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Abstract
A novel fiber curvature sensor without temperature cross interference based on a single hole twin eccentric core fiber has been proposed. Anti-resonant mechanism combined with inline Mach-Zehnder interference (MZI) structure are applied to the measurands detection. The spectrum is composed of a comb spectrum caused by the inline MZI and several dominant resonant wavelengths induced by anti-resonant effect. The curvature sensitivity of −1.54dB/m−1 can be achieved by intensity demodulation of the selected dip of Gaussian fitting. Similarly, the temperature sensitivity of 70.71pm/°C and 34.17pm/°C are respectively achieved by tracking coherent decrease point obtained by the FFT band pass filter method and Gaussian fit dip. Consequently, a relatively higher resolution of temperature measurement can be realized by the two methods mentioned above. The proposed sensor has a great potential for structural health monitoring, such as buildings, towers, bridges, and many other infrastructures due to its compact structure, easy fabrication and without cross impacts.
© 2017 Optical Society of America
1. Introduction
Optical fiber curvature sensors have been widely used in structure health monitoring and distributed sensing applications, etc [1,2]. Compared with the traditional curvature sensor based on mechanical and electronic technologies, the fiber type has more profound intrinsic advantages, such as compact size, high sensitivity and immune to electromagnetic interference, etc. However, curvature measurement is easy to be influenced by the external environment such as temperature variation in practical applications [3,4]. In order to avoid temperature interference, many compensation or independent detection methods have been proposed and conducted [5,6]. One of the most common ways is the crossing matrix method, but it also has the cross interference and is difficult to distinguish the dual-parameters stated above [7–9]. By contrast, the cascaded structure is regarded as a relatively effective method to avoid the crosstalk. For example, some inline interference structures cascaded with fiber Bragg grating (FBG) [10–12] and long period grating (LPG) [13–15] are adopted. Nevertheless, the whole structure is large size, complex and difficult to fabricate. Therefore, some new structures or mechanisms have been proposed to overcome these shortcomings.
Recently, different kinds of special fiber device have been used for curvature and temperature sensing, such as a LPG in a dual-concentric-core fiber [16], eccentric core fiber Bragg gratings [17], multi-core optical fiber [18] and Hollow Annular Core Fiber [19]. Moreover, some odd shape of special fibers based on anti-resonant mechanism is also proposed. The most typical structure is the nested in a hollow-core fiber [20–23]. Additionally, hexagram hollow core fiber [24], hollow-core nodeless anti-resonant fiber [25] and hollow core photonic crystal fiber [26] based on hollow-core fiber [27–29] are also selected as good alternatives for temperature, curvature and twist sensing, etc, while most of these special fibers are only used for a single parameter detection. As a consequence, an anti-resonant mechanism combined with inline interference structure is a better candidate for multi-parameters measurement without crossing interference.
In this paper, we demonstrated a novel fiber sensor by the integration of an anti-resonant mechanism and an inline MZI. A newest special fiber, namely single hole twin eccentric cores fiber (YOEC, 125μm) is designed to generate anti-resonant effect and form inline MZ structure. Thus, it is clear that the spectrum is composed of two parts, corresponding to the comb spectrum generated by the MZI structure and several resonant wavelengths formed by the anti-resonant effect. The wavelength and intensity demodulation is used for the temperature and curvature, respectively. The two measurands detection are realized by tracking the intensity variation and wavelength shift of the coherent decrease point obtained by the FFT band pass filter method and Gaussian fit dip. That is, there is only wavelength shift without intensity variation when detecting the temperature. In a similar way, the curvature measurement merely experiences intensity variation while no wavelength shifts. Hence, simultaneous measurement of the above mentioned two parameters without cross sensitivity can be achieved. Furthermore, the size of the sensor head is only 2.6mm, which is suitable for the engineering application due to the compact structure and easy fabrication.
2. Structure of single hole twin eccentric cores fiber and principle
Compared with traditional regular twin core fiber, the characteristic of the designed single hole twin eccentric cores fiber is that the fiber core is replaced by a large air hole and one of a fiber core is suspended on the inner surface of the cladding. As shown in Fig. 1(a), another core is asymmetrical distributed outside of the air hole. It can be seen from Fig. 1(b) that the core1 is suspended in the air hole which locates in the middle of the fiber, while core2 is inserted into the cladding, corresponding to the eccentric core.
Fig. 1 (a) The cross section microscope images of the single hole twin eccentric cores fiber; (b) Three-dimensional stereoscopic schematic diagram of the single hole twin eccentric cores fiber.
In view of the working principle of the single hole twin eccentric cores fiber, the optical field distribution in the whole fiber is of great importance. We select the full-vector finite element method to analyze the optical properties in this special fiber. Figure 2(a) shows that the size of the core and air hole are 9.1μm and 40μm, respectively. The cladding is identical to the common SMF. It is obvious that LP01 mode possesses the dominant power in the air hole which is shown in Fig. 2(b). Figure 2(c) indicates that the cladding modes are full filled in the whole cladding. Moreover, it also can be seen from Figs. 2(b) and 2(c) that optical fields will exist in the two cores as well due to the refractive index higher than cladding and air hole. As a result, an inline MZ interference structure is formed.
Fig. 2 (a) The aperture size of the single hole twin eccentric cores fiber; (b) The mode field distribution in the middle air hole; (c) The mode field distribution in the cladding.
A section of single hole twin eccentric cores fiber with the length of 2.6mm is fusion spliced between two single mode fibers (SMFs). It is widely known that the reflection and refraction will be generated when the beams transmit between different mediums. Specifically, for the beams transmitting from optically dense medium to the optically thin medium, these two effects both exist only when the incidence angle is smaller than the critical angle. As shown in Fig. 3(a), the part of transmitted light beams are scattered back into the core at the anti-resonant wavelength. At the same time, another part of the light beams are leaking into the cladding and then leaking out to the external environment at the resonant wavelength. Thus, the anti-resonant mechanism is formed in this optical waveguide [25–27]. The sensing fiber cladding modes are excited by the two collapsed splicing points due to the mode filed mismatch. For this reason, there are also core modes within the two cores based on the optical fiber mode coupling theory [17]. The multimode inline MZI is formed owing to the excited cladding modes and core mode.
Fig. 3 (a) Guiding mechanism of the single hole twin eccentric cores fiber; (b) Beam propagation simulation of the anti-resonant effect at the wavelength of 1570nm.
In order to clearly observe the optical field distribution in single hole twin eccentric cores fiber, a full-vector beam propagation simulation is conducted. The length of the proposed special fiber is selected as 2.6mm which is same as the one we have used in the experiment. The incident wavelength is selected as 1570nm and the beam propagation direction is along z-axis. Then the optical intensity distribution is simulated as shown in Fig. 3(b). It is apparent that a smaller part of the beams leaking out to the external environment which is the resonant wavelength as above mentioned. Meanwhile, most part of the beams form the anti-resonant effect which is more perceptual intuition in Fig. 3(b). Additionally, part of beam is also transmitting in air hole and cladding. Therefore, an inline MZI structure is formed at the same time. This phenomenon is consistent with the transmission path in Fig. 3(a).
3. Theoretical analysis of the spectrum
According to the analysis of section 2, the transmission spectrum of the proposed structure is governed by the two effects of anti-resonant and inline MZI. It should be noticed that the back-scattering beams experience several times of reflections in the cladding. Thus, a Fabry-Perot (FP) resonator is formed in the silica cladding. The anti-resonant effect in single hole twin eccentric cores fiber can be regarded as a reflective FP interferometer [28]. Consequently, the transmission of the anti-resonant effect can be expressed as [30]:
where F represents the fringe finesse coefficient of the multiple-beam interferometer. A and l are the intensity coefficient of the whole anti-resonant effect and optical path of the anti-resonant beams. and are the wavelength of the spectrum and effective refractive index of the cladding, respectively. In addition, the wavelength under the resonant condition can be derived from the following equation [24]:where d is the thickness of the single hole twin eccentric cores fiber cladding, and m is the resonance order. n1 and n2 are the refractive index of the single hole twin eccentric cores fiber cladding and the air, respectively.The proposed structure also generates the MZ interference other than an anti-resonant effect. There are several modes formed the inline MZ structure, as seen in Figs. 3(a) and 3(b), including fiber core modes, lower and higher order cladding modes. The dominant interference is formed between fiber core modes and lower order cladding modes. Therefore, the transmission of the multimode interference can be normalized as:
where Bi is the intensity coefficient of the comb spectrum. is the effective refractive index difference between fiber core mode and cladding modes. L is the physical length of the special fiber cladding, and i represents the order of the cladding modes.As we all know, higher order cladding modes have higher thermo-optic coefficient [13]. On the basis of this theory, the band pass filter method is adopted in the Fast Fourier Transform (FFT) to select the suitable cladding modes. Then the inline MZI signal is recovered by an Inverse Fast Fourier Transform (IFFT) method. The spectrum after the band pass filtering processing of the initial spectrum is displayed in the Fig. 4, which demonstrates a sinusoidal waveform. Therefore, the environment temperature can be precisely monitored by the FFT band pass filter method in conjunction with anti-resonant effect.
The total transmission of the proposed fiber sensor is the sum of the two parts due to the combination of the aforementioned two structures. In order to compare with experiment spectrum, the simulation parameters of A, Bi, F, d and L are selected as 1.4 × 10−3, 9 × 10−4, 1000, 45.55μm and 2.6mm, respectively. As shown in Fig. 5(a), the two transmission spectrums respectively represent the experiment and simulation spectrum, which is composed of three dominant dips and a uniformed comb spectrum. The resonant wavelengths generated in the simulation spectrum are attributed to the leaking out light beams. What’s more, the simulation result is quite consistent with the experiment spectrum, which is not uniformed owing to the scattered back light of the anti-resonant effect. The resonant wavelength of the FP cavity formed by the silica cladding and air hole can be obtained by a Gaussian fits method, which is shown in Fig. 5(b). The three dominant resonant wavelengths, namely dip1, dip2 and dip3, are consistent with the Fig. 5(a). Since the superposition spectrum has both the characteristics of the inline MZI and anti-resonant effect, it can be regarded as a good candidate to be applied to the multi-parameters simultaneous measurement.
Fig. 5 (a) The experiment and simulation spectrum; (b) The experiment spectrum and the Gaussian fits of the dip.
4. Experimental results and discussions
As described from section 3, the proposed sensor has been shown to be a potential tool for multi-parameters measurement. A curvature and temperature experiment is conducted to investigate the sensing properties. The schematic diagram of the experimental setup for curvature measurement is exhibited in Fig. 6. Especially, an electronic control method is selected to reduce the artificial error of the whole experimental setup, which contains broadband light source (BBS), optical spectrum analyzer (OSA, Yokogawa AQ6370c) and two-dimensional (2D) translation stages. The original interval between the fixed and translational stage is L = 16cm. The sensor head is placed in the middle of the two stages with a slight tension to keep fiber straight initially. The distance between the two stages on the smooth lead rail can be adjusted 50μm at one time by personal computer (PC).
The curvature variation can be derived from 0.94m−1 to 2.10m−1 according to the equation of Rsin(L/2R) = (L-d)/2. In this experiment, dip2 is selected to monitor the curvature variation trend, corresponding to the resonant wavelength of 1570nm. The intensity of the actual wavelength decreases as the curvature increases, which is shown in Fig. 7(a). The actual wavelength circled by the red ellipse is about 1571nm, and the inset is the enlarged view of the intensity variation. For actual wavelength, the intensity varies while the wavelength shifts hardly. Likewise, a Gaussian fitting method is also applied to the curvature measurement. Figure 7(b) reflects that there is also only intensity variation without wavelength shift. The Gaussian fitting resonant wavelength of dip2 undergoes intensity decreasing when the curvature increases from 0.94m−1 to 2.1m−1.
Fig. 7 (a) The intensity variation of the actual resonant wavelength with the curvature increased; (b) The intensity variation of the Gaussian fits resonant wavelength (dip2) with curvature increasing from 0.94m−1 to 2.1m−1.
The curvature sensitivity can be obtained by tracking the coherent decrease point in Figs. 7(a) and 7(b), dip2 and 1571nm are selected as tracking wavelength, respectively. Both the intensities of the two wavelengths are fitted in Fig. 8. It can be seen that the sensitivities of −1.54dB/m−1 and −1.31dB/m−1 can be achieved by the linear fit of dip2 and actual resonate wavelength with the curvature increasing from 0.94m−1 to 2.1m−1. Moreover, the linear fit of the wavelength shift is a horizontal line, which suggests the wavelength fluctuation can be neglected in curvature experiment. It should be noted that the phenomenon of the tiny wavelength fluctuation is introduced by the light source shiver. The curvature sensitivity is relatively small owing to the fact that the incidence angle is always smaller than the critical angle when the curvature varies in a tiny range. Therefore, the leaking out power of the resonant wavelength is less than the scatted back power because the bending merely changes the incidence angle. The intensity demodulation is used for the curvature measurement, which can avoid the cross impacts of temperature variation well.
Fig. 8 Linear fit of dip2 and actual resonate wavelength about the sensitivities of −1.54dB/m−1 and −1.31dB/m−1 with the curvature increasing from 0.94m−1 to 2.1m−1, respectively.
Temperature is of great significance in the field of engineering system, and three methods are adopted to detect the temperature variation at the same time. Temperature measurement is realized by heating a TEC module from 20°C to 55°C. In order to more precisely measure the temperature variation, a Gaussian fit combined with a FFT band pass filter method is applied to demodulate the anti-resonant spectrum. As shown in Fig. 9(a), we select the typical loss peaks to track the temperature variation with the wavelength window from 1550nm to 1590nm. Besides, dip2 obtained by Gaussian fit is also used for temperature measurement. It is apparent that both of the two types of selected dips have a red shift. The length variation of the sensing fiber cladding can be ignored here due to the lower thermal expansion coefficient of the cladding. Besides, the effective refractive index of the sensing fiber cladding changes faster than the air hole. Therefore, it can be seen that the wavelength shift of the two selected dips are relatively smaller owing to the lower thermo-optic coefficient.
Fig. 9 (a) Gauss fit of the transmission spectrum with temperature from 20°C to 55°C at the state of straight line; (b) FFT band pass filter of the higher order cladding modes for temperature measurement.
The FFT band pass filter method is adopted to filter out the higher order cladding modes in section 3. Figure 9(b) is the recovery spectrum by FFT band pass filter and IFFT,and its response to temperature measurement with the step of 10°C. It is easy to find the selected coherent decrease point has an obvious red shift. Based on this, a relatively higher resolution of the temperature measurement can be achieved by combining the Gaussian fits with FFT band pass filter method. The former method can acquire a general range of the temperature variation, and the later can achieve a precise measurement value.
The temperature sensitivity can be obtained by linear fit of the tracking coherent decrease point. Figure 10 illustrates that the three different methods achieve the temperature sensitivity of 70.71pm/°C, 34.17 pm/°C and 23.57 pm/°C. The sensitivity of FFT band pass filter method is twice and triple of the Gaussian fits and actual anti-resonant wavelength method, respectively. The experimental results verify that the higher order cladding modes are more sensitive to the anti-resonant light beams. Furthermore, the intensity linear fit curve of the tracking dips are approximate a horizontal line, that is the intensity of the selected dips nearly no variation. Consequently, the temperature detection can only use the wavelength demodulation method. From Figs. 8 and 10, curvature and temperature can be demodulated by tracking the power and wavelength shift of the resonant wavelength, respectively. Overall, the two measurands can be measured simultaneously without cross impacts.
5. Conclusions
In this work, we proposed and experimentally demonstrated a novel fiber sensor based on anti-resonant effect combined with inline MZI. Simultaneous measurement of curvature and temperature without cross sensitivity can be achieved by Gaussian fits and FFT band pass filter method. The curvature sensitivity is 1.54dB/m−1 by demodulating the intensity variation of the selected Gaussian fits dip. As well as tracking the coherent decrease point obtained by the FFT band pass filter method and Gaussian fit dip, the temperature sensitivity of 70.71pm/°C and 34.17pm/°C are achieved, respectively. Thus, a high resolution of the temperature measurement can be realized by the two methods stated above. It should be noticed that the proposed sensor head is a section of the single hole twin eccentric cores fiber whose length is only 2.6mm. Therefore, it shows great potential to be developed in the applications of the structural health monitoring, such as buildings, towers, bridges, and many other infrastructures.
Funding
National Natural Science Foundation of China (NSFC) Grant (No. 61275083) and (No. 61290315); Natural Science Foundation of Hubei Province Grant (No. 2014CFA051).
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