Optical fiber axial micro-displacement sensor based on Mach-Zehnder interferometer Changyu Shen,1,2 Youqing Wang,1 Jinlei Chu,1,* Yanfang Lu,1 Yi Li,1 and Xinyong Dong1 1
Institute of Optoelectronic Technology, China Jiliang University, Hangzhou, 310018, China 2 Department of Electronics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada * [email protected]
Abstract: A Mach-Zehnder interferometer (MZI) based fiber axial microdisplacement sensor was proposed. The MZI was constructed by a bowknot-type taper (BTT) combining with a fiber core-offset between two single mode fibers (SMFs). The axial micro-displacement of the core offset is correlated with the MZI transmission spectrum and varied with the interferometer arm length. For the arm length L of 12, 18, 24 and 30 mm, the proposed sensors showed high sensitivity of −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, and temperature errors of −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C, respectively. The theoretical simulations of the energy distributions were also given. The obtained sensitivity of −0.385 dB/μm is about 150 times high than that of the current similar existing axial micro-displacement sensor. ©2014 Optical Society of America OCIS codes: (060.2370) Fiber optics sensors; (060.2340) Fiber optics components; (280.4788) Optical sensing and sensors.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
H. R. Alemohammad, E. Foroozmehr, B. S. Cotten, and E. C. Toyserkani, “A dual-parameter optical fiber sensor for concurrent strain and temperature measurement: design, fabrication, packaging, and calibration,” J. Lightwave Technol. 31(8), 1198–1204 (2013). C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “A polarization-maintaining fiber loop mirror based sensor for liquid refractive index absolute measurement,” Sens. Actuators B Chem. 168(20), 360–364 (2012). C. Shen, Y. Zhang, W. Zhou, and J. Albert, “Au-coated tilted fiber Bragg grating twist sensor based on surface Plasmon resonance,” Appl. Phys. Lett. 104(7), 071106 (2014). O. Levy, B. Z. Steinberg, M. Nathan, and A. Boag, “Ultrasensitive displacement sensing using photonic crystal waveguides,” Appl. Phys. Lett. 86(10), 104102 (2005). Z. Xu, L. Cao, C. Gu, Q. He, and G. Jin, “Micro displacement sensor based on line-defect resonant cavity in photonic crystal,” Opt. Express 14(1), 298–305 (2006). R. Yang, Y. S. Yu, Y. Xue, C. Chen, Q. D. Chen, and H. B. Sun, “Single S-tapered fiber Mach-Zehnder interferometers,” Opt. Lett. 36(23), 4482–4484 (2011). K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18(21), 2239–2241 (2006). Z. Tian and S. S.-H. Yam, “In-line abrupt taper optical fiber Mach–Zehnder interferometric strain sensor,” IEEE Photon. Technol. Lett. 21(3), 161–163 (2009). B. Dong and J. Hao, “Temperature-insensitive and intensity-modulated embedded photonic-crystal-fiber modal interferometer based micro-displacement sensor,” J. Opt. Soc. Am. B 28(10), 2332–2336 (2011). Q. Wu, A. M. Hatta, P. Wang, Y. Semenova, and G. Farrell, “Use of a bent single SMS fiber structure for simultaneous measurement of displacement and temperature sensing,” IEEE Photon. Technol. Lett. 23(2), 130– 132 (2011). C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “Temperature-insensitive optical fiber two-dimensional micrometric displacement sensor based on an in-line Mach–Zehnder interferometer,” J. Opt. Soc. Am. B 29(5), 1136–1140 (2012). J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22(15), 1129–1131 (1997). C. Shen, J. Chu, Y. Lu, D. Chen, C. Zhong, Y. Li, X. Dong, and S. Jin, “High Sensitive Micro-Displacement Sensor Based on M-Z Interferometer by a Bowknot Type Taper,” IEEE Photon. Technol. Lett. 26(1), 62–65 (2014).
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31984
14. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). 15. C. Shen, C. Zhong, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, J. Wang, and H. Gong, “Polarization-dependent curvature sensor based on an in-fiber Mach-Zehnder interferometer with a difference arithmetic demodulation method,” Opt. Express 20(14), 15406–15417 (2012).
1. Introduction Optical fiber sensors have received considerable attentions in various sensing applications for the advantages of inexpensive, compact, light weight, immune to electromagnetic interference [1–5]. Micro-displacement is an important physical parameter and should be precisely monitored in various industrial and scientific processes [4, 5]. Recently, optical fiber MachZehnder interferometer (MZI) based on tapered structures have attracted lots of interests in micro-displacement, strain and refractive index sensing applications. R. Yang [6] proposed a single S-tapered fiber MZI with a refractive index sensitivity and strain sensitivity of 1590 nm/RIU and −60 pm/με, respectively. K. Q. Kieu [7] reported a biconical fiber taper MZI sensor with a temperature sensitivity and strain sensitivity of 10pm/°C and 95 pm/με, respectively. Z. Tian [8] proposed an in-line abrupt taper optical fiber MZI strain sensor with a sensitivity of 2000 nm/ε. Bo Dong [9] proposed an embedded single mode fiber (SMF)photonic-crystal-fiber (PCF) based MZI micro-displacement sensor with a sensitivity of 0.0024 dB/μm. Qiang Wu [10] proposed a bent SMF-multimode fiber (MMF)-SMF displacement sensor with a sensitivity of 5.89 pm/μm. However, these displacement sensors either sensitivity is not high, or need to use the wavelength demodulation, which was suffered from the cross sensitivity of the temperature and the displacement (or strain). We have reported a two-dimensional micro-displacement sensor based on in-line MZI previously, which was formed by inserting a polarization maintaining fiber (PMF) between two conventional SMFs using an offset fusion spliced means [11]. Sensitivities of −0.669dB/μm on the slow axis direction and −0.301dB/μm on the fast axis direction of the PMF were obtained. However, it is difficult to make an offset fusion between PMF and SMF. In this paper, a fiber MZI constructed by a core-offset connection of two SMFs and a bowknot-type taper (BTT) is proposed. The BTT, as shown in Fig. 1 (b) and 1(c), is different from the ordinary down-taper. In BBT, by adjusting the taper diameter to match the propagation constant of the mode in the taper with that of the resonant mode of interest, one can couple most of the light into the sphere [12]. For the symmetric structure of the BTT, as the light propagating through this taper, due to the little sphere on the center of the BTT, the light from the left side of the taper will be mostly coupled into the little sphere, and then be coupled into the fiber core of the right side of the taper. It is benefit to control the intensity distribution of fiber core and cladding of SMF1. On the core offset connecting point of the MZI, as SMF1 and SMF2 are in alignment, with the offset value of zero, no interference spectrum was observed. However, as a certain degree offset of the two fiber cores on the other end of the MZI occurred, the interference fringe appeared. Using this design, the microdisplacement on the vertical direction of the fiber axis was detected [13]. However, compared with the micro-displacement on the vertical direction of the fiber axis, the axial microdisplacement along the fiber axis is different and complex. In our design, the core offset value is about 5 μm along the right end of the SMF1 on x axis. The axial micro-displacement of the SMF2 is responded to the MZI transmission spectrum. The fringe visibility of the interference patterns is determined by the value of the axial micro-displacement. And the sensitivity of the sensor varies with interferometer arm lengths were investigated simultaneously. 2. Sensor fabrication and principle The schematic diagram of the proposed sensor is shown in Fig. 1(a). An amplified spontaneous emission (ASE) source of 1450 to 1650 nm wavelength range is used as the light source. The output spectrum is detected with an optical spectrum analyzer (OSA, AQ6370, Advantest, Japan). The maximum resolution of the OSA is 20 pm. The core and cladding diameters of the SMF are 9 μm and 125 μm, respectively. The BTT is formed under modified
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31985
parameters with a commercial electric-arc fusion splicer (Fujikura FSM-60s) by an insufficient-tapered fusion splicing method [13]. The diameter and length of the taper area are ~85μm and ~100μm, respectively. The pictures of the BTT and the offset connect joint are shown in Fig. 1(b) and 1(c), respectively.
Fig. 1. (a) Schematic diagram of the proposed micro-displacement sensor. (b) The partial enlarged drawing of the MZI. (c) Pictures of the BTT and the boundary between SMF1 and SMF2 shown on the fusion splicer screen and the BTT’s micrograph.
After propagating through the BTT, the phase difference Φ m of the light between the core and the cladding modes can be described as [14], m Φ m = 2πΔneff L/λ
(1)
m core clad where Δneff = neff − neff is the effective refractive index difference between the core and the core clad and neff are the effective refractive indices of the fiber core and mth cladding modes. neff fiber cladding, respectively. λ is the center wavelength of the input light. L is the effective length of the interferometer. The intensity I of the interference patterns is,
I = I1 + I 2 + 2 I1 I 2 cos(Φ m )
(2)
where I1 and I2 are the intensities of the light coupled into the core of SMF2. And the fringe visibility K of the interference pattern can be described as, K=
2 I1 I 2
(3) I1 + I 2 From Eq. (3), we can see that the fringe visibility K of the interference pattern is mainly decided by I1 and I2, which come from Icore and Icladding of SMF1, respectively. The light propagating angles θi (i = core, cladding) from SMF1 to SMF2 are related to the numerical aperture of the fiber (NAi) and the refractive index of the surrounding medium n0,
θi = arc sin( NAi / n0 )
(4)
where NAi is correlated with the arm length between the center of the taper and the offset. At the cross section of SMF2, light from SMF1 appears to form a cone and projection onto the SMF 2 with the radius R1 and R2, respectively, Dcore + d tan θ core R1 = 2 tan θ core
#222296 - $15.00 USD (C) 2014 OSA
(5)
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31986
Dcladding + d tan θ cladding R2 = 2 tan θ cladding
(6)
where d is the value of the micro-displacement, Dcore and Dcladding are the diameters of the fiber core and cladding of SMF2, respectively. θ core and θ cladding are decided by Eq. (4). The light coupled into the fiber core of SMF2 from the core and cladding of SMF1 is determined by the sizes of the radiating areas of the SMF1 and reception areas of the SMF2, S S × I core = T ×I S1 π R12 core
(7)
S S × I cladding = T ×I S2 π R22 cladding
(8)
I1 = T I2 = T
where T is the Fresnel transmission coefficient, S is the cross section area of the fiber core, S1 is the projection area of the light from the fiber core of SMF1 to the surface of SMF2. S2 is the projection area of the light from the fiber cladding of SMF1 to the surface of SMF2. S is the area of SMF2 core. Finally, the fringe visibility K of the interference patterns can be described as, K=
2 R1 R2 I core I cladding
(9) I core R22 + I cladding R12 As the SMF2 had an axial micro-displacement along the z axis direction, the couple efficiency from Icore and Icladding to I1 and I2 will be adjusted, which will induce a change on the visibility of the interference patterns. The axial micro-displacement of the SMF2 along the z axis direction can be obtained by monitoring the fringes amplitude variation of the interference patterns. 3. Results and discussion Figure 2 shows the transmission spectra of the MZI corresponding to the axial microdisplacement variation of the SMF2 along z axis direction. It can be seen that the fringe visibility K decreased with the increasing of micro-displacement ranging from 0 to 49 μm. The interferences between the core mode and the cladding modes were analyzed by using the fast Fourier transform method. Figure 3 shows the spatial frequency spectra of the interference patterns of Fig. 2 for the micro-displacements of 0 and 49 μm. It can be seen that there are many cladding modes are excited. As the micro-displacement is 0, the no.1 exited cladding mode is dominant cladding mode. Other excited higher order cladding modes are weak. The interference pattern is mainly formed by the interference of the dominant strong cladding mode with the core mode. Other weak cladding modes should also interference with the core mode, which will slightly modulate the main interference pattern. However, as the micro-displacement is 49 μm, the previous no.1 exited cladding mode almost disappeared. The interference pattern is mainly formed by the interference of the no.2 cladding mode with the core mode. Obviously, the intensity of no.2 cladding mode is lower than that of no.1 cladding mode. Moreover, the intensities of no.3 to no.6 cladding modes are only slightly lower than that of no.2 caldding mode. So the interferences between the core mode and these cladding modes will seriously modulate the main interference pattern, which will lead to a decreasing of the fringe visibility. In addition, the red shifts of the resonant wavelengths in interference patterns may be owe to the interferences between the high order cladding modes and core mode.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31987
Fig. 2. Transmission spectra of the MZI corresponding to different axial micro-displacements.
Fig. 3. Spatial frequency spectra of the proposed sensor.
The fringes visibility variation and resonant wavelength shifts of the interference patterns as a function of axial micro-displacement variation of the SMF2 along z axis direction are depicted in Fig. 4. We selected the resonant wavelength of 1520.6 nm in the interference pattern as the experimental parameters. Linear fitting with slopes of −0.362 dB/μm and 0.076 nm/μm were obtained, which are almost 150 times and 11 times high than that of the embedded SMF-photonic-crystal-fiber based MZI micro-displacement sensor [9] and that of bent SMF-multimode fiber-SMF displacement sensor [10], respectively. The experiments were carried out at a room temperature (25 °C). In addition, whether by fringe visibility changes or by the shift of the resonant wavelength to measure the axial micro-displacement, this sensor shows relative good linearity of R2 = 0.9715 and R2 = 0.9942, respectively.
Fig. 4. Fringes visibility variations and resonant wavelength shifts as a function of the microdisplacements.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31988
However, as shown in Fig. 4, we found that the fringe visibility is not strictly linearly decreased with the increasing of the axial micro-displacement. The relative visibility for the axial micro-displacement of 9 μm is almost equal to that of the axial micro-displacement of zero. Experimental results showed that, firstly, the fringe visibility will increase with the increasing of the displacement as the displacement is smaller than a certain displacement value. And then, as the displacement is larger than the certain displacement value, the fringe visibility decreased gradually and linearly. The certain displacement value, we defined it as dc, is related to the interferometer arm lengths L. In order to further study this phenomenon, series of the proposed sensors with different interferometer arm lengths were fabricated. Figure 2 and Fig. 5 showed the contrastive interference patterns of sensors with interferometer arm lengths of 12mm, 18mm, 24mm and 30mm, respectively.
Fig. 5. Interference patterns of proposed sensors varied with the micro-displacements for arm lengths of (a) 18, (b) 24 and (c) 30 mm, respectively.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31989
Fig. 6. Fringe visibilities as a function of micro-displacements under different arm lengths.
For the four kinds of sensors, the relationships between the displacements and the fringe visibilities variation are shown in Fig. 6. It can be seen that under each kind of condition, the fringe visibility of the interference pattern increased a bit for a small range of displacement. And then, it tends to decrease uniformly with the increasing of the displacement. Therefore, there is a turning point of the visibility, which corresponding to dc. For the interferometer arm lengths of 12 mm, 18 mm, 24 mm and 30 mm, the values of dc are 9 μm, 22 μm, 41 μm and 52 μm, respectively. The energy distributions were simulated as shown in Fig. 7 and Fig. 8. Figures 7(a) and 7(b) show the distributions of Icore and Icladding with interferometer arm length of 12 mm for the displacement of 0 μm . It can be seen that the power coupled from fiber core to cladding when the light propagates through the BBT (z = 1000μm), which leads to the normalized intensity transmitted in the fiber core declining form 1 to 0.75, meanwhile the normalized intensity transmitted in the fiber cladding increase from 0 to 0.2. Then, as the light propagates through the core-offset (z = 13000μm), the normalized intensity of Icore and Icladding are 0.5 and 0.145 respectively.
(a)
Fig. 7. (a) Icore and (b) Icaldding distributions with an interferometer arm lengths of 12 mm for the displacement of 0 μm.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31990
The normalized intensity of I1 and I2 with four interferometer arm lengths corresponding to different axial micro-displacements will be obtained in the same way. The simulation results of I1 and I2 distribution with interferometer arm lengths of 12mm, 18mm, 24mm and 30mm are shown in Fig. 8. Both of I1 and I2 decrease with the increasing of microdisplacement and I1 decreases much faster than I2. Hence, the value of I1 is gradually close to that of I2, which results in the increasing of the fringe visibility. The visibility reaches its maximum at value of dc when I1 equal to I2. As the axial displacement continues to increase, the value difference between I1 and I2 increases gradually, and then the visibility of the interference patterns will decrease uniformly.
Fig. 8. I1 and I2 distributions with four different interferometer arm lengths of 12 mm, 18 mm, 24 mm, and 30 mm under different axial micro-displacements.
As the micro-displacement is larger than of dc, the visibility of the interference patterns varied with the axial micro-displacement linearly. With the arm length L of 12 mm, 18 mm, 24 mm and 30 mm in the total micro-displacement measurement ranges, the sensitivities were −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, respectively. The obtained sensitivity of −0.385 dB/μm is about 150 times high than that of embedded SMF-photoniccrystal-fiber based MZI micro-displacement sensor [9]. The measurement accuracy is easily disturbed by the light source power fluctuations with the use of light intensity demodulation method. However, in our previous work, a difference arithmetic demodulation method has been demonstrated [15]. Therefore, we can use the similar method to eliminate the impact of the light source fluctuation on measurement accuracy. In addition, like other MZI based sensor using core offset means, there is a big insertion loss in experiment. However, to obtain the value of the micro-displacement, we only need to measure the relative power variations of the resonance dips. So the accuracy of the experiment results will not be influenced by the insertion loss. The axial micro-displacement experimental measurements were performed in a temperature controlled environment, and the temperature variation was less than ± 0.1 °C. But in practical applications, the surrounding temperature was not invariable. Consequently, the influence of temperature on the proposed displacement sensor was investigated. The total MZI part was placed into a temperature controlled container with a temperature increasing #222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31991
from 20 to 80 °C. The temperature responses of the proposed micro-displacement sensors are shown in Fig. 9. We selected the micro-displacement of 30 μm as the experimental parameters for the measuring of the influence of temperature variation. As the surrounding temperature increased from 20 to 80 °C, the maximum temperature error were −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C corresponding to interferometer arm lengths of 12, 18, 24, 30 mm, respectively.
Fig. 9. Temperature errors of the proposed sensors for the micro-displacement of 30 μm.
4. Conclusion In conclusion, a simple and compact axial micro-displacement MZI sensor has been demonstrated. The MZI sensor was constructed by an offset connecting of two SMFs and a BTT in one of the two SMFs. The axial micro-displacement can be measured by detecting the visibility variations of the interference patterns. Four kinds of the MZI with different interferometer arm lengths have been investigated simultaneously. For the arm length L of 12, 18, 24 and 30 mm, the proposed sensors showed high sensitivity of −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, with the temperature errors of −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C, respectively. Benefited from the using of visibility demodulation method, the temperature cross-sensitivity effects on the proposed sensor can be neglected in practical applications. The cost-efficient demodulation method and simple fabrication process shows the proposed sensor has a great potential for many sensing applications. Acknowledgments This work was supported by General Administration of Quality Supervision, Inspection and Quarantine of China (Grant No. 201510066-02), National Natural Science Foundation of China (Grant No. 61405185) and Science and Technology Department of Zhejiang Province (Grant No. 2014C33065).
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31992
Institute of Optoelectronic Technology, China Jiliang University, Hangzhou, 310018, China 2 Department of Electronics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada * [email protected]
Abstract: A Mach-Zehnder interferometer (MZI) based fiber axial microdisplacement sensor was proposed. The MZI was constructed by a bowknot-type taper (BTT) combining with a fiber core-offset between two single mode fibers (SMFs). The axial micro-displacement of the core offset is correlated with the MZI transmission spectrum and varied with the interferometer arm length. For the arm length L of 12, 18, 24 and 30 mm, the proposed sensors showed high sensitivity of −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, and temperature errors of −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C, respectively. The theoretical simulations of the energy distributions were also given. The obtained sensitivity of −0.385 dB/μm is about 150 times high than that of the current similar existing axial micro-displacement sensor. ©2014 Optical Society of America OCIS codes: (060.2370) Fiber optics sensors; (060.2340) Fiber optics components; (280.4788) Optical sensing and sensors.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
H. R. Alemohammad, E. Foroozmehr, B. S. Cotten, and E. C. Toyserkani, “A dual-parameter optical fiber sensor for concurrent strain and temperature measurement: design, fabrication, packaging, and calibration,” J. Lightwave Technol. 31(8), 1198–1204 (2013). C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “A polarization-maintaining fiber loop mirror based sensor for liquid refractive index absolute measurement,” Sens. Actuators B Chem. 168(20), 360–364 (2012). C. Shen, Y. Zhang, W. Zhou, and J. Albert, “Au-coated tilted fiber Bragg grating twist sensor based on surface Plasmon resonance,” Appl. Phys. Lett. 104(7), 071106 (2014). O. Levy, B. Z. Steinberg, M. Nathan, and A. Boag, “Ultrasensitive displacement sensing using photonic crystal waveguides,” Appl. Phys. Lett. 86(10), 104102 (2005). Z. Xu, L. Cao, C. Gu, Q. He, and G. Jin, “Micro displacement sensor based on line-defect resonant cavity in photonic crystal,” Opt. Express 14(1), 298–305 (2006). R. Yang, Y. S. Yu, Y. Xue, C. Chen, Q. D. Chen, and H. B. Sun, “Single S-tapered fiber Mach-Zehnder interferometers,” Opt. Lett. 36(23), 4482–4484 (2011). K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18(21), 2239–2241 (2006). Z. Tian and S. S.-H. Yam, “In-line abrupt taper optical fiber Mach–Zehnder interferometric strain sensor,” IEEE Photon. Technol. Lett. 21(3), 161–163 (2009). B. Dong and J. Hao, “Temperature-insensitive and intensity-modulated embedded photonic-crystal-fiber modal interferometer based micro-displacement sensor,” J. Opt. Soc. Am. B 28(10), 2332–2336 (2011). Q. Wu, A. M. Hatta, P. Wang, Y. Semenova, and G. Farrell, “Use of a bent single SMS fiber structure for simultaneous measurement of displacement and temperature sensing,” IEEE Photon. Technol. Lett. 23(2), 130– 132 (2011). C. Zhong, C. Shen, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, and J. Wang, “Temperature-insensitive optical fiber two-dimensional micrometric displacement sensor based on an in-line Mach–Zehnder interferometer,” J. Opt. Soc. Am. B 29(5), 1136–1140 (2012). J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22(15), 1129–1131 (1997). C. Shen, J. Chu, Y. Lu, D. Chen, C. Zhong, Y. Li, X. Dong, and S. Jin, “High Sensitive Micro-Displacement Sensor Based on M-Z Interferometer by a Bowknot Type Taper,” IEEE Photon. Technol. Lett. 26(1), 62–65 (2014).
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31984
14. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). 15. C. Shen, C. Zhong, Y. You, J. Chu, X. Zou, X. Dong, Y. Jin, J. Wang, and H. Gong, “Polarization-dependent curvature sensor based on an in-fiber Mach-Zehnder interferometer with a difference arithmetic demodulation method,” Opt. Express 20(14), 15406–15417 (2012).
1. Introduction Optical fiber sensors have received considerable attentions in various sensing applications for the advantages of inexpensive, compact, light weight, immune to electromagnetic interference [1–5]. Micro-displacement is an important physical parameter and should be precisely monitored in various industrial and scientific processes [4, 5]. Recently, optical fiber MachZehnder interferometer (MZI) based on tapered structures have attracted lots of interests in micro-displacement, strain and refractive index sensing applications. R. Yang [6] proposed a single S-tapered fiber MZI with a refractive index sensitivity and strain sensitivity of 1590 nm/RIU and −60 pm/με, respectively. K. Q. Kieu [7] reported a biconical fiber taper MZI sensor with a temperature sensitivity and strain sensitivity of 10pm/°C and 95 pm/με, respectively. Z. Tian [8] proposed an in-line abrupt taper optical fiber MZI strain sensor with a sensitivity of 2000 nm/ε. Bo Dong [9] proposed an embedded single mode fiber (SMF)photonic-crystal-fiber (PCF) based MZI micro-displacement sensor with a sensitivity of 0.0024 dB/μm. Qiang Wu [10] proposed a bent SMF-multimode fiber (MMF)-SMF displacement sensor with a sensitivity of 5.89 pm/μm. However, these displacement sensors either sensitivity is not high, or need to use the wavelength demodulation, which was suffered from the cross sensitivity of the temperature and the displacement (or strain). We have reported a two-dimensional micro-displacement sensor based on in-line MZI previously, which was formed by inserting a polarization maintaining fiber (PMF) between two conventional SMFs using an offset fusion spliced means [11]. Sensitivities of −0.669dB/μm on the slow axis direction and −0.301dB/μm on the fast axis direction of the PMF were obtained. However, it is difficult to make an offset fusion between PMF and SMF. In this paper, a fiber MZI constructed by a core-offset connection of two SMFs and a bowknot-type taper (BTT) is proposed. The BTT, as shown in Fig. 1 (b) and 1(c), is different from the ordinary down-taper. In BBT, by adjusting the taper diameter to match the propagation constant of the mode in the taper with that of the resonant mode of interest, one can couple most of the light into the sphere [12]. For the symmetric structure of the BTT, as the light propagating through this taper, due to the little sphere on the center of the BTT, the light from the left side of the taper will be mostly coupled into the little sphere, and then be coupled into the fiber core of the right side of the taper. It is benefit to control the intensity distribution of fiber core and cladding of SMF1. On the core offset connecting point of the MZI, as SMF1 and SMF2 are in alignment, with the offset value of zero, no interference spectrum was observed. However, as a certain degree offset of the two fiber cores on the other end of the MZI occurred, the interference fringe appeared. Using this design, the microdisplacement on the vertical direction of the fiber axis was detected [13]. However, compared with the micro-displacement on the vertical direction of the fiber axis, the axial microdisplacement along the fiber axis is different and complex. In our design, the core offset value is about 5 μm along the right end of the SMF1 on x axis. The axial micro-displacement of the SMF2 is responded to the MZI transmission spectrum. The fringe visibility of the interference patterns is determined by the value of the axial micro-displacement. And the sensitivity of the sensor varies with interferometer arm lengths were investigated simultaneously. 2. Sensor fabrication and principle The schematic diagram of the proposed sensor is shown in Fig. 1(a). An amplified spontaneous emission (ASE) source of 1450 to 1650 nm wavelength range is used as the light source. The output spectrum is detected with an optical spectrum analyzer (OSA, AQ6370, Advantest, Japan). The maximum resolution of the OSA is 20 pm. The core and cladding diameters of the SMF are 9 μm and 125 μm, respectively. The BTT is formed under modified
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31985
parameters with a commercial electric-arc fusion splicer (Fujikura FSM-60s) by an insufficient-tapered fusion splicing method [13]. The diameter and length of the taper area are ~85μm and ~100μm, respectively. The pictures of the BTT and the offset connect joint are shown in Fig. 1(b) and 1(c), respectively.
Fig. 1. (a) Schematic diagram of the proposed micro-displacement sensor. (b) The partial enlarged drawing of the MZI. (c) Pictures of the BTT and the boundary between SMF1 and SMF2 shown on the fusion splicer screen and the BTT’s micrograph.
After propagating through the BTT, the phase difference Φ m of the light between the core and the cladding modes can be described as [14], m Φ m = 2πΔneff L/λ
(1)
m core clad where Δneff = neff − neff is the effective refractive index difference between the core and the core clad and neff are the effective refractive indices of the fiber core and mth cladding modes. neff fiber cladding, respectively. λ is the center wavelength of the input light. L is the effective length of the interferometer. The intensity I of the interference patterns is,
I = I1 + I 2 + 2 I1 I 2 cos(Φ m )
(2)
where I1 and I2 are the intensities of the light coupled into the core of SMF2. And the fringe visibility K of the interference pattern can be described as, K=
2 I1 I 2
(3) I1 + I 2 From Eq. (3), we can see that the fringe visibility K of the interference pattern is mainly decided by I1 and I2, which come from Icore and Icladding of SMF1, respectively. The light propagating angles θi (i = core, cladding) from SMF1 to SMF2 are related to the numerical aperture of the fiber (NAi) and the refractive index of the surrounding medium n0,
θi = arc sin( NAi / n0 )
(4)
where NAi is correlated with the arm length between the center of the taper and the offset. At the cross section of SMF2, light from SMF1 appears to form a cone and projection onto the SMF 2 with the radius R1 and R2, respectively, Dcore + d tan θ core R1 = 2 tan θ core
#222296 - $15.00 USD (C) 2014 OSA
(5)
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31986
Dcladding + d tan θ cladding R2 = 2 tan θ cladding
(6)
where d is the value of the micro-displacement, Dcore and Dcladding are the diameters of the fiber core and cladding of SMF2, respectively. θ core and θ cladding are decided by Eq. (4). The light coupled into the fiber core of SMF2 from the core and cladding of SMF1 is determined by the sizes of the radiating areas of the SMF1 and reception areas of the SMF2, S S × I core = T ×I S1 π R12 core
(7)
S S × I cladding = T ×I S2 π R22 cladding
(8)
I1 = T I2 = T
where T is the Fresnel transmission coefficient, S is the cross section area of the fiber core, S1 is the projection area of the light from the fiber core of SMF1 to the surface of SMF2. S2 is the projection area of the light from the fiber cladding of SMF1 to the surface of SMF2. S is the area of SMF2 core. Finally, the fringe visibility K of the interference patterns can be described as, K=
2 R1 R2 I core I cladding
(9) I core R22 + I cladding R12 As the SMF2 had an axial micro-displacement along the z axis direction, the couple efficiency from Icore and Icladding to I1 and I2 will be adjusted, which will induce a change on the visibility of the interference patterns. The axial micro-displacement of the SMF2 along the z axis direction can be obtained by monitoring the fringes amplitude variation of the interference patterns. 3. Results and discussion Figure 2 shows the transmission spectra of the MZI corresponding to the axial microdisplacement variation of the SMF2 along z axis direction. It can be seen that the fringe visibility K decreased with the increasing of micro-displacement ranging from 0 to 49 μm. The interferences between the core mode and the cladding modes were analyzed by using the fast Fourier transform method. Figure 3 shows the spatial frequency spectra of the interference patterns of Fig. 2 for the micro-displacements of 0 and 49 μm. It can be seen that there are many cladding modes are excited. As the micro-displacement is 0, the no.1 exited cladding mode is dominant cladding mode. Other excited higher order cladding modes are weak. The interference pattern is mainly formed by the interference of the dominant strong cladding mode with the core mode. Other weak cladding modes should also interference with the core mode, which will slightly modulate the main interference pattern. However, as the micro-displacement is 49 μm, the previous no.1 exited cladding mode almost disappeared. The interference pattern is mainly formed by the interference of the no.2 cladding mode with the core mode. Obviously, the intensity of no.2 cladding mode is lower than that of no.1 cladding mode. Moreover, the intensities of no.3 to no.6 cladding modes are only slightly lower than that of no.2 caldding mode. So the interferences between the core mode and these cladding modes will seriously modulate the main interference pattern, which will lead to a decreasing of the fringe visibility. In addition, the red shifts of the resonant wavelengths in interference patterns may be owe to the interferences between the high order cladding modes and core mode.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31987
Fig. 2. Transmission spectra of the MZI corresponding to different axial micro-displacements.
Fig. 3. Spatial frequency spectra of the proposed sensor.
The fringes visibility variation and resonant wavelength shifts of the interference patterns as a function of axial micro-displacement variation of the SMF2 along z axis direction are depicted in Fig. 4. We selected the resonant wavelength of 1520.6 nm in the interference pattern as the experimental parameters. Linear fitting with slopes of −0.362 dB/μm and 0.076 nm/μm were obtained, which are almost 150 times and 11 times high than that of the embedded SMF-photonic-crystal-fiber based MZI micro-displacement sensor [9] and that of bent SMF-multimode fiber-SMF displacement sensor [10], respectively. The experiments were carried out at a room temperature (25 °C). In addition, whether by fringe visibility changes or by the shift of the resonant wavelength to measure the axial micro-displacement, this sensor shows relative good linearity of R2 = 0.9715 and R2 = 0.9942, respectively.
Fig. 4. Fringes visibility variations and resonant wavelength shifts as a function of the microdisplacements.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31988
However, as shown in Fig. 4, we found that the fringe visibility is not strictly linearly decreased with the increasing of the axial micro-displacement. The relative visibility for the axial micro-displacement of 9 μm is almost equal to that of the axial micro-displacement of zero. Experimental results showed that, firstly, the fringe visibility will increase with the increasing of the displacement as the displacement is smaller than a certain displacement value. And then, as the displacement is larger than the certain displacement value, the fringe visibility decreased gradually and linearly. The certain displacement value, we defined it as dc, is related to the interferometer arm lengths L. In order to further study this phenomenon, series of the proposed sensors with different interferometer arm lengths were fabricated. Figure 2 and Fig. 5 showed the contrastive interference patterns of sensors with interferometer arm lengths of 12mm, 18mm, 24mm and 30mm, respectively.
Fig. 5. Interference patterns of proposed sensors varied with the micro-displacements for arm lengths of (a) 18, (b) 24 and (c) 30 mm, respectively.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31989
Fig. 6. Fringe visibilities as a function of micro-displacements under different arm lengths.
For the four kinds of sensors, the relationships between the displacements and the fringe visibilities variation are shown in Fig. 6. It can be seen that under each kind of condition, the fringe visibility of the interference pattern increased a bit for a small range of displacement. And then, it tends to decrease uniformly with the increasing of the displacement. Therefore, there is a turning point of the visibility, which corresponding to dc. For the interferometer arm lengths of 12 mm, 18 mm, 24 mm and 30 mm, the values of dc are 9 μm, 22 μm, 41 μm and 52 μm, respectively. The energy distributions were simulated as shown in Fig. 7 and Fig. 8. Figures 7(a) and 7(b) show the distributions of Icore and Icladding with interferometer arm length of 12 mm for the displacement of 0 μm . It can be seen that the power coupled from fiber core to cladding when the light propagates through the BBT (z = 1000μm), which leads to the normalized intensity transmitted in the fiber core declining form 1 to 0.75, meanwhile the normalized intensity transmitted in the fiber cladding increase from 0 to 0.2. Then, as the light propagates through the core-offset (z = 13000μm), the normalized intensity of Icore and Icladding are 0.5 and 0.145 respectively.
(a)
Fig. 7. (a) Icore and (b) Icaldding distributions with an interferometer arm lengths of 12 mm for the displacement of 0 μm.
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31990
The normalized intensity of I1 and I2 with four interferometer arm lengths corresponding to different axial micro-displacements will be obtained in the same way. The simulation results of I1 and I2 distribution with interferometer arm lengths of 12mm, 18mm, 24mm and 30mm are shown in Fig. 8. Both of I1 and I2 decrease with the increasing of microdisplacement and I1 decreases much faster than I2. Hence, the value of I1 is gradually close to that of I2, which results in the increasing of the fringe visibility. The visibility reaches its maximum at value of dc when I1 equal to I2. As the axial displacement continues to increase, the value difference between I1 and I2 increases gradually, and then the visibility of the interference patterns will decrease uniformly.
Fig. 8. I1 and I2 distributions with four different interferometer arm lengths of 12 mm, 18 mm, 24 mm, and 30 mm under different axial micro-displacements.
As the micro-displacement is larger than of dc, the visibility of the interference patterns varied with the axial micro-displacement linearly. With the arm length L of 12 mm, 18 mm, 24 mm and 30 mm in the total micro-displacement measurement ranges, the sensitivities were −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, respectively. The obtained sensitivity of −0.385 dB/μm is about 150 times high than that of embedded SMF-photoniccrystal-fiber based MZI micro-displacement sensor [9]. The measurement accuracy is easily disturbed by the light source power fluctuations with the use of light intensity demodulation method. However, in our previous work, a difference arithmetic demodulation method has been demonstrated [15]. Therefore, we can use the similar method to eliminate the impact of the light source fluctuation on measurement accuracy. In addition, like other MZI based sensor using core offset means, there is a big insertion loss in experiment. However, to obtain the value of the micro-displacement, we only need to measure the relative power variations of the resonance dips. So the accuracy of the experiment results will not be influenced by the insertion loss. The axial micro-displacement experimental measurements were performed in a temperature controlled environment, and the temperature variation was less than ± 0.1 °C. But in practical applications, the surrounding temperature was not invariable. Consequently, the influence of temperature on the proposed displacement sensor was investigated. The total MZI part was placed into a temperature controlled container with a temperature increasing #222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31991
from 20 to 80 °C. The temperature responses of the proposed micro-displacement sensors are shown in Fig. 9. We selected the micro-displacement of 30 μm as the experimental parameters for the measuring of the influence of temperature variation. As the surrounding temperature increased from 20 to 80 °C, the maximum temperature error were −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C corresponding to interferometer arm lengths of 12, 18, 24, 30 mm, respectively.
Fig. 9. Temperature errors of the proposed sensors for the micro-displacement of 30 μm.
4. Conclusion In conclusion, a simple and compact axial micro-displacement MZI sensor has been demonstrated. The MZI sensor was constructed by an offset connecting of two SMFs and a BTT in one of the two SMFs. The axial micro-displacement can be measured by detecting the visibility variations of the interference patterns. Four kinds of the MZI with different interferometer arm lengths have been investigated simultaneously. For the arm length L of 12, 18, 24 and 30 mm, the proposed sensors showed high sensitivity of −0.362 dB/μm, −0.385 dB/μm, −0.332 dB/μm and −0.235dB/μm, with the temperature errors of −0.056 dB/°C, −0.036 dB/°C, −0.044 dB/°C, −0.048 dB/°C, respectively. Benefited from the using of visibility demodulation method, the temperature cross-sensitivity effects on the proposed sensor can be neglected in practical applications. The cost-efficient demodulation method and simple fabrication process shows the proposed sensor has a great potential for many sensing applications. Acknowledgments This work was supported by General Administration of Quality Supervision, Inspection and Quarantine of China (Grant No. 201510066-02), National Natural Science Foundation of China (Grant No. 61405185) and Science and Technology Department of Zhejiang Province (Grant No. 2014C33065).
#222296 - $15.00 USD (C) 2014 OSA
Received 2 Sep 2014; revised 1 Oct 2014; accepted 29 Oct 2014; published 18 Dec 2014 29 Dec 2014 | Vol. 22, No. 26 | DOI:10.1364/OE.22.031984 | OPTICS EXPRESS 31992
