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A novel distributed fiber optic pressure sensor based on an all-solid photonic band gap fiber is proposed and experimentally demonstrated. The sensor is fabricated by splicing a piece of the photonic crystal fiber (PCF) with a single-mode fiber (SMF), and the free end face of the PCF is filmed with a reflectivity of 99%. The cladding mode is excited at the fiber splice, resulting in the interference between the cladding mode and the core mode. The pressure position can be located by measuring the phase difference of the interferometer, and the pressure can be interrogated by measuring the height of the valley in the white-light optical spectrum. The experimental results show that the pressure and its position along the PCF can be simultaneously interrogated.
©2012 Optical Society of America
1. Introduction
The photonic crystal fiber (PCF) has attracted significant attention over several years with its outstanding advantages, such as high birefringence, flexible dispersion characteristics, low temperature cross sensitivity, and special wave-guiding mechanism [1–4]. Based on these features, PCFs have resulted in a number of novel devices and sensing applications. PCFs based sensors have demonstrated the capabilities of measuring various parameters, such as strain, temperature, refractive, pressure, etc [5–9]. However, it was generally assumed in such a way as to realize the single-point sensor, and there is few reports on the PCF based distributed sensors.
The distributed fiber optic sensor is currently one kind of the most promising sensors and has been extensively investigated during past decades. Distributed fiber optic pressure sensors can measure the pressure along the fiber and have been widely used in homeland security, intrusion detection, health monitoring and other fields [10–12]. Prof. Hotate’s group reported a mode coupling method to fabricate a distributed fiber-optic stress sensor by using a polarization-maintaining fiber [13]. The mode-coupling within a polarization-maintaining fiber induced by an external force could be used to measure the stress on the fiber. Prof. Julian’s group developed a polarization diversity detection system for distributed sensing of polarization mode coupling in high birefringence fibers [14]. The system, based on the optical Kerr effect, is capable of locating disturbance points along a length of fiber. Ref [15] demonstrates a distributed fiber optic pressure sensor based on the highly birefringent PCF, in which the interference is formed between two orthogonally polarized modes.
In this paper, we demonstrate experimentally an all-solid photonic band gap fiber based distributed fiber optic pressure sensor. This sensor is in fact an in-line modal interferometer. The fiber in-line modal interferometer based on a PCF can be fabricated in a number of ways, and their properties and applications have been widely investigated [16–20]. This distributed sensor is simply constructed by splicing a piece of a PCF with a single-mode fiber (SMF). Interrogated by fiber optic white-light interferometry, the pressure and the pressure location can be simultaneously measured.
2.Operation principle
The distributed fiber optic sensor is fabricated by splicing a SMF with a piece of an all-solid photonic band gap fiber, and the free end face of the PCF is filmed with a reflectivity of 99% before it is spliced with the SMF. The PCF is provided by YANGTZE OPTICAL FIBER AND CABLE (YOFC, China), and its cross section is shown in Fig. 1 . The fiber includes five rings of holes arranged in a regular hexagonal pattern. The PCF has a center-to-center distance between the holes of Λ = 8.5μm and an average hole diameter of d = 2.9μm. The core diameter Dco = 11.4μm, and the outer diameter of the PCF is 125μm. Figure 1(a) is the end face of the PCF without the reflector, and Fig. 1(b) is the filmed end face. Unlike the traditional PCF, The PCF is solid without any air holes, and these holes in Fig. 1(a) are full of Ge. The PCF core is also solid and constructed by the pure silica. A PCF with the length of 8cm is spliced with a commercial SMF by using the technique reported in [21], and the splicing loss is ~1.2dB. At the fiber splice, a collapsed region is formed between the PCF and the SMF due to strong electric arc discharges [22]. The fiber splice of the sensor is shown in Fig. 2 .
Fig. 1 The cross section of the all-solid photonic band gap fiber. (a) Without the reflector, (b) With the reflector.
The operation principle of the sensor is shown in Fig. 3 . At the collapsed region, the propagation mode is divided into two beams due to the mode-field mismatch, and part of the fiber core mode couples from the fundamental core mode to the cladding mode. The fundamental core mode and the cladding mode propagate along the PCF with different effective refractive index. The filmed end is used to reflect the light back. Then the cladding modes re-couple back into the core and interfere with the fundamental core mode at the collapsed region, forming a Michelson interferometer (MI) [23], as shown in Fig. 3(a). The phase difference leading to spatial interference is caused by different effective refractive index between the core and cladding mode. When the PCF is not pressed, the optical phase difference Δφ induced by scanning wavelength from λ1 to λ2 can be described as [24]
where Δneff is the difference of the effective refractive index of two beams in the PCF, L is the length of the PCF. The OPD between two adjacent valleys is 2π. So Δneff can be obtained by using the Eq. (1) when we measure two wavelengths of two adjacent valleys.When the PCF sensor is pressed, the two propagation modes are re-split into two beams. One beam is the core mode; and another beam is the cladding mode. The two modes are reflected by the end face mirror, and go through the pressure point again. The pressure results in the light intensity exchanging between the core mode and the cladding mode. Finally, the two beams interfere with each other at the fiber splice. Thus a Mach-Zehnder interferometer is formed in the PCF, as shown in Fig. 3(b). So, when the pressure is applied on the PCF, the OPD between the two interferometric beams can be expressed as
where L' is the distance from the pressure point to the end face of the PCF. From Eq. (2), we can obtain the pressure position L' when we measure the OPD Δφ.In this work, we assume that only one position on the PCF is pressed. A light beam is spatially separated into two beams at the fiber splice due to the mode-field mismatch, generating the cladding mode. When the two modes pass the pressure point for the first time, the external force induces the re-splitting between the core mode and cladding mode. The reflected beams recombine at the splice point, and the interference is formed. The electric field of the core mode detected at the black reflection is expressed as Eco, and the electric field of the cladding mode is expressed as Ecl. The interference signal caused by Eco and Ecl is given as a time-averaged intensity, i.e. [25],
where r is a constant, τ is the time delay between the two beams, ω0 is the angular frequency of the input light, c is the light velocity in free space, h is the power coupling coefficient which is the ratio between the power coupled from one mode to the other mode and the noncoupled power at the pressure point, and Δω is the bandwidth of the input light which depends on the line width of the tunable Fabry-Perot filter used in our experiment. Δneff0 denote the values of the Taylor expansion of Δneff at ω = ω0.To normalize the signal shown in Eq. (3), we consider the interference between two identically modes (a combination of the core and core modes or a combination of the cladding and cladding modes). In this case, signal I at τ = 0 is given as
From Eqs. (3) and (4), the normalized signal is written asThus,A square relation exists between h and the coupling coefficient k, which is expressed as h = k2, so,From Eq. (7), we can obtain the relationship between the normalization light power IN and the coupling coefficient k, as shown in Fig. 4 with the inset figure for detail observation, we discover that they have an approximately linear relationship when k<0.3 (h<0.09, the condition satisfies the weak coupling condition). So, the applied pressure must be small enough to meet the weak coupling condition, if we want to obtain a linear relationship between the pressure and the power change.When two beams penetrate a perturbed region in the fiber, they would couple with each other and the coupling coefficient k would vary with the perturbation. When the weak coupling condition is satisfied, the coupling coefficient k changes with the transversely applied pressure P linearly [26]. Thus, the normalized light power IN is proportional to the applied pressure P. The normalized light power reflects the magnitude of the external pressure, and it can be denoted by measuring the height of the valley in the white-light optical spectrum of the interferometer.
3. Experiment and discussion
Figure 5 is the schematic diagram illustrating the mechanism of interrogating the distributed fiber optic pressure sensor. A broadband amplified spontaneous emission (ASE) source, ranged from 1525 nm to 1565 nm, is used to illuminate the sensor through a 2 × 2 coupler. A sawtooth wave is triggered by a computer to drive a fiber Fabry–Pérot tunable filter (FFP-TF). The FFP-TF has a bandwidth of 0.1 nm and a free-spectrum range (FSR) of 65 nm. The wavelength-swept light is divided into two beams. One beam is injected into the PCF sensor line, and the reflected light is photo-detected by PD1. Another beam is injected into an etalon that has a comb standard wavelength. The etalon has an FSR of 0.8 nm (100 GHz), and a finesse of 14. The wavelength thermal stability of the etalon is better than 0.7 GHz from 0 °C to 70 °C. A fiber Bragg grating with bandwidth of 0.7 nm is series-connected with the etalon to remove one peak from the spectrum of the etalon, making a marker on the spectrum to identify the fixed wavelength of all other peaks. The fixed wavelength of the etalon is used to calibrate the output wavelength of the FFP-TF because of the large hysteresis caused by the piezoelectric transducer. After the spectra of a sensor and etalon are sampled into a computer, the wavelength calibration is firstly performed to change the spectrum of the sensor from sampling sequence to wavelength sequence by using the spectrum of the etalon. Then a digital resample is performed to obtain the optical spectrum of the PCF sensor head with a resolution of 1 pm [27].
When the PCF was not pressed, the white-light optical spectrum of the interferometer is shown in Fig. 6 within the wavelength range from 1531nm to 1560nm. The two adjacent valleys in the optical spectrum were marked by two vertical lines and the wavelengths were λ1 = 1545.964nm and λ2 = 1553.342nm, respectively. The Δneff was measured to be 2.034 × 10−3 by using Eq. (1). Then, a pressure was applied on the PCF, which leaded to the interferometric optical spectrum changed due to the change of the OPD. We mounted the PCF onto an aluminum plate, and a thin steel bar with the diameter of 0.8 millimeter was placed on the PCF transversely. Six positions on the PCF with a spatial separation of 1cm were interrogated. Figure 7 shows six optical spectra when the PCF was pressed at six different locations. In the six optical spectra, we measured the pressure positions by using the wavelengths of two adjacent valleys. The calculated results are shown in Table 1 . There are ± 0.1cm variation between the experimental results and the real distance for an 8cm-long PCF. The difference is caused by the errors in determining the wavelength of a valley and the inaccuracy of the pressure locations.
Fig. 7 The interference patterns with pressure on different points, the distances from the pressure point to the filmed end are: (a) 1cm, (b) 2cm, (c) 3cm, (d) 4cm, (e) 5cm, (f) 6cm.
Table 1. Identification of Pressure Position
The pressure response of the sensor at a fixed position was also investigated by measuring the height of the valley on the white-light optical spectrum. At a position, eight different external forces, which were 10, 13, 20, 23, 30, 33, 40, 43 N respectively, were applied. In our experiment, the pressure was applied on the PCF through a thin steel bar. The diameter of the coated PCF is 250μm, the contacted area is the fiber coating layer, and the length of the fiber in contact with the steel bar is 0.8 mm. One end of the thin steel bar was put on the PCF, and the other end was fixed on the aluminum plate. In this way the real force applied to the sensor was approximately half the force loaded on the thin steel bar. Since the contacted area is 2 × 10−6m2, the pressure corresponds to the force can be evaluated, based on a calculation with the equation P = F/S [28]. Thus, the forces 10, 13, 20, 23, 30, 33, 40, 43N, applied on the PCF, are corresponding to pressures, 363, 471, 725, 834, 1088, 1197, 1451, 1559-pis, respectively. With the increase of the external force, the height of the valley descended distinctly. The relationships between the pressure and the height of the valley are shown in Fig. 8 . It is observed that the height of the valley linearly decreased with the increase of the pressure, as theoretically predicted in section 2.
Fig. 8 The relationships between the pressure and the valley at different pressure location, apart from the fiber splice: (a) 1cm, (b) 2cm, (c) 3cm, (d) 4cm, (e) 5cm, (f) 6cm.
In Fig. 8, we notice that the pressure sensitivity is different at different positions. The sensitivity is 0.00007, 0.00032, 0.00013, 0.00014, 0.00025 and 0.00017 V/psi, respectively, when the pressure is applied on the PCF with 1cm increment apart from the fiber splice. This can be understood by the followed explanation. The sensitivity is decided by the initial phase of the interferometer. At different pressure position, the OPD of the interferometer is different, thus the initial phase of the interferometer is changed with pressure position. When the initial phase is nπ + π/2, the sensitivity is highest, and at the initial phase of nπ, the sensitivity is lowest. However, at a fixed position, we can obtain a linear output between the pressure and the height of the valley.
This sensor might have problem dealing with the application of more than two pressure points. The sensor might suffer cross-sensitivity with two pressure points, which could limit the practicability as a distributed pressure sensor. A further work on the multi-point measurement is being investigated in our lab.
4. Conclusion
In conclusion, we have demonstrated a novel distributed fiber optic pressure sensor based on a section of all-solid photonic band gap fiber. The sensor is used to locate the position of the pressure point and measure the pressure simultaneously. The distributed fiber optic pressure sensor is easy to fabricate at a low cost with a common fusion splicer and cleaver, and it is anticipated to be used in the security alert, civil building, and smart structure and so on.
Acknowledgments
This work is supported by Natural Scientific Foundation of China (51075037), Defense Equipments Foundation of China (9140A05060411BQ0115), Aeronautics Key Foundation of China (20110343004), and the Doctoral Foundation of Education Ministry of China (20101101110014).
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