- Email: [email protected]
Angle sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber
Accepted Manuscript Title: Angle sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber Author: Chun-Liu Zhao Rui Wang Yumeng Zhou Luo Niu Huaping Gong PII: DOI: Reference:
S0030-4026(16)31593-5 http://dx.doi.org/doi:10.1016/j.ijleo.2016.12.043 IJLEO 58673
To appear in: Received date: Accepted date:
19-9-2016 12-12-2016
Please cite this article as: Chun-Liu Zhao, Rui Wang, Yumeng Zhou, Luo Niu, Huaping Gong, Angle sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.12.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Angle sensor based on two cascading abrupt-
tapers modal interferometer in single mode fiber
Chun-Liu Zhao*, Rui Wang, Yumeng Zhou, Luo Niu, Huaping Gong
Institute of Optoelectronic Technology, China Jiliang University, Hangzhou, 310018, People’s Republic of China
Corresponding author: [email protected]
Abstract—In this paper, a simple-fabricated and high sensitive angel sensor based on single mode optical fiber is proposed. The sensor consists of two cascading abrupt-tapers with different sizes, manufactured by CO2 laser. The cladding modes will be excited in the first taper and interfere with the core mode in the second taper. When the angle applied on the sensor, the length between the two tapers will change. At the same time, the first taper is bend which affects the ratios and the effective indices of the core mode and the cladding modes excited by the first taper. As a consequence, the interference pattern will have a shift. By monitoring the shift of the interference pattern, the angle measurement is achieved. Experimental results show that the sensor has good linear relationships in some certain measurement range. The angle measurement sensitivity is as high as 601.8nm/º in the measurement range of 0.0575º and 0.075º. Index Terms—Angle sensor, abrupt-taper, modal interferometers
I. INTRODUCTION
O
ptical fiber sensor technology offers the possibility of developing a variety of physical sensors for a wide range of physical parameters, such as refractive index, temperature, strain, displacement, curvature, etc [1-5]. One of the techniques in optical sensor measurement is angle measurement. Angle measurement is being used in wide area. For instance, this type of measurement can be integrated into precision rotation stages to control the angular positioning of the optical and mechanical components such as in using to control the direction of cars, the kinematics of robot arms and the tilt angles of aircrafts in industry [6, 7]. Recently, several types of optical fiber angle sensors have been widely studied [8-11] However, these sensors may suffer from either relatively low sensitivity, or complicated and expensive fabrication process. For instance, a novel all-fiber inclinometer using tunable Mach–Zehnder interferometers with an extinction ratio of >30.4 dB is produced by introducing two abrupt tapers in a short length of highly Er/Yb co-doped fiber [11]. The abrupt tapers partially convert the core mode into cladding modes and interference occurs when the phase difference between the core and cladding modes accumulate to π after a certain propagation length. The maximal wavelength shift for the resonant transmission dips can reach 40.8 nm when the inclination angle, θ, varies from 0° to 32°. In this letter, an angle sensor based on two abrupt-tapers modal interferometer in a single mode fiber (SMF) is proposed. The sensor head is manufactured only by CO2 laser and a standard SMF. The cladding modes will be excited in the first abrupt-taper section. After propagation, they will interfere with the core mode at the second abrupt-taper section. When an angle is applied on the sensor, the first taper is applied with a sharp bending. This affects the ratios of the core mode and the cladding modes excited by the first taper. At the same time, the effective indices of the core and the cladding modes will change. Further, the increase of the angle also elongates the length between the two tapers, and changes the optical path difference between the core mode and cladding modes. As a consequence, the interference wavelength will have a shift. So that we can realize the angle measurement by observing the shift of the interference pattern. Experimental results show that the sensor has good linear relationships in some certain measurement range. The angle measurement sensitivity is as high as 601.8 nm/ º in the measurement range of 0.0575º and 0.075º. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10-5 º in the range of 0.0575º to 0.075º. II. FABRICATION SETUP AND EXPERIMENT The proposed sensor, as shown in Fig. 1, consists of an input SMF, two abrupt-tapers and an output SMF. The sensor head, two cascading abrupt-tapers, is manufactured in a standard SMF by a high-frequency pulsed CO2 laser (CO2-H10, Han's Laser) with a maximum average output power of 10 W. The SMF is fixed on two 3-D translation stages, which are used to adjust the heating position within the SMF section, while a weight (20 g) is used to apply a constant tension to the ends of the fiber. The middle of the SMF was exposed to the CO2 laser beam and tapering occurred because of the tension applied to the SMF. After completing the first abrupt-taper, we moved the SMF about 10mm to the left to fabricate the second abrupt taper at the same procedure. The fabrication method of two cascading abrupt-tapers is same as Ref. [5]. The transmission spectra during manufacturing process of tapers are recorded using a broadband source (BBS) range from 1450 nm to 1640 nm and a high-resolution (20 pm) optical spectrum analyzer (OSA, Yokogawa AQ6370). There is no any interference pattern when only one abrupt-taper is fabricated on the SMF, and the transmission loss is about 15 dB. The interference pattern will appear after two cascading abrupt-taper structures are formed. And a great quantity studies demonstrate that the visibility of the interference pattern will be better only when the cascading two abrupt-tapers structures are at different sizes. What’s more, the waist of the first taper should be shorter than the second one. The dotted line in Fig. 2 shows the transmission intensity spectrum when only one abrupt-taper is fabricated in the SMF, while the solid line shows the spectrum of two closely cascading abrupt-tapers structure, ~8 mm apart. The waist diameter and total taper length of the first abrupt-taper are 66.4 μm and 174 μm, respectively, while the parameters of the second abrupt-taper are 94 μm and 145 μm, respectively. In the proposed structure, a few interference dips can be observed. For instance, dip 1 is at ~1502 nm wavelength whose depth is more than 25 dB, while dip 2 is at ~1553 nm wavelength whose depth is more than 15 dB. III. SENSING PRINCIPLE
Fig. 3 shows the experimental setup for the angle test. In our experiments, the left end of the first taper (taper 1) is fixed on the left translation station, while the second taper (taper 2) hangs in the air. The initial separation of two translation stations is 40 mm. In order to change the angles between the two tapers accurately, the right moveable translation stage is moved forward at 0.1 mm every time, as shown is Fig. 3 (b). Compared with our works in Ref. [5], the angle measurement is created by moving the translation stage perpendicular to the horizontal axis. As mentioned above, the modal interference is realized by two cascading abrupt-tapers. When the fundamental mode in the core propagates along the SMF into the taper 1, many cladding modes with different effective indexes can be excited. After propagation, they will interfere with the core mode at the taper 2, whose waist is smaller than the taper 1. When the angle θ changes as shown in Fig. 3, the taper 1 is applied with a bending. This affects the ratios of the core mode and the cladding modes excited by the taper 1. At the same time, the effective indices of the core and the cladding modes will change a little. Further, the increase of the angle also elongates the length between the two tapers, and changes the optical path difference between the core mode and cladding modes. As a consequence, the interference wavelength will have a shift. As we all know, the transmission spectrum of the interferometer as a periodic function of the wavelength is given as [12] I = 𝐼1 + 𝐼2 + 2√𝐼1 𝐼2 cos Φ𝑚 (1) where I1 and I2 are the transmission intensities of two interfering modes and Φ𝑚 is defined as Φ𝑚 = (2𝜋⁄𝜆)(𝑛𝑐𝑜 − 𝑛𝑐𝑙,𝑚 )𝐿 (2) where 𝑛𝑐𝑜 and 𝑛𝑐𝑙,𝑚 are the effective indices of the core mode and m-order cladding mode respectively. When Φ𝑚 is satisfied with the interference cancellation as Φ𝑚 = (2k + 1)π (3) the resonant dip wavelength of an interferometer is given by λ = (2⁄(2𝑘 + 1))(𝑛𝑐𝑜 − 𝑛𝑐𝑙,𝑚 )𝐿 (4) where k is an integer, L is the length between two tapers, nco and ncl,m are the effective index of the core mode and the m-order cladding mode, respectively. In our case, when the angle θ applied on the sensor (the translation stage moves), L changes. nco and ncl,m may also change. The results show that L, nco and ncl,m affect the resonant dip wavelength together. IV. RESULTS AND DISCUSSION Fig. 4 shows the transmission spectra of the proposed sensor when the right moveable translation stage is moved forward at 0.1 mm every time. When the translation stage moved forward, the angle increase. It can be seen that the interference pattern is shifted towards a longer wavelength direction when the angle increases. When the movement distance changed from 0 mm to 3 mm, which means the angle was varied from 0 º to 0.075º, the interference dip 2 has a red wavelength shift from 1547.8896 nm to 1565.3854 nm, more obvious than dip 1. The wavelength shift of the dip 2 in response to the applied angle is shown in Fig. 5. The linear relationships between the wavelength and the angle are shown in some certain measurement ranges. For the sensitivity, it is just the slope of the curve. The sensor has a sensitivity of 28.646 nm/ º for angles between 0º and 0.0175º. For angles between 0.0175º and 0.04º, the sensor has a sensitivity of 199.22 nm/ º. And the fitting degrees are 0.9022 and 0.9909, respectively, as shown in Fig. 5 (a). The sensor has a sensitivity of 139.5 nm/ º for angles between 0.04º and 0.0575º. For angles between 0.0575º and 0.075º, the sensor has a sensitivity of 601.8 nm/ º. And the fitting degrees are 0.9558 and 0.9962, respectively, as shown in Fig. 5 (b). The high angle sensitivity of the proposed sensor is benefit to the thin taper structure. Moreover, the angle sensitivity is determined by the thin-taper sizes. The sensitivity will be higher when the taper is thinner, since the thinner taper is affected more by the angle changing. As shown above, the proposed sensor has very high sensitivity. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10 -5 º in the range of 0.0575º to 0.075º. Further, it is noticed that there are different sensitivities at different testing ranges. The main reason may be L, nco and ncl,m affect the resonant dip wavelength together. The cladding modes will be excited with different ratios for different angles, and their effective indices will change with the applied angel. In order to investigate the number and distribution of the involved interfering modes, we use the fast Fourier transform (FFT) method to analysis the spatial frequency spectra of the interferometers. Fig. 6 shows the spatial frequency spectra. We can use it to analyze the mode interferometer. When the angle increased from 0° to 0.075°, it has one principal maximum values and seven secondary maximums from zero frequency point to 0.15, induced by the interference between the fundamental core mode and some of other cladding modes. The frequency at near 0.02 is caused by the interference between the fundamental core mode and the lowest order cladding mode. The others are caused by the interference between the fundamental core mode and the higher order cladding modes. As shown in Fig. 6, the ratios among all the interference frequencies are changed when the applied angle is different. At the same time, the peak frequencies are shifted, especially for the interferences by higher order modes. Fig. 7 shows the relative amplitude of the first principal maximum and other six secondary maximums, when the angle changes from 0° to 0.075°, the proportion continues changes. Fig. 8 shows the center frequency of the first principal maximum and other
six secondary maximums, when the angle increase, the center frequency changes, means one or more different cladding modes interfere with the core mode generate a new interference spectrum. The variation of the amplitude proportion and spatial frequency lead to the change of interference dip. The theoretical results are accordance with the analysis in the sensing principle part. Two properties of the sensor are affected by the mode coupling changing which occurs in the thin tapers. The first is there are different angle sensitivities at different angle testing ranges, as discussed above. The second is that the angle sensing range with a linear response is limited by the mode coupling changing too. The linear sensing range is just the range in which the mode coupling occurs between certain modes. So we can enlarge the linear angle measurement range by increase the size of the taper in which mode coupling is not easy to change by the applied angle. Considering the angle sensitivity and the linear angle measurement range, we need balance two requirements and chose a suitable thin-taper size. The proposed modal interferometer is made of the single mode fiber and is sensitivity to temperature. This property will cause an angle-temperature cross sensitivity. Fig. 9 shows the relationship of the wavelength of the dip 2 with temperature under the 0° angle. The temperature sensitivity is about 0.09 nm/℃, which is small compared with the angle sensitivities. When the proposed angle sensor works under room temperature, the temperature effect can be ignored. But the angle resolution will be limited. For comparison, we illustrated the performance of the proposed angle sensor and other angle sensors, as shown in Table 1. The proposed angle sensor has high sensitivity and is more suitable for micron-angle measurement.
V. CONCLUSION In conclusion, we propose an angle sensor based on two cascading abrupt-tapers modal interferometer in a standard SMF. The cladding modes will be excited in the first abrupt-taper section and interfere with the core mode after propagation to the second abrupt-taper section. When the angle θ applied on the sensor, the length between the two tapers will change. At the same time, the first taper is bend which affects the ratios and the effective indices of the core mode and the cladding modes excited by the first taper. As a consequence, the interference pattern will have a shift so that we can realize the angle measurement by observing the shift of the interference pattern. The sensor has good linear relationships in some certain measurement range. The angle sensitivity is as high as 601.8 nm/ º in the measurement range of 0.0575º and 0.075º. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10-5 º in the range of 0.0575º to 0.075º. In conclusion, the proposed angle sensor is simple-fabricated and inexpensive, which is very suitable for angle measurement in practical applications. ACKNOWLEDGMENTS This work was supported by the International Technological Cooperation Program of Zhejiang (China) under Grant No. 2013C24018 and the National Natural Science Foundation of China (NSFC) under Grant No. 61108058.
REFERENCES W. Liang, Y. Huang, Y. Xu et al., “Highly sensitive fiber Bragg grating refractive index sensors,” Applied Physics Letters, vol. 86, no. 15, pp. 151122 151122-3, 2005. [2] Q. W, Z. CL, H. S et al., “High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror,” Opt Lett, vol. 36, no. 9, pp. 15481550, 2011. [3] W. Qian, C.-L. Zhao, X. Dong et al., “Intensity measurement based temperature-independent strain sensor using a highly birefringent photonic crystal fiber loop mirror,” Optics Communications, vol. 283, no. 24, pp. 5250–5254, 2010. [4] C. Shen, and C. Zhong, “Novel Temperature-Insensitive Fiber Bragg Grating Sensor For Displacement Measurement,” Sensors and Actuators A: Physical, vol. 170, pp. 51–54, 2011. [5] L. Niu, C.-L. Zhao, H. Gong et al., “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Optics Communications, vol. 333, pp. 11–15, 2014. [6] A. Khiat, F. Lamarque, C. Prelle et al., “High-resolution fibre-optic sensor for angular displacement measurements,” Measurement Science and Technology, vol. 21, no. 2, pp. 283-293, 2010. [7] L. Yuan, X. Lin, Y. Liang et al., “Applications of angled-mirror in fiber-optic sensors,” Optics Laser Technology, vol. 32, no. 4, pp. 255-260, 2000. [8] M. L.-A. Sergio Rota-Rodrigo, Jens Kobelke, Kay Schuster,, and a. O. F. a. José Luis Santos, “Multimodal Interferometer Based on a Suspended Core Fiber for Simultaneous Measurement of Physical Parameters,” Journal of Lightwave Technology, vol. 33, no. 12, pp. 2468-2473, 2015. [9] X. Y. Hui Yu, Zhengrong Tong, Ye Cao, and Ailing Zhang, “Temperature-Independent Rotational Angle Sensor Based on Fiber Bragg Grating,” IEEE Sensors Journal, vol. 11, no. 5, pp. 1233-1235, 2011. [10] S. K. K. H. Y. Au, H. Y. Fu, W. H. Chung, and H. Y. Tam, “Temperature-Insensitive Fiber Bragg Grating Based Tilt Sensor With Large Dynamic Range,” Journal of Lightwave Technology, vol. 29, no. 11, pp. 1714-1720, 2011. [11] Z.-Z. F. Nan-Kuang Chen, Jheng-Jyun Wang, Shien-Kuei Liaw, and Hsiang-Chen Chui, “Interferometric Interrogation of the Inclination and Displacement of Tapered Fiber Mach-Zehnder Interferometers,” IEEE Sensors Journal, vol. 13, no. 9, pp. 3437-3441, 2013 [12] C.-L. Z. Wenwen Qian, Chi Chiu Chan, “Temperature Sensing Based on Ethanol-Filled Photonic Crystal Fiber Modal Interferometer,” IEEE Sensors Journal, vol. 12, no. 8, pp. 2593-2597, 2012. [1]
CO2 Laser Lens
BBS
OSA Taper 1 Taper 2 Weight
Fig.1 The fabrication setup for fiber tapering.
Transmission Intensity(dB)
0 -5 -10 -15
dip 2
-20 dip 1
-25 -30 1450
1500
1550 Wavelength(nm)
two cascading abrupt-tapers on SMF only one abrupt-taper on SMF 1600
Fig. 2 Initial light transmission intensity spectrum of two closely cascading abrupt-tapers structure. The blue line shows the transmission intensity spectrum when only one abrupt-taper is fabricated in the SMF, while the red line shows the spectrum of two closely cascading abrupt-tapers structure, ~8mm apart.
BBS
Taper 1 Taper 2
OSA
Angle Translation Station
Translation Station
(a)
(b) Fig.3 The experimental setup for angle sensor test.
Translation Movement
Fig.4 Wavelength shift of the interference pattern when the right moveable translation stage is moved forward at 0.1 mm every time from 0mm to 3mm, which means the angle varies from 0º to 0.075º.
Fig.5 Wavelength shift of interference pattern of the dip 2 in response to the angle.
Fig. 6. The spatial frequency spectra of the modal interference measured at different angle.
Fig. 7 Relative amplitude of the first principal maximum and other six secondary maximums.
Fig. 8. Center frequency changes of the first principal maximum and other six secondary maximums.
1640
Wavelength (nm)
1620 dip 1
1600
dip 2
1580 1560 1540 1520 10
20
30
40
50
60
70
80
90
100
110
Temperature (℃) Fig.9 The relationship of the wavelength of the dip 2 with temperature
120
Table 1. Performance Comparison of Angle Sensors Type Sensitivity PCF based MMI PCF [8] FBG rotational angle sensor [9] FBG tilt sensor [10] Er/Yb co-doped fiber based MZIs [11] Proposed sensor
Angle Range
9.17 pm/ º 0.743nm/º
0°~90° -21°~21°
0.0395 nm/ º 1.275 nm/ º
-30°~30° 0º~32º
601.8nm/ º
0.0575º~0.075º
S0030-4026(16)31593-5 http://dx.doi.org/doi:10.1016/j.ijleo.2016.12.043 IJLEO 58673
To appear in: Received date: Accepted date:
19-9-2016 12-12-2016
Please cite this article as: Chun-Liu Zhao, Rui Wang, Yumeng Zhou, Luo Niu, Huaping Gong, Angle sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.12.043 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Angle sensor based on two cascading abrupt-
tapers modal interferometer in single mode fiber
Chun-Liu Zhao*, Rui Wang, Yumeng Zhou, Luo Niu, Huaping Gong
Institute of Optoelectronic Technology, China Jiliang University, Hangzhou, 310018, People’s Republic of China
Corresponding author: [email protected]
Abstract—In this paper, a simple-fabricated and high sensitive angel sensor based on single mode optical fiber is proposed. The sensor consists of two cascading abrupt-tapers with different sizes, manufactured by CO2 laser. The cladding modes will be excited in the first taper and interfere with the core mode in the second taper. When the angle applied on the sensor, the length between the two tapers will change. At the same time, the first taper is bend which affects the ratios and the effective indices of the core mode and the cladding modes excited by the first taper. As a consequence, the interference pattern will have a shift. By monitoring the shift of the interference pattern, the angle measurement is achieved. Experimental results show that the sensor has good linear relationships in some certain measurement range. The angle measurement sensitivity is as high as 601.8nm/º in the measurement range of 0.0575º and 0.075º. Index Terms—Angle sensor, abrupt-taper, modal interferometers
I. INTRODUCTION
O
ptical fiber sensor technology offers the possibility of developing a variety of physical sensors for a wide range of physical parameters, such as refractive index, temperature, strain, displacement, curvature, etc [1-5]. One of the techniques in optical sensor measurement is angle measurement. Angle measurement is being used in wide area. For instance, this type of measurement can be integrated into precision rotation stages to control the angular positioning of the optical and mechanical components such as in using to control the direction of cars, the kinematics of robot arms and the tilt angles of aircrafts in industry [6, 7]. Recently, several types of optical fiber angle sensors have been widely studied [8-11] However, these sensors may suffer from either relatively low sensitivity, or complicated and expensive fabrication process. For instance, a novel all-fiber inclinometer using tunable Mach–Zehnder interferometers with an extinction ratio of >30.4 dB is produced by introducing two abrupt tapers in a short length of highly Er/Yb co-doped fiber [11]. The abrupt tapers partially convert the core mode into cladding modes and interference occurs when the phase difference between the core and cladding modes accumulate to π after a certain propagation length. The maximal wavelength shift for the resonant transmission dips can reach 40.8 nm when the inclination angle, θ, varies from 0° to 32°. In this letter, an angle sensor based on two abrupt-tapers modal interferometer in a single mode fiber (SMF) is proposed. The sensor head is manufactured only by CO2 laser and a standard SMF. The cladding modes will be excited in the first abrupt-taper section. After propagation, they will interfere with the core mode at the second abrupt-taper section. When an angle is applied on the sensor, the first taper is applied with a sharp bending. This affects the ratios of the core mode and the cladding modes excited by the first taper. At the same time, the effective indices of the core and the cladding modes will change. Further, the increase of the angle also elongates the length between the two tapers, and changes the optical path difference between the core mode and cladding modes. As a consequence, the interference wavelength will have a shift. So that we can realize the angle measurement by observing the shift of the interference pattern. Experimental results show that the sensor has good linear relationships in some certain measurement range. The angle measurement sensitivity is as high as 601.8 nm/ º in the measurement range of 0.0575º and 0.075º. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10-5 º in the range of 0.0575º to 0.075º. II. FABRICATION SETUP AND EXPERIMENT The proposed sensor, as shown in Fig. 1, consists of an input SMF, two abrupt-tapers and an output SMF. The sensor head, two cascading abrupt-tapers, is manufactured in a standard SMF by a high-frequency pulsed CO2 laser (CO2-H10, Han's Laser) with a maximum average output power of 10 W. The SMF is fixed on two 3-D translation stages, which are used to adjust the heating position within the SMF section, while a weight (20 g) is used to apply a constant tension to the ends of the fiber. The middle of the SMF was exposed to the CO2 laser beam and tapering occurred because of the tension applied to the SMF. After completing the first abrupt-taper, we moved the SMF about 10mm to the left to fabricate the second abrupt taper at the same procedure. The fabrication method of two cascading abrupt-tapers is same as Ref. [5]. The transmission spectra during manufacturing process of tapers are recorded using a broadband source (BBS) range from 1450 nm to 1640 nm and a high-resolution (20 pm) optical spectrum analyzer (OSA, Yokogawa AQ6370). There is no any interference pattern when only one abrupt-taper is fabricated on the SMF, and the transmission loss is about 15 dB. The interference pattern will appear after two cascading abrupt-taper structures are formed. And a great quantity studies demonstrate that the visibility of the interference pattern will be better only when the cascading two abrupt-tapers structures are at different sizes. What’s more, the waist of the first taper should be shorter than the second one. The dotted line in Fig. 2 shows the transmission intensity spectrum when only one abrupt-taper is fabricated in the SMF, while the solid line shows the spectrum of two closely cascading abrupt-tapers structure, ~8 mm apart. The waist diameter and total taper length of the first abrupt-taper are 66.4 μm and 174 μm, respectively, while the parameters of the second abrupt-taper are 94 μm and 145 μm, respectively. In the proposed structure, a few interference dips can be observed. For instance, dip 1 is at ~1502 nm wavelength whose depth is more than 25 dB, while dip 2 is at ~1553 nm wavelength whose depth is more than 15 dB. III. SENSING PRINCIPLE
Fig. 3 shows the experimental setup for the angle test. In our experiments, the left end of the first taper (taper 1) is fixed on the left translation station, while the second taper (taper 2) hangs in the air. The initial separation of two translation stations is 40 mm. In order to change the angles between the two tapers accurately, the right moveable translation stage is moved forward at 0.1 mm every time, as shown is Fig. 3 (b). Compared with our works in Ref. [5], the angle measurement is created by moving the translation stage perpendicular to the horizontal axis. As mentioned above, the modal interference is realized by two cascading abrupt-tapers. When the fundamental mode in the core propagates along the SMF into the taper 1, many cladding modes with different effective indexes can be excited. After propagation, they will interfere with the core mode at the taper 2, whose waist is smaller than the taper 1. When the angle θ changes as shown in Fig. 3, the taper 1 is applied with a bending. This affects the ratios of the core mode and the cladding modes excited by the taper 1. At the same time, the effective indices of the core and the cladding modes will change a little. Further, the increase of the angle also elongates the length between the two tapers, and changes the optical path difference between the core mode and cladding modes. As a consequence, the interference wavelength will have a shift. As we all know, the transmission spectrum of the interferometer as a periodic function of the wavelength is given as [12] I = 𝐼1 + 𝐼2 + 2√𝐼1 𝐼2 cos Φ𝑚 (1) where I1 and I2 are the transmission intensities of two interfering modes and Φ𝑚 is defined as Φ𝑚 = (2𝜋⁄𝜆)(𝑛𝑐𝑜 − 𝑛𝑐𝑙,𝑚 )𝐿 (2) where 𝑛𝑐𝑜 and 𝑛𝑐𝑙,𝑚 are the effective indices of the core mode and m-order cladding mode respectively. When Φ𝑚 is satisfied with the interference cancellation as Φ𝑚 = (2k + 1)π (3) the resonant dip wavelength of an interferometer is given by λ = (2⁄(2𝑘 + 1))(𝑛𝑐𝑜 − 𝑛𝑐𝑙,𝑚 )𝐿 (4) where k is an integer, L is the length between two tapers, nco and ncl,m are the effective index of the core mode and the m-order cladding mode, respectively. In our case, when the angle θ applied on the sensor (the translation stage moves), L changes. nco and ncl,m may also change. The results show that L, nco and ncl,m affect the resonant dip wavelength together. IV. RESULTS AND DISCUSSION Fig. 4 shows the transmission spectra of the proposed sensor when the right moveable translation stage is moved forward at 0.1 mm every time. When the translation stage moved forward, the angle increase. It can be seen that the interference pattern is shifted towards a longer wavelength direction when the angle increases. When the movement distance changed from 0 mm to 3 mm, which means the angle was varied from 0 º to 0.075º, the interference dip 2 has a red wavelength shift from 1547.8896 nm to 1565.3854 nm, more obvious than dip 1. The wavelength shift of the dip 2 in response to the applied angle is shown in Fig. 5. The linear relationships between the wavelength and the angle are shown in some certain measurement ranges. For the sensitivity, it is just the slope of the curve. The sensor has a sensitivity of 28.646 nm/ º for angles between 0º and 0.0175º. For angles between 0.0175º and 0.04º, the sensor has a sensitivity of 199.22 nm/ º. And the fitting degrees are 0.9022 and 0.9909, respectively, as shown in Fig. 5 (a). The sensor has a sensitivity of 139.5 nm/ º for angles between 0.04º and 0.0575º. For angles between 0.0575º and 0.075º, the sensor has a sensitivity of 601.8 nm/ º. And the fitting degrees are 0.9558 and 0.9962, respectively, as shown in Fig. 5 (b). The high angle sensitivity of the proposed sensor is benefit to the thin taper structure. Moreover, the angle sensitivity is determined by the thin-taper sizes. The sensitivity will be higher when the taper is thinner, since the thinner taper is affected more by the angle changing. As shown above, the proposed sensor has very high sensitivity. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10 -5 º in the range of 0.0575º to 0.075º. Further, it is noticed that there are different sensitivities at different testing ranges. The main reason may be L, nco and ncl,m affect the resonant dip wavelength together. The cladding modes will be excited with different ratios for different angles, and their effective indices will change with the applied angel. In order to investigate the number and distribution of the involved interfering modes, we use the fast Fourier transform (FFT) method to analysis the spatial frequency spectra of the interferometers. Fig. 6 shows the spatial frequency spectra. We can use it to analyze the mode interferometer. When the angle increased from 0° to 0.075°, it has one principal maximum values and seven secondary maximums from zero frequency point to 0.15, induced by the interference between the fundamental core mode and some of other cladding modes. The frequency at near 0.02 is caused by the interference between the fundamental core mode and the lowest order cladding mode. The others are caused by the interference between the fundamental core mode and the higher order cladding modes. As shown in Fig. 6, the ratios among all the interference frequencies are changed when the applied angle is different. At the same time, the peak frequencies are shifted, especially for the interferences by higher order modes. Fig. 7 shows the relative amplitude of the first principal maximum and other six secondary maximums, when the angle changes from 0° to 0.075°, the proportion continues changes. Fig. 8 shows the center frequency of the first principal maximum and other
six secondary maximums, when the angle increase, the center frequency changes, means one or more different cladding modes interfere with the core mode generate a new interference spectrum. The variation of the amplitude proportion and spatial frequency lead to the change of interference dip. The theoretical results are accordance with the analysis in the sensing principle part. Two properties of the sensor are affected by the mode coupling changing which occurs in the thin tapers. The first is there are different angle sensitivities at different angle testing ranges, as discussed above. The second is that the angle sensing range with a linear response is limited by the mode coupling changing too. The linear sensing range is just the range in which the mode coupling occurs between certain modes. So we can enlarge the linear angle measurement range by increase the size of the taper in which mode coupling is not easy to change by the applied angle. Considering the angle sensitivity and the linear angle measurement range, we need balance two requirements and chose a suitable thin-taper size. The proposed modal interferometer is made of the single mode fiber and is sensitivity to temperature. This property will cause an angle-temperature cross sensitivity. Fig. 9 shows the relationship of the wavelength of the dip 2 with temperature under the 0° angle. The temperature sensitivity is about 0.09 nm/℃, which is small compared with the angle sensitivities. When the proposed angle sensor works under room temperature, the temperature effect can be ignored. But the angle resolution will be limited. For comparison, we illustrated the performance of the proposed angle sensor and other angle sensors, as shown in Table 1. The proposed angle sensor has high sensitivity and is more suitable for micron-angle measurement.
V. CONCLUSION In conclusion, we propose an angle sensor based on two cascading abrupt-tapers modal interferometer in a standard SMF. The cladding modes will be excited in the first abrupt-taper section and interfere with the core mode after propagation to the second abrupt-taper section. When the angle θ applied on the sensor, the length between the two tapers will change. At the same time, the first taper is bend which affects the ratios and the effective indices of the core mode and the cladding modes excited by the first taper. As a consequence, the interference pattern will have a shift so that we can realize the angle measurement by observing the shift of the interference pattern. The sensor has good linear relationships in some certain measurement range. The angle sensitivity is as high as 601.8 nm/ º in the measurement range of 0.0575º and 0.075º. When an optical spectrum analyzer with 20 pm resolution is used, the angle’s resolution can achieve to 3.3×10-5 º in the range of 0.0575º to 0.075º. In conclusion, the proposed angle sensor is simple-fabricated and inexpensive, which is very suitable for angle measurement in practical applications. ACKNOWLEDGMENTS This work was supported by the International Technological Cooperation Program of Zhejiang (China) under Grant No. 2013C24018 and the National Natural Science Foundation of China (NSFC) under Grant No. 61108058.
REFERENCES W. Liang, Y. Huang, Y. Xu et al., “Highly sensitive fiber Bragg grating refractive index sensors,” Applied Physics Letters, vol. 86, no. 15, pp. 151122 151122-3, 2005. [2] Q. W, Z. CL, H. S et al., “High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror,” Opt Lett, vol. 36, no. 9, pp. 15481550, 2011. [3] W. Qian, C.-L. Zhao, X. Dong et al., “Intensity measurement based temperature-independent strain sensor using a highly birefringent photonic crystal fiber loop mirror,” Optics Communications, vol. 283, no. 24, pp. 5250–5254, 2010. [4] C. Shen, and C. Zhong, “Novel Temperature-Insensitive Fiber Bragg Grating Sensor For Displacement Measurement,” Sensors and Actuators A: Physical, vol. 170, pp. 51–54, 2011. [5] L. Niu, C.-L. Zhao, H. Gong et al., “Curvature sensor based on two cascading abrupt-tapers modal interferometer in single mode fiber,” Optics Communications, vol. 333, pp. 11–15, 2014. [6] A. Khiat, F. Lamarque, C. Prelle et al., “High-resolution fibre-optic sensor for angular displacement measurements,” Measurement Science and Technology, vol. 21, no. 2, pp. 283-293, 2010. [7] L. Yuan, X. Lin, Y. Liang et al., “Applications of angled-mirror in fiber-optic sensors,” Optics Laser Technology, vol. 32, no. 4, pp. 255-260, 2000. [8] M. L.-A. Sergio Rota-Rodrigo, Jens Kobelke, Kay Schuster,, and a. O. F. a. José Luis Santos, “Multimodal Interferometer Based on a Suspended Core Fiber for Simultaneous Measurement of Physical Parameters,” Journal of Lightwave Technology, vol. 33, no. 12, pp. 2468-2473, 2015. [9] X. Y. Hui Yu, Zhengrong Tong, Ye Cao, and Ailing Zhang, “Temperature-Independent Rotational Angle Sensor Based on Fiber Bragg Grating,” IEEE Sensors Journal, vol. 11, no. 5, pp. 1233-1235, 2011. [10] S. K. K. H. Y. Au, H. Y. Fu, W. H. Chung, and H. Y. Tam, “Temperature-Insensitive Fiber Bragg Grating Based Tilt Sensor With Large Dynamic Range,” Journal of Lightwave Technology, vol. 29, no. 11, pp. 1714-1720, 2011. [11] Z.-Z. F. Nan-Kuang Chen, Jheng-Jyun Wang, Shien-Kuei Liaw, and Hsiang-Chen Chui, “Interferometric Interrogation of the Inclination and Displacement of Tapered Fiber Mach-Zehnder Interferometers,” IEEE Sensors Journal, vol. 13, no. 9, pp. 3437-3441, 2013 [12] C.-L. Z. Wenwen Qian, Chi Chiu Chan, “Temperature Sensing Based on Ethanol-Filled Photonic Crystal Fiber Modal Interferometer,” IEEE Sensors Journal, vol. 12, no. 8, pp. 2593-2597, 2012. [1]
CO2 Laser Lens
BBS
OSA Taper 1 Taper 2 Weight
Fig.1 The fabrication setup for fiber tapering.
Transmission Intensity(dB)
0 -5 -10 -15
dip 2
-20 dip 1
-25 -30 1450
1500
1550 Wavelength(nm)
two cascading abrupt-tapers on SMF only one abrupt-taper on SMF 1600
Fig. 2 Initial light transmission intensity spectrum of two closely cascading abrupt-tapers structure. The blue line shows the transmission intensity spectrum when only one abrupt-taper is fabricated in the SMF, while the red line shows the spectrum of two closely cascading abrupt-tapers structure, ~8mm apart.
BBS
Taper 1 Taper 2
OSA
Angle Translation Station
Translation Station
(a)
(b) Fig.3 The experimental setup for angle sensor test.
Translation Movement
Fig.4 Wavelength shift of the interference pattern when the right moveable translation stage is moved forward at 0.1 mm every time from 0mm to 3mm, which means the angle varies from 0º to 0.075º.
Fig.5 Wavelength shift of interference pattern of the dip 2 in response to the angle.
Fig. 6. The spatial frequency spectra of the modal interference measured at different angle.
Fig. 7 Relative amplitude of the first principal maximum and other six secondary maximums.
Fig. 8. Center frequency changes of the first principal maximum and other six secondary maximums.
1640
Wavelength (nm)
1620 dip 1
1600
dip 2
1580 1560 1540 1520 10
20
30
40
50
60
70
80
90
100
110
Temperature (℃) Fig.9 The relationship of the wavelength of the dip 2 with temperature
120
Table 1. Performance Comparison of Angle Sensors Type Sensitivity PCF based MMI PCF [8] FBG rotational angle sensor [9] FBG tilt sensor [10] Er/Yb co-doped fiber based MZIs [11] Proposed sensor
Angle Range
9.17 pm/ º 0.743nm/º
0°~90° -21°~21°
0.0395 nm/ º 1.275 nm/ º
-30°~30° 0º~32º
601.8nm/ º
0.0575º~0.075º