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Abstract
We propose, analyze, and experimentally demonstrate a highly sensitive and stable fiber-laser pressure-sensing system based on an unequal-arm Mach-Zehnder interferometer (MZI) merged with a Sagnac interferometer (SI). The unequal-arm MZI structure consists essentially of two single-mode fibers of different lengths, and the SI structure uses a section of polarization-maintaining fiber, which acts as a sensing head. Moreover, in the proposed sensing system, the MZI and SI structures both act as a cascade filter. Given the asymmetric MZI and cascade filter structure laser mode hopping is effectively suppressed, so minor variations in environmental parameters cause a stable shift of the interference spectrum. The experimental results show that the proposed system can be used to make accurate pressure measurements. The −3 dB linewidth of the reflection interference peak produced by the proposed system is less than 0.02 nm, and the signal-to-noise ratio (SNR) can exceed 45 dB. With a 1-m-long sensor head, the proposed system provides a pressure sensitivity of 29.275 nm/MPa, and the interference spectrum of the sensing system fluctuates less than ±0.02 nm over 1 h. The proposed sensing system thus offers the attractive characteristics of good sensing linearity and stability, high SNR, and high sensitivity.
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1. Introduction
Fiber optical sensors have attracted significant attention in recent years because they offer high sensitivity, low cost, compact size, high resolution, and multiplexing capabilities [1,2]. Pressure measurements are very important in numerous fields, such as water conservancy, hydrophones, railway transport, intelligent buildings, aerospace, military, and pipelines [3–6]. At present, various optical-fiber sensing structures see wide use for pressure measurements, including fiber Bragg gratings [5,7], Sagnac interferometers (SIs) [8], Mach-Zehnder interferometers (MZIs) [9,10], and Fabry-Perot interferometers [11,12]. For example, Luo et al. [13] proposed a gas pressure sensor based on phase-shifted fiber Bragg gratings modulated by a hollow cavity. The device offers a temperature sensitivity of 8.92 pm/°C, and the pressure sensitivity is 1.22 nm/MPa. Pressure-sensing systems based on fiber interferometers have relatively high sensitivities, as exemplified by the miniature fiber-optic-tip Fabry-Perot interferometer pressure sensor proposed by Liu et al. [14], which has a sensitivity of 2.13 nm/kPa. Moreover, a MZI based on processed hollow-core fibers has been demonstrated for pressure sensing with a sensitivity of 9.35 nm/MPa [15], and Hou et al. [10] designed a poly dimethyl siloxane sealed microfiber MZI for measuring pressure and temperature in seawater. The system has a pressure sensitivity of 13.31 nm/MPa. Zhang et al. [4] used a rectangular-lattice photonic crystal fiber to construct a multifunctional sensor based on the SI structure; the sensor can be used to measure pressure, curvature stress, and temperature and the pressure sensitivity is about 11.15 nm/MPa. In recent years, various types of fiber laser sensors have been proposed, including distributed feedback lasers [16,17], distributed Bragg reflection fiber lasers [18,19], and fiber ring lasers [20,21]. Lin et al. [22] proposed and demonstrated an in-fiber MZI sensor based on an Er-doped fiber peanut structure fiber ring laser with a temperature sensitivity of 0.158 nm/°C, a refractive index sensitivity of −19.55 nm/RIU, a −3 dB spectral linewidth of 0.15 nm, and a signal-to-noise ratio (SNR) of almost 24 dB. In addition, the wavelength fluctuation within 200 minutes is about 0.32 nm. Cai et al. [23] proposed a multiwavelength fiber ring laser temperature sensor based on a mixed gain medium and a SI. With a 1.7-m-long polarization-maintaining fiber (PMF) in the SI, the temperature sensitivity is 1.8063 ± 0.00933 nm/°C, the SNR of the sensor exceeds 42 dB, the −3 dB linewidth is less than 0.08 nm, and the wavelength fluctuations remain within ±0.08 nm.
In this paper, we use a ring fiber-laser oscillator structure in conjunction with an unequal-arm MZI cascaded with a SI structure to propose a highly sensitive and stable pressure-sensing system with high interrogation performance. The key component in the proposed sensing system is the asymmetric MZI and the cascaded filter structure. Under the asymmetric MZI structure and dual-mode selection mechanism implemented by the cascaded dual-filter structure, the system embodies a strong narrow-band filter that is easy to use to obtain high sensitivity and stability, narrow-band laser sensing at the interference peak. Thus, the proposed sensing system has an interference peak with a −3 dB linewidth of less than 0.02 nm and a SNR greater than 45 dB. With a 1-m-long sensor head, the proposed system provides a pressure sensitivity of 29.275 nm/MPa, and the sensing stability of the system over 1 h is ±0.02 nm. The proposed sensing system is novel, stable, and sensitive and can be used to measure pressure in various applications.
2. Principles and simulations
Figure 1 shows a schematic diagram of the proposed fiber-laser pressure-sensing system with unequal-arm MZI and SI structure. In the main ring, an Er-doped fiber amplifier (EDFA) serves as pump source and gain medium for the sensing system. An isolator allows the light in the laser oscillation loop to propagate in only one direction. The polarization controller (PC2) modifies the polarization state of the light, and the dispersion-compensation fiber compensates for the dispersion of the sensing system. The optical fiber coupler (OC3) with a coupling ratio of 10 : 90 allows 10% of the light to enter the observation system (OSA; resolution = 0.02 nm), with the remaining 90% of the light continuing to propagate in the loops. The main ring is connected to the cascade structure with a 50 : 50 fiber coupler OC2. The MZI structure consists of two optical couplers OC1 and OC2, and the two arms of differing lengths of single-mode fiber. The SI structure is composed of a section of PMF and a polarization controller (PC1). To obtain a high-quality laser-sensing signal, a wavelength-selective element is inserted into the laser cavity. Here, the unequal-arm MZI and the SI structure both act as cascade filters in the sensing system. In addition, the SI structure serves as a pressure-sensing head.
Fig. 1. Schematic of proposed highly sensitive and stable fiber-laser pressure-sensing system with unequal-arm MZI and SI structure: EDFA: erbium-doped fiber amplifier, ISO: isolator, PC: polarization controller, OC: optical coupler, DCF: dispersion compensation fiber, PMF: polarization-maintaining fiber, OSA: optical spectrum analyzer.
The schematic diagram of light propagation in Fig. 1 shows that the fiber laser oscillation structure in the proposed sensing system produces a highly coherent light field with gain, which then passes through the cascade structure. The initial light field E0 can be expressed by the Jones matrix:
The electric field E1in at the input of the cascade structure can be expressed as
where g is the gain, L0 is the length of the gain medium, and $\beta = {{2\pi {n_{\textrm{eff}}}} / \lambda }$ is the propagation constant, where λ is wavelength and neff is the effective refractive index of the fundamental mode. Upon passing through OC2 and OC1, the light field is split into two fields E3 and E4 propagating in opposite directions:Similarly, after the light field E4 travels anticlockwise through the PMF and PC1, the light field E3′ can be expressed as
Due to the effect of the isolator in the optical path, E1out′ no longer propagates in the optical path; however, E2out′ continues to transmit through PC2. Therefore, the electric field E5 can be expressed as
From Eqs. (1) to (8), we obtain the transmission function T of the proposed system as follows:
Guided by the theoretical results, we simulate the important spectral features in the proposed sensing system. Figure 2 shows the simulation results for the parameters BPMF = 5.1 × 10−4, θ = π/2, k1 = k2 = 0.5, k3 = 0.9, and neff = 1.445. Figure 2(a) shows a diagram of the transmission spectrum of the cascade structure, which is a periodic multipeak spectrum. This result is clearly modulated by the MZI and SI structure. Figure 2(b) shows the gain of EDFA, which reflects the spectral characteristics of the light source. Figure 2(c) shows the interference spectrum of the proposed sensing structure, which is obtained from Eq. (9). Finally, Fig. 2(d) shows the periodic function of the proposed sensing structure; its spectral spectrum characteristics are related to the gain and the interference period of the SI.
Fig. 2. Simulation of optical spectrum of proposed system: (a) transmission spectrum of cascade structure, (b) gain of EDFA, (c) interference spectrum of proposed sensing structure, (d) periodic function of proposed sensing structure.
In the proposed sensing system, when the PMF (sensor head) is under pressure, its birefringence changes, which varies the phase difference δ, thereby modifying the transmission function T. Moreover, during the experiment, the length difference ΔL = L1 − L2 of the MZI structure takes on several fixed values, and the coupling ratios k1, k2, and k3 in OC1, OC2, and OC3 are constant. We thus make θ1 = π/2 during the experiment by adjusting PC1 in the SI loop. Thus, from Eq. (9), the transmission function T simplifies to
Although the periodic function of the sensing system is modulated by g [as shown by the simulation result in Fig. 2(d)], the period of the system remains constant. Therefore, the periodic function of the proposed sensing system can be written as
In the transmission spectrum, the transmission peaks (from the laser) appear when the phase δ satisfies
From Eq. (12), we get the wavelength of the interference peak of the sensing structure:
where m is a random integer. When a section of the PMF in the SI structure is subjected to pressure, its birefringence BPMF and length L change. Eq. (13) gives the shift of the interference peak. The relationship between the shift Δλpeak in the interference peak and the change ΔP of pressure is3. Experiment and discussion
In the experiment, we tested the response of the proposed sensing system with a 1-m-long PMF section serving as the sensor head. Figure 3(a) shows that the spectrum obtained from the experiment is consistent with the simulation result in Fig. 2(c). Moreover, the experimental results reveal a strong mode-suppression effect, and the interference peak (narrow-band laser) of the system has a high SNR, which can exceed 45 dB. In addition, the −3 dB linewidth of the interference peak is less than 0.02 nm (OSA; resolution = 0.02 nm). Figure 3(b) shows that the intensity of the interference peak changes when the EDFA current increases, which shows that the critical current is approximately 60 mA for the laser sensing system. The system begins to produce high-coherence narrow band lasing (interference peaks) as the EDFA current increases above the critical current [this critical current is shown by point a in Fig. 3(b)], and the amplitude of the interference peaks (narrow-band laser) quickly increases. The system then reaches gain saturation, and the intensity of the interference peak asymptotically approaches a constant.
Fig. 3. Characteristics of spectrum for proposed sensing system: (a) SNR and −3 dB linewidth of interference peak, (b) intensity of interference peak as a function of EDFA current.
During the experiment, we tested in the first step how the length differences ΔL = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.5 m in the MZI structure and LPMF = 1 m in the SI structure affect the stability of the sensing system. The system was tested every 5 minutes for 1 hour at room temperature, and the results are given in Fig. 4.
Fig. 4. Unequal-arm MZI affects the performance of the sensing system: (a) intensity of interference spectrum for different arm lengths of MZI, (b) spectral stability over time for different differences in arm length of MZI.
Figure 4(a) shows the intensity of the interference spectrum for the different arm lengths of the MZI. As ΔL increases to a perfect difference in length, the number of laser modes decreases, and several stable laser modes remain. Proper adjustment of the length difference (e.g., ΔL = 1.5 m) can suppress lasing, which suppresses mode hopping. We hypothesize that one of the most important physical reasons for this phenomenon is the difference in arm length in the MZI, which produces a fixed phase difference in the propagation of the highly coherent light field. This phase difference affects the laser modes, only several of which will lase in the system. At the same time, the dual-mode selection implemented by the cascaded dual-filter structure significantly weakens the mode competition, so mode hopping is suppressed. Therefore, a difference in arm length will affect lasing, and the proper arm length difference may makes the system more stable.
Figure 4(b) shows that the wavelength of the interference peaks fluctuates ±0.075, ±0.045, ±0.035, ±0.02, ±0.025, and ±0.035 nm as ΔL goes from 0.0 to 2.5 m in steps of 0.5 m, respectively. The experimental results show that, when ΔL = 1.5 m, the system is most stable, and the wavelength of the interference peaks fluctuates within ±0.02 nm. These results show that the length difference of the unequal-arm MZI is closely related to the system’s stability, which is consistent with the spectral analysis of Fig. 4(a).
We next analyze how the sensitivity of the sensing system depends on the length difference ΔL = 0.0, 0.5, 1.0, 1.5, and 2.0 m in the MZI structure with LPMF = 1 m in the SI structure. In addition, we test the repeatability of the results (see Fig. 5).
Fig. 5. Wavelength of the interference peaks as a function of pressure for various length differences showing the sensitivity of the proposed sensing system.
Figure 5 shows that, upon increasing the length difference ΔL, the sensitivity of the proposed pressure-sensing system remains essentially constant, so the experimental results indicate that varying the length difference ΔL of the MZI structure in the sensing system does not affect the sensitivity of the system. Regarding repeatability, Fig. 5 shows a slight hysteresis between the pressure rising and decreasing, which is especially clear when ΔL = 0.5 and 2.0 m. This minor hysteresis is tentatively attributed to two effects: the first is the minor mode hopping phenomenon, which degrades the stability of the system, and the second is that the stress of the PMF is not fully released during the experiment.
In the second step, we tested how variation in the length of the PMF affects the performance of the proposed sensing system. We tested the sensing system with sensor-head lengths LPMF = 1 and 1.5 m in the SI structure and a length difference ΔL = 1.5 m in the MZI structure. Figure 6 shows how the wavelength of the interference peaks from the sensor heads vary with length (LPMF = 1 and 1.5 m) and for a range of pressure. With increasing pressure, the wavelengths of the interference peaks all redshift. In addition, Figs. 6(a) and 6(b) show that the sensitivity is related to the length of the PMF: a shorter PMF enhances the sensitivity.
Fig. 6. Peak as a function of wavelength for different pressure changes with a PMF length of (a) LPMF = 1 m and (b) LPMF = 1.5 m.
Figure 7 shows the sensitivity of the sensing system with PMF lengths (sensor head) of 1 and 1.5 m. When the length of the sensor head is 1 m (1.5 m), the pressure sensitivity is 29.21 and 29.27 (28.18 and 26.71) nm/MPa, respectively. The linear analysis shown in Fig. 7 indicates that the sensitivity is related to the length of the PMF: a shorter PMF enhances the sensitivity and improves the repeatability. However, the repeatability tests reveal a slight hysteresis between rising and falling pressure, especially the wavelength is slightly longer when the pressure decreases. This phenomenon is amplified as LPMF increases. We attribute this phenomenon mainly to residual stress in the PMF, which would lead to a shift Δλpeak [from Eq. (14)], and a longer PMF would enhance this phenomenon. Thus during such experiments, a shorter PMF should be prioritized for the pressure sensor head.
Fig. 7. Wavelength of peak as a function of pressure to show response of the proposed sensing system with PMF lengths (a) LPMF = 1 m, (b) LPMF = 1.5 m.
To clearly demonstrate the performance of the proposed system, we compare in Table 1 the pressure sensitivity obtained with the proposed scheme and that obtained from other recently reported pressure sensing schemes. Table 2 then compares the performance of the proposed laser sensing system with that of other recently reported laser sensing systems. The comparison shows that the proposed scheme is more sensitive to pressure and offers a narrower −3 dB linewidth, a higher SNR, and is more stable.
Table 1. Comparison with sensitivities of previous fiber laser pressure sensing schemes
Table 2. Comparison with performances of previous fiber laser sensing systems
4. Conclusion
In conclusion, we have proposed, analyzed, and experimentally demonstrated a fiber-laser pressure-sensing system based on an unequal-arm Mach-Zehnder cascaded with a Sagnac structure. The proposed pressure-sensing system combines fiber-laser technology, sensing technology, interference technology, and filtering technology. The results demonstrate that the stability and sensitivity of the proposed system are closely related to the unequal-arm MZI structure and to the dual-filter structure. Experimental results show that the proposed system accurately measures pressure and can generate an intense, stable reflection spectrum with a stability of ±0.02 nm over 1 h. The SNR of the proposed sensing system exceeds 45 dB, and the −3dB linewidth is less than 0.02 nm. For a 1-m-long sensor head, the proposed system offers a pressure sensitivity of 29.275 nm/MPa. In summary, the proposed sensing technique is characterized by high stability, narrow linewidth, high SNR, and high sensitivity, making it suitable for pressure measurements in various applications.
Funding
National Natural Science Foundation of China (61801134, 61835003); Guizhou Science and Technology Department ((2019)1127).
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 maybe obtained from the authors upon reasonable request.
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