response under the condition when the FP spectrum is flat, and its frequency is 1269.25 MHz with 3-dB bandwidth of 153 MHz. Then we keep the contrast ratio of the spectrum envelope unchanged and tune the envelope FSR. As shown in Figs. 8(b) and 8(c), the RF response passband will shift when the envelope FSR varies from 11.4 nm to 29.0 nm, while the response intensity almost stays unchanged. The 3-dB bandwidth is also affected by the changes of envelope FSR, which obtains the minimum value at round 19 nm. However, when we keep the FSR of the spectrum envelope unchanged and tune the envelope contrast ratio, the response intensity will undergo increase when the contrast ratio decreases from 0.220 to 0.099, which are depicted in Figs. 8(e) and 8(f). The response frequency remains stable in this case, while the 3-dB bandwidth experiences obvious fluctuations and reaches the minimum when the contrast ratio is about 0.16. Compared with their counterpart one with the same spectrum FSR and no envelope, the RF response frequency of two conditions above is slightly less than that of flat spectrum condition.
These simulation results indicate that both envelope FSR and envelope contrast ratio will influence the RF response of HCF-FP. Therefore, in the actual cavity length measurement experiment, it is necessary to take the existence of spectral envelope and its effects on the RF response into consideration and calibrate the measurement results for the interrogation accuracy. Another important thing shouldn’t be ignored is the optical spectrum envelope phenomenon will also be obtained when the cavity lengths of two FPs are very close, that is, the Vernier effect. The simulation results above suggest that the cavity length differences of the multiplexing FP sensors need to be greater than a certain length, under which no obvious Vernier effect will occur, otherwise the demodulation of FPs will be inaccurate. The theoretical minimal distinguishable difference will be discussed later.
Besides the cavity length difference between adjacent FP sensors, the minimum detectable cavity length is another key factor also determining the multiplexing capacity under the double-sideband format, which failed to be discussed and analyzed in previous report about the interferometer-type-sensor interrogation system based on RF technique [36]. Therefore, we then calculate the shortest measurable cavity length and its corresponding RF frequency and discuss the impacts of optical bandwidth and SMF length respectively. Here, we judge the minimum measurable cavity length on the basis that the response peak corresponding to FP is completely separated from the baseband and the relationship between the center frequency and FP FSR satisfies Eq. (5). First, we fix the length of SMF to be 25 km and limit optical bandwidth to be 20–52 nm. From the results in Fig. 9(a), it can be found that the shortest detectable cavity length will decrease rapidly with the increase of optical bandwidth and then tends to be stable. The variations of corresponding center frequency exhibit similar trend. Then we fix the optical bandwidth to be 35 nm and changes the length of SMF from 10 km to 50 km to change the systematic dispersion. As Fig. 9(b) shown, the minimum cavity length almost stays unchanged with SMF length increasing, while the corresponding frequency will experience an obvious decline.
Fig. 9. The variations of shortest measurable cavity length and its corresponding RF frequency with the changes of (a) light source bandwidth and (b) SMF length.
These results can provide some feasible suggestions to further optimize the performance of this demodulation system. On the one hand, increasing the optical bandwidth of the system can significantly improve the shortest measurable cavity length, which will be helpful for a better multiplexing capacity. It should be noted that the optical bandwidth not only depends on the light source, but also is limited by the operation bandwidth of EOM, EDFA and other devices. Of course, it can also be seen in Fig. 9(a) that the minimum detectable cavity length cannot be reduced infinitely due to the existence of RF baseband. On the other hand, although systematic dispersion couldn’t help us to obtain shorter detectable cavity length directly, it can reduce the response frequency and improve the multiplexing capacity to some extent. For a certain bandwidth limited by experiment devices like PD or VNA, more dispersion might result in more intensive RF passbands, which can realize simultaneous measurement for more sensors. However, longer SMF also means more transmission loss, which puts forward higher requirements for the power compensation.
Based on the calculation and analysis above, we can simulate the theoretical multiplexing capacity of this interrogation system. Here, we confine the cavity length of FP sensors to be less than 1 mm, the corresponding FSR of which is about 1.2 nm around 1550 nm, and require every adjacent two RF passbands shouldn’t overlap each other. For example, Fig. 10 gives the reflection spectrum and frequency domain response of nine multiplexing FPs with different cavity lengths when the optical bandwidth is 32 nm, the SMF length is 25 km and maximum RF frequency is limited to be 1 GHz. It is obvious in Fig. 10(b) that every RF passband is clear and independent of each other, corresponding to only one FP sensor respectively.
Fig. 10. (a) Optical spectrum and (b) frequency domain response of nine FPs with different cavity lengths when the optical bandwidth is 32 nm, the SMF length is 25 km.
According to these requirements, we discuss the influences of different optical bandwidth and SMF length on multiplexing capacity, and the results are as Fig. 11 shows. When we fix the length of SMF to be 25 km and change the optical bandwidth from 32 nm to 48 nm, the total number of multiplexing FPs under 1 mm will increase with the optical bandwidth, while the RF frequency of corresponding response passbands experiences similar variation trend. However, when it comes to different SMF length, although the multiplexing capacity also increases, the RF frequency will undergo a sharp decrease, which is more obvious for the FPs with longer cavity. Among the calculation results present in Fig. 11, this interrogation system could demodulate 27 FP sensors with different cavity lengths < 1 mm at the same time when the optical bandwidth covers C-band and the length of optical fiber is 40 km. This multiplexing capacity can be further expanded in many ways, such as appropriately increasing the optical bandwidth and systematic dispersion, using other fabrication processes to realize the FP structures with longer cavity, and adopting the hybrid multiplexing method mentioned in the previous section.
Fig. 11. The variations of multiplexing capacity with the changes of different (a)-(b) optical bandwidth and (c)-(d) SMF length.
Based on the simulation results in Fig. 11, we can also find out the theoretical minimal distinguishable difference of two adjacent FP cavity length. It can be seen from the equation for estimating the FSR of HCF-FP structure and the calculated curve in the Fig. 12(a), the FSR of FP is not proportional to the cavity length. Especially when the cavity length is relatively short, the variations of FSR will be more severe. Since the response frequency of FPs is closely related with the FSR, the minimal distinguishable difference may be different for the FPs with different cavity lengths. Besides, as we discuss in the previous part, the optical bandwidth and SMF length also influence the minimum resolvable cavity length to some extent. For example, longer SMF length will introduce higher dispersion coefficient into the system, which will reduce the response passband broadening phenomenon and finally obtain smaller distinguishable cavity length. To be more specific, from the simulated results present in Figs. 12(b) and 12(c), it can be found that both optical bandwidth and SMF length will affect the minimal distinguishable difference, especially when the FP cavity length is less than 200 µm. However, when it comes to the situation when the FP cavity length is relatively long, optical bandwidth will hardly influence the resolvable difference, while the SMF length will still have great impacts on it. For the proposed demodulation system with optical bandwidth of 35 nm and SMF length of 25 km, the theoretical minimal distinguishable cavity length difference is no more than 50 µm.
Fig. 12. (a) The variations of FSR with different FP cavity length. The theoretical minimal distinguishable cavity length difference under different (b) optical bandwidth and (c) SMF length.
Last but not least, we investigate the influences of Gaussian line shape of light source and optical bandwidth on the accuracy of demodulation results. In order to evaluate the reliability of our interrogation scheme more comprehensively, we simulate the conditions when the broadband light sources have Gaussian line shapes with different 3 dB bandwidth, and compare the results with the case of uniform optical source. As shown in Fig. 13(a), for an HCF-FP sensor with a certain cavity length, whether the broadband light source has Gaussian line shape will not affect its corresponding RF frequency, that is, the existence of Gaussian distribution will not change the demodulation results of FP cavity length. Similarly, as for the different optical bandwidth, although there exist differences in the minimum measurable cavity length, the corresponding response frequency of a certain FP will stay stable under different optical bandwidths, which are present in Fig. 13(b).
Fig. 13. The variations of RF frequency under different (a) Gaussian bandwidth and (b) optical bandwidth.
5. Conclusions
In this paper, we present and demonstrate a microwave photonics interrogation system for multiplexing FP sensors. The experiment results indicate that this system obtains outstanding simultaneous demodulation ability with high speed for compact fiber HCF-FP sensors with short cavity length in submillimeter scale, indicating it to be a good candidate for the quasi-distributed FP sensing networks. Furthermore, due to its good demodulation performance in hybrid multiplexing system, our proposed system would have great potential in the sensing applications of multi-parameter measurement which requires different kinds of sensors to participate.
Funding
National Natural Science Foundation of China (61675078).
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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