- Email: [email protected]
Sensitivity dependence of fiber loop mirror on the length of high birefringence fiber
Sensors and Actuators A 247 (2016) 393–396
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Sensitivity dependence of fiber loop mirror on the length of high birefringence fiber Peng Zu a , Chi Chiu Chan b,∗ , Ping Lam So c a b c
Energy Research Institute, Nanyang Technological University, 637553, Singapore School of Chemical and Biomedical Engineering, Nanyang Technological University, 637457, Singapore School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
a r t i c l e
i n f o
Article history: Received 30 March 2016 Received in revised form 14 June 2016 Accepted 15 June 2016 Available online 18 June 2016
a b s t r a c t A model of fiber loop mirror with the distinct concepts of sensing length and total length is established. The sensitivity dependence of fiber loop mirror on the sensing length and total length is discussed theoretically and experimentally. The sensor sensitivity showed being linearly dependent of the ratio of the sensing length and the total length. The experimental results well support the predications by the model. © 2016 Elsevier B.V. All rights reserved.
Keywords: Sensitivity Optical fiber sagnac interferometer (OFSI) Fiber loop mirror
1. Introduction Thanks to the great advances in optical-fiber communication technologies, optical fiber Sagnac interferometer (OFSI) was first demonstrated more than 35 years ago [1]. At the beginning, OFSI was used in fiber optic gyroscope (FOG) systems to detect the rotation with respect to inertial system by means of Sagnac effect [2]. In order to guarantee the accuracy of rotation measurement, any type of non-reciprocity other than rotation should be avoided or reduced to a certain extent such as Faraday rotation, thermal effect, mechanical forces and so on. However, from a different perspective, these non-reciprocal phenomena also offered new opportunities for measuring these parameters. For example, temperature sensor based on OFSI was reported in 1997 [3]. Current sensor based on non-birefringent OFSI was proposed in 1988 [4]. Since then, more OFSI-based sensors or devices were presented parallel to the long inevitable development period of FOG [5–11]. Although this kind of sensors employs the same OFSI structures, their principle, which is modal interference, has nothing to do with Sagnac effect. In order to distinguish this kind of sensors from FOG for convenient description in the following discussion, we call it fiber loop mirror (FLM) sensors. The significant distinctions between FOG and FLM sensors are their operating light modes and their ways to accumulate the
∗ Corresponding author. E-mail address: [email protected] (C.C. Chan). http://dx.doi.org/10.1016/j.sna.2016.06.023 0924-4247/© 2016 Elsevier B.V. All rights reserved.
optical phase difference (OPD). FOG systems operate on single polarization mode and the OPD is generated by Sagnac effect. This linearly polarized light is split into two light waves by the 3 dB polarization maintaining (PM) coupler. If the fiber loop of FOG is rotated, the light wave propagating along the same direction is some kind of “slower” and has to “chase” the rotation while the light wave couterpropagating is some kind of “faster”, so the OPD between the two light waves occurs by means of the relativity theory. This OPD is proportional to the length of the polarization maintaining fiber (PMF) within the Sagnac loop. The typical length of PMF in a practical FOG system is around 1 km [12]. FLM sensors operate on two orthogonal polarization modes and the OPD is generated by means of birefringence effect. The nonpolarized light is split into two light waves by a non-PM 3 dB coupler. Both of the couterpropagating light waves decompose into two orthogonal linearly polarized light wave components along the fast and slow axes respectively when they enter the high birefringence fiber (HBF), of which one component propagates faster than the other due to birefringence effect. The Sagnac loop serves to beat together the fast and slow components so that interference can be produced. The sensitivities of FLM sensors depend on the length of the HBF within the Sagnac loop, but the dependence relationship was not clearly elaborated in the literatures. Sometimes, even contradictory conclusions were reported. For example, some researchers tended to believe longer HBF length within the Sagnac loop gave a higher sensitivity [13,14]. Meanwhile, some researchers observed the phenomenon that the sensitivity was irrelative to the HBF length [15] while some researcher just assumed this
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Fig. 1. Schematic diagram of the structure of FLM. Inset: the cross section of traditional PMF, pander fiber.
Table 1 Parameters chosen for the FLMs and their results. FLM
L0 (cm)
L (cm)
L0 /L
(pm/)
A B C D E F G H
4.9 4.7 5.1 2.0 10.2 47.6 4.3 9.3
6.5 17.1 52.2 50.0 50.5 50.7 4.7 9.7
0.75 0.27 0.10 0.04 0.20 0.94 0.87 0.96
19.580 6.408 2.438 1.021 5.476 25.305 22.530 26.407
conclusion [16]. In our previous work, we found that higher sensitivity can be obtained with shorter HBF length [17]. Nonetheless, in most of the works, the HBF lengths within the FLM sensors were just randomly chosen without clear guideline. One possible reason for these contradictory conclusions is that the sensitivity property of FLM sensors was confused with FOG. Another possible reason is that only part of the HBF within the Sagnac loop worked as the sensing element, which was very common among various FLM sensors [5,13,18]. For instance, Zhao demonstrated a curvature sensor with 100 cm PMF but only 14.2 cm was used as sensing element [14]. Kim proposed a temperature sensor by using PCF with 20 cm length infiltrated while the remaining 80 cm length unfilled [19]. Chen carried out a humidity sensor based on partly chemically etched HBF [20]. This partially involved HBF makes the conditions more complex. In this work, we establish a model of FLM sensors and investigate the sensitivity dependency on the HBF length in order to clarify these confusions existing in the literatures. 2. Operating principle A typical FLM is configured simply by splicing a section of HBF and a single mode fiber (SMF) 3 dB coupler to form a Sagnac loop, which is shown in Fig. 1. The whole length of the HBF is denoted as L, whilst partial length of the HBF functions as birefringence sensitive element for sensing measurement, which is denoted as L0 . An OPD is introduced between the two orthogonal polarization modes due to the birefringence of HBF. Hence, an approximately sinusoidal interference spectrum is produced as the two beams beat together again at the coupler, which is given by [5] T = (1 − cos)/2
(1)
where = 2BL/ is the OPD between the two orthogonal modes; where B and L are the birefringence and length of the HBF, respectively; is the wavelength of the light. If the condition = 2m
(m is an integer) is fulfilled, the transmission spectrum reaches its minimum. The wavelength of the m-th order fringe on the transmission spectrum can be given as m = BL/m
(2)
Hence, the period of the interference spectrum or the free spectral range (FSR) between the two adjacent transmission dips S can be given by S = 2 /BL
(3)
Eq. (3) shows that the FSR (S) is inversely proportional to L. Usually, the sensitivity of FLM sensors is described by spectrum shift or dip wavelength shift. By considering the relationship between the spectrum shift and OPD i.e. = S/2 and substituting Eq. (3) into this equation, the sensitivity can be deduced as [10] =
B L0 B L
(4)
Eq. (4) shows both the sensing length (L0 ) and the total length (L) contribute to the sensitivity. From Eq. (4) we can predict in some special cases: (i) If L = const, the sensitivity is proportional to the sensing length (L0 ); (ii) If L0 = const, the sensitivity is inversely proportional to the total HBF length (L); (iii) If L = L0 , which means the full length of HBF is used for sensing measurement, Eq. (4) becomes = (B/B), which is the maximum sensitivity. Meanwhile, the sensitivity is independent on the HBF length (L). 3. Experimental results and discussion In order to verify the above predictions, a series of FLM sensors with different sensing and total lengths of HBF were fabricated. The sensitivities of these sensors were measured by taking strain test. The HBF employed was traditional PMF, panda fiber (PM1550-HP), whose cross section is shown in the inset in Fig. 1. The birefringence of the PMF was 3.3 × 10−4 . A section of PMF was
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Fig. 2. Transmission spectra of the FLMs with different HBF-lengths (a) 6.5 cm (b) 17.1 cm (c) 52.2 cm.
Fig. 3. (a) Transmission spectrum of FLM A shifts with the applied strain (b) Relationship between the wavelength shift and the applied strain for FLMs A, B and C (L0 = 5 cm).
Fig. 4. (a) Relationship between the wavelength shift and the applied strain for FLMs D, E and F (L = 50 cm) (b) Relationship between the sensitivity and the length ratio.
removed coating and attached to the translation stages with a resolution of 0.01 mm for strain applying. The transmission spectra were monitored with an amplified spontaneous emission (ASE, 1520–1620 nm) light source and an optical spectrum analyzer (OSA, AQ6370). We designed 3 experiments to verify the 3 special cases. The sensing lengths, total lengths used in these FLMs and their sensitivities are listed in Table 1. The first experiment is designed to verify the case (i). FLM A, B and C are used in this experiment with the same sensing lengths of around 5 cm but different total lengths of 6.5, 17.1 and 52.2 cm, respectively. The transmission spectra of FLM A, B and C are showed in Fig. 2. They are all similar sinusoidal waveforms, whose extinction ratios are about 30 dB. The differences among the spectra are their FSRs, which are 58.52, 19.58 and 8.89 nm for FLM A, B and C, respectively. This result shows the FSR is inversely proportional to the total HBF length (L), which well supports the prediction of Eq. (3). In order to compare the sensitivities of these 3 FLMs, the same amount of strain was applied on the PMFs from 0 to 4m with an interval of 0.4m through the translation stages. The leftmost dip on the transmission spectrum of FLM A was chosen as an example to show the variation trend detailedly in Fig. 3(a). A red shift from 1526.16 to 1605.46 nm, totally 79.30 nm, occurred as the strain was
increased from 0 to 4m. The relationships between the strain and the wavelength shift of the transmission spectra of the 3 FLMs are shown in Fig. 3(b). The linear fit method was applied to the curves with high goodness of fit R2 values and the corresponding sensitivities of FLM A, B and C are 19.58, 6.408 and 2.438pm/, respectively, which have the approximate relationship of 19.58: 6.408: 2.438 ≈ 1/6.5: 1/17.1: 1/52.2. This result well support the prediction of case (i), i.e. ∝ 1/L, which means the sensitivity of FLM sensor is inversely proportional to the total HBF length provided the sensing lengths are the same. This experiment shows the total length of HBF affects the sensitivity significantly although it doesn’t get involved into the sensing directly. This conclusion is also in accordance with the experimental result in ref [17]. The second experiment is designed to verify the case (ii). FLM D, E and F are used in this experiment with the same total length of around 50 cm but different sensing lengths of 2.0, 10.2 and 47.6 cm respectively. The transmission spectra are similar to the previous ones. The strain test was carried out as the same method with previous experiment. The relationships between the strain and the wavelength shift of the transmission spectra of the 3 FLMs are shown in Fig. 4(a). The linear fit method was applied to the curves with high goodness of fit R2 values and the corresponding sensitivities of FLM D, E and F are 1.021, 5.476 and 25.305pm/
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P. Zu et al. / Sensors and Actuators A 247 (2016) 393–396
respectively, which have the approximate relationship of 2.0: 10.2: 47.6 ≈ 1.021: 5.476: 25.305. This result well support the prediction of case (ii), i.e. ∝ L0 , which means the sensitivity of FLM sensor is proportional to the sensing length provided the total HBF lengths are the same. It also explains why researchers tended to use longer HBF length to achieve a higher sensitivity [13,14]. The third experiment is designed to verify the case (iii). FLM F, G and H are used in this experiment with the total HBF lengths of 50.7, 4.7 and 9.7 cm respectively. In this experiment, the full length of HBF was used as the sensing length, i.e. L = L0 . However, because the stick points between the fiber and the translation stages needed to avoid the splicing points, the actual sensing lengths, which are 47.6, 4.3 and 9.7 cm respectively, are slightly shorter than the according total length. The strain test was carried out similarly. The sensitivities for FLM F, G and H are 25.305, 22.530, 26.407pm/ respectively. These sensitivities are so close that they can be considered as almost equal. The small differences among them are caused because the actual sensing lengths are slightly shorter than their according total HBF length. Therefore, we can conclude that if the full length of the HBF is used for sensing, i.e. L = L0, the sensitivity is independent on the HBF length. This experimental result supports very well the prediction of case (iii). This conclusion is also in accordance with the phenomenon reported in Ref. [15]. In order to further verify Eq. (4), all the sensitivity data from FLM A to H are plot in Fig. 4(b). Liner fit is applied to the data and it shows a good linear relationship between the sensitivity and length ratio (L0 /L) with a high goodness-of-fit coefficient of 0.9974. It means the sensitivity is proportional to the length ratio, i.e. ∝ L0 /L. Specially, if L = L0 (case iii), i.e. L0 /L = 1, the obtained sensitivity reaches its maximum sensitivity can be achieved. From Fig. 4(b), we can tell that this maximum sensitivity is 27.014 pm/. The achieved sensitivities of FLM F, G and H are quite close to this maximum value. 4. Conclusions In this work, we first pointed out the confusion and contradictory results in the literatures with regards to the sensitivity dependency of FLM sensors on the HBF length used within the Sagnac loop. Then, we distinguish the roles of sensing length and total length of HBF. With these concepts explained, a model of FLM is established and the equations are re-deduced. The equations show the sensitivity of FLM sensors is linear proportional to the length ratio. The experimental results well support the theoretical analysis. This model provides more insights on the sensitivity dependence on the HBF length and these conclusions can be used as the guideline for the FLM sensors. Acknowledgement This work was supported by the ENERGY MARKET AUTHORITY (LA/CONTRACT NO. NRF2013EWT-EIRP001-006)
References [1] B. Culshaw, The optical fibre Sagnac interferometer: an overview of its principles and applications, Meas. Sci. Technol. 17 (2006) R1–R16. [2] V. Vali, R.W. Shorthill, Fiber ring interferometer, Appl. Opt. 15 (1976) 1099–1100. [3] A.N. Starodumov, L.A. Zenteno, D. Monzon, E. De La Rosa, Fiber Sagnac interferometer temperature sensor, Appl. Phys. Lett. 70 (1997) 19–21. [4] P. Nicati, P. Robert, Stabilised current sensor using Sagnac interferometer, J. Phys. E: Sci. Instrum. 21 (1988) 791. [5] C. Zhao, Y. Jin, J. Kang, H. Gong, X. Dong, Recent progress of fiber loop mirror-based sensors in China Jiliang University, Photonic Sensors 2 (2012) 29–36. [6] P. Zu, C.C. Chan, W.S. Lew, Y.X. Jin, Y.F. Zhang, H.F. Liew, et al., Magneto-optical fiber sensor based on magnetic fluid, Opt. Lett. 37 (Febraury) (2012) 398–400. [7] P. Zu, C.C. Chan, L.W. Siang, Y.X. Jin, Y.F. Zhang, L.H. Fen, et al., Magneto-optic fiber Sagnac modulator based on magnetic fluids, Optics Lett. 36 (2011) 1425–1427. [8] P. Zu, C.C. Chan, Y.X. Jin, Y.F. Zhang, X.Y. Dong, Fabrication of a temperature-insensitive transverse mechanical load sensor by using a photonic crystal fiber-based Sagnac loop, Meas. Sci. Technol. 22 (2011). [9] P. Zu, C.C. Chan, Y.X. Jin, T.X. Gong, Y.F. Zhang, L.H. Chen, et al., A temperature-Insensitive twist sensor by using low-birefringence photonic-Crystal-Fiber-Based sagnac interferometer, IEEE Photonics Technol. Lett. 23 (2011) 920–922. [10] X.Y. Dong, H.Y. Tam, P. Shum, Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer, Appl. Phys. Lett. 90 (April) (2007). [11] P. Zu, C.C. Chan, W.S. Lew, Y.X. Jin, H.F. Liew, L.H. Chen, et al., High extinction ratio magneto-Optical fiber modulator based on nanoparticle magnetic fluids, IEEE Photonics J. 4 (August) (2012) 2012. [12] H.C. Lefevre, The Fiber-Optic Gyroscope, second edition, Artech House Publishers, 2014, pp. 23. [13] A.M.R. Pinto, M. Lopez-Amo, Photonic crystal fibers for sensing applications, J. Sensors 2012 (2012) 21. [14] Y. Zhao, Y. Jin, H. Liang, J. Wang, X. Dong, Curvature sensor based on fiber loop mirror with polarization maintaining fiber, Microwave Opt. Technol. Lett. 53 (2011) 2066–2068. [15] H.Y. Fu, H.Y. Tam, L.-Y. Shao, X. Dong, P.K.A. Wai, C. Lu, et al., Pressure sensor realized with polarization-maintaining photonic crystal fiber-based Sagnac interferometer, Appl. Optics 47 (2008) 2835–2839 (2008/05/20). [16] W.W. Qian, C.L. Zhao, S.L. He, X.Y. Dong, S.Q. Zhang, Z.X. Zhang, et al., High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror, Optics Lett. 36 (2011) 1548–1550. [17] P. Zu, C.C. Chan, G.W. Koh, W.S. Lew, Y. Jin, H.F. Liew, et al., Enhancement of the sensitivity of magneto-optical fiber sensor by magnifying the birefringence of magnetic fluid film with Loyt-Sagnac interferometer, Sens. Actuators, B 191 (2014) 19–23. [18] O. Frazão, J. Baptista, J. Santos, Recent advances in high-birefringence fiber loop mirror sensors, Sensors 7 (2007) 2970¨C2983. [19] B.H. Kim, S.H. Lee, A.X. Lin, C.L. Lee, J. Lee, W.T. Han, Large temperature sensitivity of Sagnac loop interferometer based on the birefringent holey fiber filled with metal indium, Opt. Express 17 (February) (2009) 1789–1794. [20] L.H. Chen, C.C. Chan, T. Li, M. Shaillender, B. Neu, P. Balamurali, et al., Chitosan-Coated polarization maintaining fiber-Based sagnac interferometer for relative humidity measurement, IEEE J. Sel. Top. Quantum Electron. 18 (September–October) (2012) 1597–1604.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Sensitivity dependence of fiber loop mirror on the length of high birefringence fiber Peng Zu a , Chi Chiu Chan b,∗ , Ping Lam So c a b c
Energy Research Institute, Nanyang Technological University, 637553, Singapore School of Chemical and Biomedical Engineering, Nanyang Technological University, 637457, Singapore School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
a r t i c l e
i n f o
Article history: Received 30 March 2016 Received in revised form 14 June 2016 Accepted 15 June 2016 Available online 18 June 2016
a b s t r a c t A model of fiber loop mirror with the distinct concepts of sensing length and total length is established. The sensitivity dependence of fiber loop mirror on the sensing length and total length is discussed theoretically and experimentally. The sensor sensitivity showed being linearly dependent of the ratio of the sensing length and the total length. The experimental results well support the predications by the model. © 2016 Elsevier B.V. All rights reserved.
Keywords: Sensitivity Optical fiber sagnac interferometer (OFSI) Fiber loop mirror
1. Introduction Thanks to the great advances in optical-fiber communication technologies, optical fiber Sagnac interferometer (OFSI) was first demonstrated more than 35 years ago [1]. At the beginning, OFSI was used in fiber optic gyroscope (FOG) systems to detect the rotation with respect to inertial system by means of Sagnac effect [2]. In order to guarantee the accuracy of rotation measurement, any type of non-reciprocity other than rotation should be avoided or reduced to a certain extent such as Faraday rotation, thermal effect, mechanical forces and so on. However, from a different perspective, these non-reciprocal phenomena also offered new opportunities for measuring these parameters. For example, temperature sensor based on OFSI was reported in 1997 [3]. Current sensor based on non-birefringent OFSI was proposed in 1988 [4]. Since then, more OFSI-based sensors or devices were presented parallel to the long inevitable development period of FOG [5–11]. Although this kind of sensors employs the same OFSI structures, their principle, which is modal interference, has nothing to do with Sagnac effect. In order to distinguish this kind of sensors from FOG for convenient description in the following discussion, we call it fiber loop mirror (FLM) sensors. The significant distinctions between FOG and FLM sensors are their operating light modes and their ways to accumulate the
∗ Corresponding author. E-mail address: [email protected] (C.C. Chan). http://dx.doi.org/10.1016/j.sna.2016.06.023 0924-4247/© 2016 Elsevier B.V. All rights reserved.
optical phase difference (OPD). FOG systems operate on single polarization mode and the OPD is generated by Sagnac effect. This linearly polarized light is split into two light waves by the 3 dB polarization maintaining (PM) coupler. If the fiber loop of FOG is rotated, the light wave propagating along the same direction is some kind of “slower” and has to “chase” the rotation while the light wave couterpropagating is some kind of “faster”, so the OPD between the two light waves occurs by means of the relativity theory. This OPD is proportional to the length of the polarization maintaining fiber (PMF) within the Sagnac loop. The typical length of PMF in a practical FOG system is around 1 km [12]. FLM sensors operate on two orthogonal polarization modes and the OPD is generated by means of birefringence effect. The nonpolarized light is split into two light waves by a non-PM 3 dB coupler. Both of the couterpropagating light waves decompose into two orthogonal linearly polarized light wave components along the fast and slow axes respectively when they enter the high birefringence fiber (HBF), of which one component propagates faster than the other due to birefringence effect. The Sagnac loop serves to beat together the fast and slow components so that interference can be produced. The sensitivities of FLM sensors depend on the length of the HBF within the Sagnac loop, but the dependence relationship was not clearly elaborated in the literatures. Sometimes, even contradictory conclusions were reported. For example, some researchers tended to believe longer HBF length within the Sagnac loop gave a higher sensitivity [13,14]. Meanwhile, some researchers observed the phenomenon that the sensitivity was irrelative to the HBF length [15] while some researcher just assumed this
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Fig. 1. Schematic diagram of the structure of FLM. Inset: the cross section of traditional PMF, pander fiber.
Table 1 Parameters chosen for the FLMs and their results. FLM
L0 (cm)
L (cm)
L0 /L
(pm/)
A B C D E F G H
4.9 4.7 5.1 2.0 10.2 47.6 4.3 9.3
6.5 17.1 52.2 50.0 50.5 50.7 4.7 9.7
0.75 0.27 0.10 0.04 0.20 0.94 0.87 0.96
19.580 6.408 2.438 1.021 5.476 25.305 22.530 26.407
conclusion [16]. In our previous work, we found that higher sensitivity can be obtained with shorter HBF length [17]. Nonetheless, in most of the works, the HBF lengths within the FLM sensors were just randomly chosen without clear guideline. One possible reason for these contradictory conclusions is that the sensitivity property of FLM sensors was confused with FOG. Another possible reason is that only part of the HBF within the Sagnac loop worked as the sensing element, which was very common among various FLM sensors [5,13,18]. For instance, Zhao demonstrated a curvature sensor with 100 cm PMF but only 14.2 cm was used as sensing element [14]. Kim proposed a temperature sensor by using PCF with 20 cm length infiltrated while the remaining 80 cm length unfilled [19]. Chen carried out a humidity sensor based on partly chemically etched HBF [20]. This partially involved HBF makes the conditions more complex. In this work, we establish a model of FLM sensors and investigate the sensitivity dependency on the HBF length in order to clarify these confusions existing in the literatures. 2. Operating principle A typical FLM is configured simply by splicing a section of HBF and a single mode fiber (SMF) 3 dB coupler to form a Sagnac loop, which is shown in Fig. 1. The whole length of the HBF is denoted as L, whilst partial length of the HBF functions as birefringence sensitive element for sensing measurement, which is denoted as L0 . An OPD is introduced between the two orthogonal polarization modes due to the birefringence of HBF. Hence, an approximately sinusoidal interference spectrum is produced as the two beams beat together again at the coupler, which is given by [5] T = (1 − cos)/2
(1)
where = 2BL/ is the OPD between the two orthogonal modes; where B and L are the birefringence and length of the HBF, respectively; is the wavelength of the light. If the condition = 2m
(m is an integer) is fulfilled, the transmission spectrum reaches its minimum. The wavelength of the m-th order fringe on the transmission spectrum can be given as m = BL/m
(2)
Hence, the period of the interference spectrum or the free spectral range (FSR) between the two adjacent transmission dips S can be given by S = 2 /BL
(3)
Eq. (3) shows that the FSR (S) is inversely proportional to L. Usually, the sensitivity of FLM sensors is described by spectrum shift or dip wavelength shift. By considering the relationship between the spectrum shift and OPD i.e. = S/2 and substituting Eq. (3) into this equation, the sensitivity can be deduced as [10] =
B L0 B L
(4)
Eq. (4) shows both the sensing length (L0 ) and the total length (L) contribute to the sensitivity. From Eq. (4) we can predict in some special cases: (i) If L = const, the sensitivity is proportional to the sensing length (L0 ); (ii) If L0 = const, the sensitivity is inversely proportional to the total HBF length (L); (iii) If L = L0 , which means the full length of HBF is used for sensing measurement, Eq. (4) becomes = (B/B), which is the maximum sensitivity. Meanwhile, the sensitivity is independent on the HBF length (L). 3. Experimental results and discussion In order to verify the above predictions, a series of FLM sensors with different sensing and total lengths of HBF were fabricated. The sensitivities of these sensors were measured by taking strain test. The HBF employed was traditional PMF, panda fiber (PM1550-HP), whose cross section is shown in the inset in Fig. 1. The birefringence of the PMF was 3.3 × 10−4 . A section of PMF was
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Fig. 2. Transmission spectra of the FLMs with different HBF-lengths (a) 6.5 cm (b) 17.1 cm (c) 52.2 cm.
Fig. 3. (a) Transmission spectrum of FLM A shifts with the applied strain (b) Relationship between the wavelength shift and the applied strain for FLMs A, B and C (L0 = 5 cm).
Fig. 4. (a) Relationship between the wavelength shift and the applied strain for FLMs D, E and F (L = 50 cm) (b) Relationship between the sensitivity and the length ratio.
removed coating and attached to the translation stages with a resolution of 0.01 mm for strain applying. The transmission spectra were monitored with an amplified spontaneous emission (ASE, 1520–1620 nm) light source and an optical spectrum analyzer (OSA, AQ6370). We designed 3 experiments to verify the 3 special cases. The sensing lengths, total lengths used in these FLMs and their sensitivities are listed in Table 1. The first experiment is designed to verify the case (i). FLM A, B and C are used in this experiment with the same sensing lengths of around 5 cm but different total lengths of 6.5, 17.1 and 52.2 cm, respectively. The transmission spectra of FLM A, B and C are showed in Fig. 2. They are all similar sinusoidal waveforms, whose extinction ratios are about 30 dB. The differences among the spectra are their FSRs, which are 58.52, 19.58 and 8.89 nm for FLM A, B and C, respectively. This result shows the FSR is inversely proportional to the total HBF length (L), which well supports the prediction of Eq. (3). In order to compare the sensitivities of these 3 FLMs, the same amount of strain was applied on the PMFs from 0 to 4m with an interval of 0.4m through the translation stages. The leftmost dip on the transmission spectrum of FLM A was chosen as an example to show the variation trend detailedly in Fig. 3(a). A red shift from 1526.16 to 1605.46 nm, totally 79.30 nm, occurred as the strain was
increased from 0 to 4m. The relationships between the strain and the wavelength shift of the transmission spectra of the 3 FLMs are shown in Fig. 3(b). The linear fit method was applied to the curves with high goodness of fit R2 values and the corresponding sensitivities of FLM A, B and C are 19.58, 6.408 and 2.438pm/, respectively, which have the approximate relationship of 19.58: 6.408: 2.438 ≈ 1/6.5: 1/17.1: 1/52.2. This result well support the prediction of case (i), i.e. ∝ 1/L, which means the sensitivity of FLM sensor is inversely proportional to the total HBF length provided the sensing lengths are the same. This experiment shows the total length of HBF affects the sensitivity significantly although it doesn’t get involved into the sensing directly. This conclusion is also in accordance with the experimental result in ref [17]. The second experiment is designed to verify the case (ii). FLM D, E and F are used in this experiment with the same total length of around 50 cm but different sensing lengths of 2.0, 10.2 and 47.6 cm respectively. The transmission spectra are similar to the previous ones. The strain test was carried out as the same method with previous experiment. The relationships between the strain and the wavelength shift of the transmission spectra of the 3 FLMs are shown in Fig. 4(a). The linear fit method was applied to the curves with high goodness of fit R2 values and the corresponding sensitivities of FLM D, E and F are 1.021, 5.476 and 25.305pm/
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respectively, which have the approximate relationship of 2.0: 10.2: 47.6 ≈ 1.021: 5.476: 25.305. This result well support the prediction of case (ii), i.e. ∝ L0 , which means the sensitivity of FLM sensor is proportional to the sensing length provided the total HBF lengths are the same. It also explains why researchers tended to use longer HBF length to achieve a higher sensitivity [13,14]. The third experiment is designed to verify the case (iii). FLM F, G and H are used in this experiment with the total HBF lengths of 50.7, 4.7 and 9.7 cm respectively. In this experiment, the full length of HBF was used as the sensing length, i.e. L = L0 . However, because the stick points between the fiber and the translation stages needed to avoid the splicing points, the actual sensing lengths, which are 47.6, 4.3 and 9.7 cm respectively, are slightly shorter than the according total length. The strain test was carried out similarly. The sensitivities for FLM F, G and H are 25.305, 22.530, 26.407pm/ respectively. These sensitivities are so close that they can be considered as almost equal. The small differences among them are caused because the actual sensing lengths are slightly shorter than their according total HBF length. Therefore, we can conclude that if the full length of the HBF is used for sensing, i.e. L = L0, the sensitivity is independent on the HBF length. This experimental result supports very well the prediction of case (iii). This conclusion is also in accordance with the phenomenon reported in Ref. [15]. In order to further verify Eq. (4), all the sensitivity data from FLM A to H are plot in Fig. 4(b). Liner fit is applied to the data and it shows a good linear relationship between the sensitivity and length ratio (L0 /L) with a high goodness-of-fit coefficient of 0.9974. It means the sensitivity is proportional to the length ratio, i.e. ∝ L0 /L. Specially, if L = L0 (case iii), i.e. L0 /L = 1, the obtained sensitivity reaches its maximum sensitivity can be achieved. From Fig. 4(b), we can tell that this maximum sensitivity is 27.014 pm/. The achieved sensitivities of FLM F, G and H are quite close to this maximum value. 4. Conclusions In this work, we first pointed out the confusion and contradictory results in the literatures with regards to the sensitivity dependency of FLM sensors on the HBF length used within the Sagnac loop. Then, we distinguish the roles of sensing length and total length of HBF. With these concepts explained, a model of FLM is established and the equations are re-deduced. The equations show the sensitivity of FLM sensors is linear proportional to the length ratio. The experimental results well support the theoretical analysis. This model provides more insights on the sensitivity dependence on the HBF length and these conclusions can be used as the guideline for the FLM sensors. Acknowledgement This work was supported by the ENERGY MARKET AUTHORITY (LA/CONTRACT NO. NRF2013EWT-EIRP001-006)
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