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To achieve a nearly zero-delay operating point in a polarization-maintaining (PM) fiber Sagnac interferometer, two identical PM fibers were incorporated so that their two main axes were orthogonally coupled to each other. A simple fiber vibration sensor system was constructed with a light emitting diode and a balanced PM fiber Sagnac interferometer, in which one of the PM fibers was used as a sensing cable and the other as a reference cable. The vibration sensor was confirmed to be temperature-compensated and generated a phase shift per unit length and unit strain of the sensor of 4.7 milliradian / (m·μɛ) when mechanical vibrations with 1 kHz sinusoidal and triangular waves were stably observed under an input power of 10 μW.
© 2011 Optical Society of America
1. Introduction
The value of fiber-optic acoustic/vibration sensors with fiber Bragg gratings (FBGs) or fiber interferometric (FI) systems has been demonstrated in a wide range of applications [1–7]. Compared with FBG sensors, the greatest merit of FI sensors lies in the fact that the sensitivity is controllable simply by varying the length of the sensing fiber. Based on this, acoustic wave sensing with FI (Mach–Zehnder or Michelson interferometer) sensors in the sea has been demonstrated [4,5]. In terms of the temporal stability of sensed signals, however, there is a problem of phase noise between the signal and reference light components in those FI sensors. To overcome this problem, it seems to be expedient to replace those FI sensors with polarization-maintaining (PM) fiber Sagnac interferometer sensors. Besides the reduction in phase noise, because PM fibers [6] and PM photonic crystal (PM-PC) fibers [7] have high induced birefringence (> 10−4), vibrations and acoustic waves cause large fluctuations in the birefringence of these fibers, which makes the FI sensor systems compact and sensitive. However, a common type of fiber Sagnac interferometer, in which two optical paths traveling along the main (Slow and Fast) axes of a PM fiber are used as a signal arm and a reference arm, does not achieve a nearly zero-delay operating point. This causes the problem that the sensitivity of the sensor strongly depends on the wavelength and linewidth of the light source because of the sinusoidally modulated transmittance spectrum. In addition, for a PM fiber Sagnac interferometer sensor, the operating point varies greatly with changes in environmental temperature because PM fiber has a large difference in thermal expansion coefficients between boron-doped stress parts and the cladding. As a result, both the temporal stability and the sensitivity of the sensor become degraded.
To solve the above problems, in this paper, we propose to introduce two identical PM fibers, whose two main axes are orthogonally coupled to each other, as part of a fiber Sagnac interferometer. The configuration involving two identical orthogonally coupled PM fibers was first reported by Dakin and Wade for temperature compensation in a polarimetric sensor [8]. Although they used this configuration in a single path, it seems to be more effective to use the configuration in a Sagnac loop. We expected that, in our application, a modified PM fiber Sagnac interferometer system would suppress the phase noise effectively and achieve a nearly zero-delay operating point and temperature compensation. In addition, because the system allows us to use an LED white light source and a photodiode for observing vibrations, a simple fiber vibration sensor system can be constructed, with the simple addition of only one polarizing element to the conventional PM fiber Sagnac interferometer temperature sensor [6]. We also demonstrated vibration sensing using the proposed system.
2. Fiber Sagnac interferometer incorporating a PM fiber
We started by examining a conventional PM fiber Sagnac interferometer temperature sensor, as shown in Fig. 1. The interferometer was composed of a 50/50 fiber coupler and a single-mode PM bare fiber one meter in length (PMF1, Nufern, PM1550G-80). Most of PMF1 (∼80 cm) was temperature-controlled. A built-in light emitting diode (LED) coupled with a single-mode fiber in an optical spectrum analyzer (ADVANTEST Q8384) was used as a white light source for input, and the output from the PM fiber Sagnac interferometer was observed with this optical spectrum analyzer. The average output power of the LED was 10 μW, and the power spectrum is shown in Fig. 2.
Figure 3 shows intensity-modulated output power spectra caused by a delay distance between two light components traveling along the slow axis and the fast axis in PMF1. The temperatures of PMF1 for these observations were (a) 15.5 deg C, (b) 18.5 deg C, and (c) 22.0 deg C, respectively. From the 4.0 nm pitch of spectral peaks, the delay distance between the two light components was estimated to be 0.6 mm, corresponding to a birefringence in PMF1 of 6 × 10−4. By increasing in temperature of PMF1, the spectral peaks were shifted toward shorter wavelengths, and by increasing the temperature by 6.5 deg C, the spectral peak shift reached 4.0 nm, corresponding to a 2π phase shift in the interference between the two light components, as shown in the magnified view (d). This system can thus operate as a temperature sensor by measuring the spectral peak shift.
Fig. 3 Output power spectra from the PM fiber Sagnac interferometer observed at sensor temperatures of (a) 15.5 deg C, (b) 18.5 deg C, and (c) 22.0 deg C, respectively. Parts of these results are superimposed in the magnified view (d).
However, the spectral peak shift did not have much influence on the output intensity, as indicated by the almost unchanged envelope of the intensity-modulated power spectra in (a), (b) and (c). This means that the system is not appropriate for measuring fast phenomena, such as vibrations or acoustic waves. To efficiently transform the spectral peak shift into a variation in output intensity, generally, a laser with a narrower oscillation linewidth in comparison with the pitch of the spectral peaks is used instead of a white light source [9]. The introduction of a laser, however, makes the measurement system complicated because the laser needs to be temperature-controlled so that its oscillation wavelength does not fluctuate, and an isolator must be coupled to the laser to prevent optical feedback instabilities. In addition, a half-wave plate must be incorporated into the Sagnac loop to equally distribute the orthogonally polarized light components.
3. Balanced fiber Sagnac interferometer incorporating PM fibers
To minimize the number of polarizing elements, we attempted to modify the PM fiber Sagnac interferometer in Fig. 1 without having to replace the LED with a laser. Figure 4 shows the proposed experimental configuration. In this system, a second PM fiber (PMF2) with almost the same specifications as PMF1 in Fig. 1 was added to the Sagnac loop. The only difference in the specifications of the fiber was the relation between the polarizing axis and the key of the connector. The slow axis of PMF1 and the fast axis of PMF2 were aligned with the key of the connector, and therefore, the two main (Fast and Slow) axes of the PM fibers were orthogonally coupled to each other. The output from the modified Sagnac interferometer was divided into two through a 50/50 fiber coupler; the two divided outputs were respectively observed with the optical spectrum analyzer and a 10 MHz amplified photodetector (Thorlabs, PDA400) connected to an oscilloscope. Figure 5 shows the output power spectrum observed at 27 deg C. By connecting the two PM fibers in this way to compensate for their birefringence, the intensity-modulation depth was considerably reduced, and only small ripples were seen on the envelope of the power spectrum, which stemmed from a small error in equipartition at the 50/50 fiber coupler. This operating point in the interference was regarded as a nearly zero-delay point in the balanced PM fiber Sagnac interferometer, which is equivalent to the condition achieved by balancing the optical path lengths between signal and reference arms of a Michelson or Mach–Zehnder interferometer.
A similar approach regarding the modified PM fiber Sagnac interferometer for improving the sensitivity of a temperature sensor has been reported [6]. In that case, the modified PM fiber Sagnac interferometer was introduced in order to adjust the spectral peak spacing appearing in an intensity-modulated power spectrum to match the resolution of an optical spectrum analyzer used. That is, to avoid a trade-off problem between the sensitivity and the resolution in the PM fiber Sagnac interferometer temperature sensor, the operating point in the interference was shifted so as to have a wide spectral peak spacing by adding a reference PM fiber cable of a different length. From this viewpoint, by using PM fibers of almost equal length in our proposed system, the spectral peak spacing was made larger than the spectral width of the LED, with the result that the spectral peak shift was efficiently transformed into a variation in output intensity.
Figure 6 shows output power spectra observed when the temperature of PMF1 was varied from 15.5 deg C to 22.0 deg C, while maintaining the temperature of PMF2 at 27 deg C. By shifting the operating point to the nearly zero-delay point, the intensity of the output power spectrum strongly depended on the temperature change of PMF1. The output power spectrum was maximized at 15.5 deg C and 22.0 deg C and minimized around 18.5 deg C, accompanied with deformation of the envelope of the power spectra due to a slight difference in the optical lengths of the PM fibers. Thus, a phase shift caused by the large thermal expansion coefficient difference in PMF1 was observed clearly as a spectral intensity variation in Fig. 6, differing from the case in Fig. 3, although both cases showed a 2π phase shift for the same temperature change. Figure 7 plots the variation in the output power as a function of temperature. When only PMF1 was subjected to a temperature variation from 15.5 deg C to 22.0 deg C in steps of 0.1 deg C, the output power, plotted as filled squares, sinusoidally varied between 140 mV and 15.7 mV, promptly reflecting the result in Fig. 6. The minimum output of 15.3 mV consisted of dark current offset (13.6 mV) and residual dc components (1.7 mV). The latter stemmed from a small error in equipartition at the 50/50 fiber coupler. Compared with this, when both PMF1 and PMF2 were subjected to temperature variation in the same way, the output power was kept constant at 85.0 mV, which corresponded to a constant interference phase of 0.54π (= cos−1 [1 – 2×(85.0 mV – 15.3 mV)/(140.0 mV – 15.3 mV)]). The observed power spectrum in this case maintained a constant shape, as shown in Fig. 5 and in the curve for 20.5 deg C shown in Fig. 6. This is because the thermal expansion in the PM fibers, causing a spectral peak shift, was almost totally cancelled out between the two PM fibers. It was thus confirmed that the proposed system involved a temperature-compensating mechanism.
Fig. 6 Output power spectra from the proposed system in Fig. 4 observed when the temperature of PMF1 was varied from 15.5 deg C to 22.0 deg C, while maintaining the temperature of PMF2 at 27 deg C.
Fig. 7 Variation in the output power from the proposed system in Fig. 4 as a function of temperature. Filled squares indicate the case where only PMF1 was subjected to temperature variation, and open squares indicate the case where both PMF1 and PMF2 were subjected to temperature variation.
4. Vibration sensing using a balanced PM fiber Sagnac interferometer and an LED
To demonstrate vibration sensing, a cylindrical piezoelectric body (3.5 cm in diameter and 3.0 cm in height) was prepared, and most of PMF2 (80 cm) was tightly coiled around it, as shown in Fig. 8. A function generator supplied ac voltage to the cylindrical piezoelectric body. An 80 cm length of PMF1 was also tightly coiled around another cylindrical body of the same size to compensate for strain in PMF2 and thus the interference phase was maintained at nearly π/2. Figure 9 shows examples of observed vibration waveforms (averaged over 225 observations) when (a) sinusoidal and (b) triangular voltage waveforms with amplitudes of 5 V, 10 V, and 15 V at 1 kHz repetition rate were applied to the cylindrical piezoelectric body. Those voltage waveforms were reproducibly-observed without being affected by the phase noise and temperature drift. Those were also exactly reproduced, revealing a proportional relation between the input and output signal intensities. Because the radius of the cylindrical piezoelectric body expanded by 25 nm when a dc voltage of 5 V was applied, the strain on PMF2 was estimated to be 1.4 μɛ (= 25 nm / 17.5 mm × 106). From the result in Fig. 9, when an ac voltage of ±5 V was applied, an output ac voltage of ±0.33 mV was obtained. The phase shift at the applied ac voltage of ±5 V was estimated to be ±5.3 milliradian (= ±sin−1[2 × 0.33 mV /(140.0 mV – 15.3 mV)]). By applying a linear approximation, the phase shift per unit length and unit strain of this sensor was calculated to be 4.7 milliradian / (m·μɛ) (= 5.3 milliradian × 100 cm / 80 cm / 1.4 μɛ) at 1 kHz measurement frequency and 10 μW input power, which can be regarded as a sensitivity index of the sensor. For more-sensitive applications, such as acoustic sensing in the air or sea, the lengths of the sensor (PMF2) and reference (PMF1) cables, and the input optical power should be increased to adjust the sensitivity to the level needed for the target application. By simple calculation assuming 100 m-length sensor and reference cables and 10 mW input power, very small repeating vibrations corresponding to several tens of pico-strain were estimated to be observable at 1 kHz measurement frequency.
Fig. 9 Examples of observed vibration waveforms when (a) sinusoidal and (b) triangular voltage waveforms with amplitudes of 5 V, 10 V, and 15 V at 1 kHz repetition rate were applied to the cylindrical piezoelectric body of the sensor system in Fig. 8.
Figure 10 shows sinusoidal vibration waveforms observed when only PMF1 was subjected to a temperature variation from 15.5 deg C to 18.5 deg C. An ac voltage of ±10 V at 1 kHz repetition rate was applied to the cylindrical piezoelectric body. As shown in Fig. 7, the interference phase at the 50/50 fiber coupler after traveling in the PM fibers was varied from −π to 0 with the corresponding temperature variation. Thus, the sensitivity of this sensor for detecting vibrations strongly depended on the interference phase. At a temperature of PMF1 of 17.0 deg C, the amplitude of the vibration waveform was maximized, which nearly corresponded to the optimal condition of an interference phase of −π/2. The proposed system ensures stable and sensitive vibration sensing so long as there is no difference in temperature between PMF1 (reference cable) and PMF2 (signal cable). This is considered to be easily achievable, taking into account the above temperature-compensating mechanism of the sensor system. Because a polarization maintaining photonic crystal (PM-PC) fiber can be temperature-compensated more efficiently than a conventional PM fiber [7], PM-PC fibers are expected to be used in Sagnac interferometer vibration sensing if their lossy characteristics and brittleness can be improved.
Fig. 10 Sinusoidal vibration waveforms observed when only PMF1 is subjected to a temperature variation from 15.5 deg C to 18.5 deg C. An ac voltage of ±10 V at 1 kHz repetition rate was applied to the cylindrical piezoelectric body.
5. Conclusions
A simple configuration of a polarization maintaining (PM) fiber Sagnac interferometer vibration sensor with a light emitting diode was proposed. A second PM fiber with almost the same specifications was added to a conventional PM fiber Sagnac interferometer temperature sensor so that the two main axes of the PM fibers were orthogonally coupled to each other in the Sagnac loop. The fiber vibration sensor system involved a temperature-compensating mechanism, resulting in a phase shift sensitivity index of 4.7 milliradian per unit length and unit strain of the sensor at 1 kHz measurement frequency and 10 μW input power. Using this system, stable vibration sensing was successfully demonstrated.
Acknowledgments
This research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology, under Grant-in Aid for Scientific Research (C), No. 21560044, and Adaptable and Seamless Technology Transfer Program (A-STEP) through Target-driven R&D, Japan Science and Technology Agency, No. AS221Z02259B.
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