A novel lateral force sensor based on a core-offset multi-mode fiber (MMF) interferometer is reported. High extinction ratio can be obtained by misaligning a fused cross section between the single-mode fiber (SMF) and MMF. With the variation of the lateral force applied to a short section of the MMF, the extinction ratio changes while the interference phase remains almost constant. The change of the extinction ratio is independent of temperature variations. The proposed force sensor has the advantages of temperature- and phase-independency, high extinction ratio sensitivity, good repeatability, low cost, and simple structure. Moreover, the core-offset MMF interferometer is expected to have applications in fiber filters and tunable phase-independent attenuators

Dong, Bo

Lit, John W.Y.

Liu, Wing-Ki

Wei, Li

Zhou, Da-Peng

Optics Express

English

Wilfrid Laurier University

Wilfrid Laurier University Scholars Commons @ Laurier Physics and Computer Science Faculty Publications Physics and Computer Science 11-2008 Temperature- and Phase-Independent Lateral Force Sensor based on a Core-Offset Multi-Mode Fiber Interferometer Bo Dong Wilfrid Laurier University Da-Peng Zhou University of Waterloo Li Wei Wilfrid Laurier University, lwei@wlu.ca Wing-Ki Liu University of Waterloo John W.Y. Lit Wilfrid Laurier University, jlit@wlu.ca Follow this and additional works at: https://scholars.wlu.ca/phys_faculty Recommended Citation Dong, Bo; Zhou, Da-Peng; Wei, Li; Liu, Wing-Ki; and Lit, John W.Y., "Temperature- and Phase-Independent Lateral Force Sensor based on a Core-Offset Multi-Mode Fiber Interferometer" (2008). Physics and Computer Science Faculty Publications. 3. https://scholars.wlu.ca/phys_faculty/3 This Article is brought to you for free and open access by the Physics and Computer Science at Scholars Commons @ Laurier. It has been accepted for inclusion in Physics and Computer Science Faculty Publications by an authorized administrator of Scholars Commons @ Laurier. For more information, please contact scholarscommons@wlu.ca. Temperature- and phase-independent lateral force sensor based on a core-offset  multi-mode fiber interferometer Bo Dong,1,* Da-Peng Zhou,2 Li Wei,1Wing-Ki Liu,2 and John W. Y. Lit1 1Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada 2Department of Physics and Astronomy, Guelph-Waterloo Physics Institute, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada *Corresponding author: dbo1978@163.com  Abstract: A novel lateral force sensor based on a core-offset multi-mode fiber (MMF) interferometer is reported. High extinction ratio can be obtained by misaligning a fused cross section between the single-mode fiber (SMF) and MMF. With the variation of the lateral force applied to a short section of the MMF, the extinction ratio changes while the interference phase remains almost constant. The change of the extinction ratio is independent of temperature variations. The proposed force sensor has the advantages of temperature- and phase-independency, high extinction ratio sensitivity, good repeatability, low cost, and simple structure. Moreover, the core-offset MMF interferometer is expected to have applications in fiber filters and tunable phase-independent attenuators. ©2008 Optical Society of America  OCIS codes:  (060.2310) Fiber optics ; (060.2370) Fiber optics sensors. References and links 1. W. Zhang, X. Dong, Q. Zhao, G. Kai, and S. Yuan,“FBG-type sensor for simultaneous measurement of force and temperature, ” IEEE. Photon. Technol. Lett. 13, 1340 –1342 (2001). 2. L. Xue, Q. Hao, J. Liu, G. Huang, T. Guo, and X. Dong, “Force sensing with temperature self-compensated based on a loop thin-wall section beam,” IEEE. Photon. Technol. Lett.18, 271-273 (2006). 3. B. Dong, Q. Zhao, L. Zhao, L. Jin, Y. Miao, T. Liao, and X. Zeng, “Simultaneous measurement of temperature and force based on a special-strain-function-chirped FBG, ” Sens. Actuators, A.147, 169-172 (2008). 4. J. Hao, Z. Cai, J. H. Ng, Y. Gong and P. Varghese, “Simultaneous temperature and lateral force measurement using simple arc-shaped FBG sensor module, ” Electron Lett. 42, 1446 –1447 (2006). 5. S. Takahashi, J. Z. Hao, Y. W. A. Lee, Z. Cai, T. T. Do and B. Y. R. Ng, “Effect of bending methods on FBG lateral force sensor,” Electron Lett. 41, 1270-1271 (2005). 6. K. S. Lau, T. L. Chan, and K. H. Wong, “Force measurement by visibility modulated fiber optic sensor,” Appl. Opt. 38, 7163-7164 (1999). 7. S. Huang, F. Luo and Y. Pan, “Fiber Optic Sensor for Measuring Distributed Forces,” J. Intel. Mater. Syst.  Struct. 5, 427 (1994.)  8. J. Canning and A. L. G. Carter, “Modal interferometer for in situ measurements of induced core index change in optical fibers,” Opt. Lett. 22, 561-563 (1997). 9. Y. Liu and L. Wei, “Low-cost high-sensitivity strain and temperature sensing using graded-index multimode fibers,” Appl. Opt. 46, 2516–2519 (2007).  10. L.V. Nguyen, D. Hwang, S. Moon, D.S. Moon, and Y. Chung, “High temperature fiber sensor with high sensitivity based on core diameter mismatch,” Opt. Express, 16,11369-11375 (2008). 11. E. Li, X. Wang, and C. Zhang, “Fiber-optic temperature sensor based on interference of selective higher-order modes,” Appl. Phys. Lett. 89, 091119 (2006).  12. E. Li, “Temperature compensation of multimode-interference-based fiber devices,” Opt. Lett. 32, 2064-2066 (2007). 13. E. Li, “Sensitivity-Enhanced Fiber-Optic Strain Sensor Based on Interference of Higher Order Modes in Circular Fibers,” IEEE Photon. Tech. Lett. 19, 1266-1268 (2007). 14. D. Zhou, L. Wei, W.K. Liu, Y. Liu, and John W. Y. Lit, “Simultaneous measurement for strain and temperature using fiber Bragg gratings and multimode fibers,” Appl. Opt. 47, 1668-1672 (2008). 15. T. Guo, A. Ivanov, C. Chen, and J. Albert, “Temperature-independent tilted fiber grating vibration sensor based on cladding-core recoupling,” Opt. Lett. 33, 1004-1006 (2008). #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19291 16. S.C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. LT-1, 312-331 (1983).   1. Introduction Different types of force sensors based on fiber Bragg grating (FBG), Mach-Zehnder (M-Z) interferometer, high-birefringence fiber, etc have been developed. Among them, the use of an FBG has to adopt the specially designed beam to realize the temperature and force discrimination [1-3], which leads to a complicated sensing structure. In addition, the force sensors with two FBGs [4, 5] to realize the temperature and force discrimination result not only in measurement errors due to the temperature-strain cross effect of the FBG sensor, but also a complicated structure and high price. Moreover, FBG is very fragile. The force sensor with M-Z interferometer [6] has to adopt a complicated sensing structure to tune the reference arm. Moreover, the fabrication of M-Z interferometer is complicated. High-birefringence fiber-based sensor [7] realized the distributed force measurement, but they did not consider the temperature influence. Compared to the above fiber sensors, the multi-mode fiber (MMF) interference sensors based on modal interference [8] have the advantages of low cost and simple structure, which have attracted much attention. Reported MMF interference sensors were focused on the strain and temperature measurement [9~14]. However, most of the MMF interference strain sensors did not consider the temperature influence [9,13]. One method to overcome the temperature influence on the MMF interference sensor has been presented by our group [14]. By connecting a fiber Bragg grating (FBG) to the MMF interferometer, simultaneous measurement of strain and temperature can be realized. However, the sensor needs to be connected to another fiber sensor such as an FBG, which makes the sensing structure more complex and increases the cost. Moreover, the temperature-strain cross effect of the sensor can not be completely eliminated, which leads to measurement errors.   In this paper, we presented a novel temperature- and phase-independent lateral force sensor based on a core-offset MMF interferometer. By misaligning a fused cross section between the SMF and MMF, a core-offset MMF interferometer with high optical intensity extinction ratio can be obtained. This extinction ratio will change with the variations of the lateral force applied to a short section of the MMF, while the interference phase will remain almost constant. Moreover, it is independent of temperature variations. Experimental results show that the extinction ratio varies quadratically with the applied force. This type of sensor has the advantages of temperature- and phase-independency, good repeatability, high extinction ratio sensitivity, low cost, and simple structure. Moreover, it is expected to be applicable to fiber filters and tunable phase-independent attenuators.  2. Operation principle   Fig. 1. Schematic diagram of the experimental setup (Insets show the interferometer structure and the sensing structure, respectively).  #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19292    As shown in Fig. 1, the core-offset MMF interferometer is a three-segment fiber structure, where a segment of MMF of length L  is connected to two standard communication SMFs. The MMF was originally designed for dispersion compensation applications, with a large dispersion parameter of −270 ps/nm/km at 1550 nm and a cutoff wavelength of 1663 nm. The core/cladding diameter of the MMF is 1.9μm/115.7μm. The SMF-MMF-SMF structure can act as an M-Z interferometer, based on intermodal interference. Many modes with different effective refractive indices can be excited when the light is coupled into the MMF from SMF1. When these modes are re-coupled back into the SMF2, they will interfere with each other. If only considering two dominant modes, the transmission spectrum is approximately a periodic function, given by  2 11 2 1 22 ( )2 cos[ ],n n LI I I I I π λ−= + +                                       (1) where 1I and 2I  are the power distributed in the lower-order and higher-order dominant modes, respectively, with 2I < 1I ; 2n  and 1n are the effective refractive indices of the two modes respectively, and λ  is the wavelength of light in vacuum. The extinction ratio ER  of the interferometer can be given by 2 1 22 1110lg( )1I IERI I+=−. Figure 2 shows the extinction ratio as a function of the power ratio 2 1/I I of the two interference modes. It can be seen that bigger power ratio of 2 1/I I gives rise to higher extinction ratio. The extinction ratio for the                  directly fused 1.9μm/115.7μm MMF interferometer without core-offset is generally lower than 4 dB, corresponding to a power ratio of 0.01. In order to obtain a high extinction ratio, we have to increase the power ratio 2 1/I I , which can be realized by manually offsetting the cores between the SMF2 and MMF at splicing section 2. The core-offset splicing is an effective method to control the modes coupling [15]. The offset dependent loss characteristic was firstly studied with a MMF about 24cm in length. The splicing section 1 is fused automatically without core-offset. Using a broadband source (BBS) with the transmission power spectrum shown as the dotted line in Fig. 3, the transmission power spectra of the interferometer are shown in Fig. 3 for different core-offset distances of d at splicing section 2. It can be seen that there is a best offset position to obtain maximum extinction ratio. The homogeneous spectra in Fig. 3 confirm that the interference is mainly produced by two Fig. 2. Extinction ratio as a function of the power ratio 2 1I I of the two interference modes Fig. 3. Transmission power spectra of the BBS and the MMF interferometer with core-offset d about 0, 4μm, 4.2μm and 5μm, respectively  #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19293dominant modes. Because other higher-order modes are very weak, they have little influence on the interference. When a lateral force is applied to a short section of the MMF, deformation is produced in the MMF, which will lead to power loss of the two modes. For a given applied lateral force, the higher-order mode with power 2I  has more power loss than that of the lower-order mode. Moreover, the power of the higher-order mode decreases much faster than that of the lower- order mode when the force increases. Thus, the power ratio of the two interference modes 2 1/I I  decreases accordingly with the increase of the lateral force, which will lead to a reduction of the extinction ratio (See Fig. 2). With a same lateral force applied to the MMF, the core-offset interferometer with higher extinction ratio will have a larger reduction in extinction ratio. The above phenomena can be applied to the measurement of the lateral force. When the lateral force is applied to a short section l of the MMF, the elongated length lΔ  of the section is far less than L , producing negligible longitudinal strain ( / 0l LΔ ≈ ). Thus the phase in Eq. (1) is only determined by the difference of the two effective mode indices at a given value of λ . The birefringence variation nΔ  per unit length of the core refractive index under the lateral force can be expressed as [16] 4kFnrlEπΔ =                                                                (2) where k is strain optical coefficient, F is the force acting on fiber of length l , and r , E  are the outer radius and Young’s Modulus of the fiber, respectively. Under the lateral force, the two interference modes approximately experience the same amount of variation according to Eq. (2). Thus the difference between two effective mode indices of 2 1n n− almost remains constant. As a result, the interference phase is independent of the lateral force, which can be applied to phase-independent force measurement.  When the ambient temperature changes, the transmission spectrum of the MMF interferometer will shift, which is related to the thermal expansion and thermo-optic coefficients of the MMF material [9,11]. Although the extinction ratio varies with the applied lateral force, it does not change with the temperature variation. This feature can be applied to temperature-independent force measurement. 3. Experimental results and discussions                        The sensing structure is shown in Fig. 1. With the above fabrication method, a core-offset MMF interferometer sensor with the MMF length about 22 cm is fabricated. The extinction ratio reaches 8 dB, as shown in Fig. 4. A section of MMF identical to the sensing MMF is used as a supporting fiber. Rotation of the MMF will lead to inhomogeneous interference spectrum mainly because part of the power in the dominant interference modes is coupled into other higher-order modes. In order to avoid the rotation of the MMF, the interferometer is supported by two fiber holders placed on an optical table, and the supporting MMF and sensing MMF are fixed between two aluminum flakes with smooth surfaces. The width of the aluminum flake is about 1 cm. The transmission spectrum of the sensor is monitored by an optical spectrum analyzer (OSA). With different forces applied to the MMF, the extinction ratio changes accordingly, while the interference phase remains constant, as shown in Fig. 5. This can also be used as a tunable phase independent attenuator.        #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19294                Figure 6 shows the responses of the extinction ratio (See the extinction ratio between the two arrow marks in Fig. 5) to different lateral forces. It can be seen that there is a good quadratic relationship between the extinction ratio and the force for the 1.9μm/115.7μm MMF-based sensor, and the correlation coefficient square reaches 0.9944. In addition, another gradient index MMF of length 150 cm and core/cladding diameter of 50.7μm/125.3μm was used to measure the lateral force with the same sensing mechanism. Again, a good quadratic relationship between the extinction ratio and the applied force is found, and the correlation coefficient square reaches 0.999, as shown in Fig. 6. The extinction ratio of the 50.7μm/125.3μm MMF-based sensor is more sensitive to the force than that of the 1.9μm/115.7μm MMF-based sensor. However, the interferometer based on the 50.7μm/125.3μm MMF needs a longer fiber, which is vulnerable to the influence of the ambient disturbance and is not suitable for smart sensing in actual measurement environment. The interferometer based on the 1.9μm/115.7μm MMF with shorter length is more suitable for the smart sensing in actual measurement environment.                  Figure 7 shows the transmission power spectra of the 1.9μm/115.7μm MMF-based sensor under different temperatures at a fixed force of 2.94 N. When the temperature increases, the spectrum has a red shift; a wavelength shift of 1.516 nm is observed when the temperature varies from 23°C to 50°C. However, the extinction ratio is unaffected when the ambient Fig. 6. Extinction ratio responses to different lateral forces   Fig. 7. Measured transmission power spectra under different temperatures at a fixed force of 2.94 N  Fig. 4. Transmission spectrum of the core-offset MMF interferometer sensor  Fig. 5. Measured transmission power spectra under different lateral forces  #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19295temperature changes. The above experimental results agree with the theoretical prediction of the temperature- and phase-independent features of the force sensor. Additional experimental results show that in the temperature range of 23°C ~ 60°C, the variation of the extinction ratio with the applied force can be well described by a quadratic relation. However, when the temperature is over 60°C, the extinction ratio and phase responses to temperature start to change erratically, which is attributed to the limitation of the thermal property of the MMF and aluminum flake materials. The operational temperature range may be extended by encapsulating temperature compensation materials with negative temperature coefficient to the sensor. In order to avoid breaking the MMF, the force is controlled in the range of 0~ 5.88N. The operational force range of the sensor can be increased by encapsulating the MMF sensing head in materials with high Young’s modulus for practical applications. In addition, in order to avoid the rotation influence of the MMF on the interference spectrum of the sensor, the encapsulating model can adopt shape of a cuboid with a given force direction. 4. Conclusion A novel and simple core-offset MMF interferometer force sensing mechanism has been presented and demonstrated experimentally. The MMF-based interferometer can be obtained by misaligning a fused cross section between the SMF and MMF. The advantages of the sensor include temperature- and phase-independency, high extinction ratio sensitivity, good repeatability, low cost, and simple structure. Moreover, the sensing mechanism shows that core-offset MMF-based interferometer can be applied to tunable phase-independent attenuators. Hence the core-offset MMF interferometer not only has the potential applications in fiber sensing but also in fiber filters and tunable phase-independent attenuators. Acknowledgment This work is supported by the Natural Science and Engineering Research Council of Canada (NSERC). The authors acknowledge Sumitomo Electric Industries, Ltd. for providing the 1.9μm/115.7μm MMF. #102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19296

Temperature- and Phase-Independent Lateral Force Sensor based on a Core-Offset Multi-Mode Fiber Interferometer

Scholars Commons

Wilfrid Laurier University 
Scholars Commons @ Laurier 
Physics and Computer Science Faculty 
Publications Physics and Computer Science 
11-2008 
Temperature- and Phase-Independent Lateral Force Sensor based 
on a Core-Offset Multi-Mode Fiber Interferometer 
Bo Dong 
Wilfrid Laurier University 
Da-Peng Zhou 
University of Waterloo 
Li Wei 
Wilfrid Laurier University, lwei@wlu.ca 
Wing-Ki Liu 
University of Waterloo 
John W.Y. Lit 
Wilfrid Laurier University, jlit@wlu.ca 
Follow this and additional works at: https://scholars.wlu.ca/phys_faculty 
Recommended Citation 
Dong, Bo; Zhou, Da-Peng; Wei, Li; Liu, Wing-Ki; and Lit, John W.Y., "Temperature- and Phase-Independent 
Lateral Force Sensor based on a Core-Offset Multi-Mode Fiber Interferometer" (2008). Physics and 
Computer Science Faculty Publications. 3. 
https://scholars.wlu.ca/phys_faculty/3 
This Article is brought to you for free and open access by the Physics and Computer Science at Scholars Commons 
@ Laurier. It has been accepted for inclusion in Physics and Computer Science Faculty Publications by an 
authorized administrator of Scholars Commons @ Laurier. For more information, please contact 
scholarscommons@wlu.ca. 
Temperature- and phase-independent lateral 
force sensor based on a core-offset  
multi-mode fiber interferometer 
Bo Dong,1,* Da-Peng Zhou,2 Li Wei,1Wing-Ki Liu,2 and John W. Y. Lit1 
1Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada 
2Department of Physics and Astronomy, Guelph-Waterloo Physics Institute, University of Waterloo, 
Waterloo, Ontario N2L 3G1, Canada 
*Corresponding author: dbo1978@163.com  
Abstract: A novel lateral force sensor based on a core-offset multi-mode 
fiber (MMF) interferometer is reported. High extinction ratio can be 
obtained by misaligning a fused cross section between the single-mode fiber 
(SMF) and MMF. With the variation of the lateral force applied to a short 
section of the MMF, the extinction ratio changes while the interference 
phase remains almost constant. The change of the extinction ratio is 
independent of temperature variations. The proposed force sensor has the 
advantages of temperature- and phase-independency, high extinction ratio 
sensitivity, good repeatability, low cost, and simple structure. Moreover, the 
core-offset MMF interferometer is expected to have applications in fiber 
filters and tunable phase-independent attenuators. 
©2008 Optical Society of America  
OCIS codes:  (060.2310) Fiber optics ; (060.2370) Fiber optics sensors. 
References and links 
1. W. Zhang, X. Dong, Q. Zhao, G. Kai, and S. Yuan,“FBG-type sensor for simultaneous measurement of force 
and temperature, ” IEEE. Photon. Technol. Lett. 13, 1340 –1342 (2001). 
2. L. Xue, Q. Hao, J. Liu, G. Huang, T. Guo, and X. Dong, “Force sensing with temperature self-compensated 
based on a loop thin-wall section beam,” IEEE. Photon. Technol. Lett.18, 271-273 (2006). 
3. B. Dong, Q. Zhao, L. Zhao, L. Jin, Y. Miao, T. Liao, and X. Zeng, “Simultaneous measurement of 
temperature and force based on a special-strain-function-chirped FBG, ” Sens. Actuators, A.147, 169-172 
(2008). 
4. J. Hao, Z. Cai, J. H. Ng, Y. Gong and P. Varghese, “Simultaneous temperature and lateral force 
measurement using simple arc-shaped FBG sensor module, ” Electron Lett. 42, 1446 –1447 (2006). 
5. S. Takahashi, J. Z. Hao, Y. W. A. Lee, Z. Cai, T. T. Do and B. Y. R. Ng, “Effect of bending methods on 
FBG lateral force sensor,” Electron Lett. 41, 1270-1271 (2005). 
6. K. S. Lau, T. L. Chan, and K. H. Wong, “Force measurement by visibility modulated fiber optic sensor,” 
Appl. Opt. 38, 7163-7164 (1999). 
7. S. Huang, F. Luo and Y. Pan, “Fiber Optic Sensor for Measuring Distributed Forces,” J. Intel. Mater. Syst.  
Struct. 5, 427 (1994.)  
8. J. Canning and A. L. G. Carter, “Modal interferometer for in situ measurements of induced core index 
change in optical fibers,” Opt. Lett. 22, 561-563 (1997). 
9. Y. Liu and L. Wei, “Low-cost high-sensitivity strain and temperature sensing using graded-index multimode 
fibers,” Appl. Opt. 46, 2516–2519 (2007).  
10. L.V. Nguyen, D. Hwang, S. Moon, D.S. Moon, and Y. Chung, “High temperature fiber sensor with high 
sensitivity based on core diameter mismatch,” Opt. Express, 16,11369-11375 (2008). 
11. E. Li, X. Wang, and C. Zhang, “Fiber-optic temperature sensor based on interference of selective higher-
order modes,” Appl. Phys. Lett. 89, 091119 (2006).  
12. E. Li, “Temperature compensation of multimode-interference-based fiber devices,” Opt. Lett. 32, 2064-2066 
(2007). 
13. E. Li, “Sensitivity-Enhanced Fiber-Optic Strain Sensor Based on Interference of Higher Order Modes in 
Circular Fibers,” IEEE Photon. Tech. Lett. 19, 1266-1268 (2007). 
14. D. Zhou, L. Wei, W.K. Liu, Y. Liu, and John W. Y. Lit, “Simultaneous measurement for strain and 
temperature using fiber Bragg gratings and multimode fibers,” Appl. Opt. 47, 1668-1672 (2008). 
15. T. Guo, A. Ivanov, C. Chen, and J. Albert, “Temperature-independent tilted fiber grating vibration sensor 
based on cladding-core recoupling,” Opt. Lett. 33, 1004-1006 (2008). 
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19291
 16. S.C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. 
LT-1, 312-331 (1983).  
 
1. Introduction 
Different types of force sensors based on fiber Bragg grating (FBG), Mach-Zehnder (M-Z) 
interferometer, high-birefringence fiber, etc have been developed. Among them, the use of an 
FBG has to adopt the specially designed beam to realize the temperature and force 
discrimination [1-3], which leads to a complicated sensing structure. In addition, the force 
sensors with two FBGs [4, 5] to realize the temperature and force discrimination result not 
only in measurement errors due to the temperature-strain cross effect of the FBG sensor, but 
also a complicated structure and high price. Moreover, FBG is very fragile. The force sensor 
with M-Z interferometer [6] has to adopt a complicated sensing structure to tune the reference 
arm. Moreover, the fabrication of M-Z interferometer is complicated. High-birefringence 
fiber-based sensor [7] realized the distributed force measurement, but they did not consider 
the temperature influence. Compared to the above fiber sensors, the multi-mode fiber (MMF) 
interference sensors based on modal interference [8] have the advantages of low cost and 
simple structure, which have attracted much attention. Reported MMF interference sensors 
were focused on the strain and temperature measurement [9~14]. However, most of the MMF 
interference strain sensors did not consider the temperature influence [9,13]. One method to 
overcome the temperature influence on the MMF interference sensor has been presented by 
our group [14]. By connecting a fiber Bragg grating (FBG) to the MMF interferometer, 
simultaneous measurement of strain and temperature can be realized. However, the sensor 
needs to be connected to another fiber sensor such as an FBG, which makes the sensing 
structure more complex and increases the cost. Moreover, the temperature-strain cross effect 
of the sensor can not be completely eliminated, which leads to measurement errors.   
In this paper, we presented a novel temperature- and phase-independent lateral force 
sensor based on a core-offset MMF interferometer. By misaligning a fused cross section 
between the SMF and MMF, a core-offset MMF interferometer with high optical intensity 
extinction ratio can be obtained. This extinction ratio will change with the variations of the 
lateral force applied to a short section of the MMF, while the interference phase will remain 
almost constant. Moreover, it is independent of temperature variations. Experimental results 
show that the extinction ratio varies quadratically with the applied force. This type of sensor 
has the advantages of temperature- and phase-independency, good repeatability, high 
extinction ratio sensitivity, low cost, and simple structure. Moreover, it is expected to be 
applicable to fiber filters and tunable phase-independent attenuators.  
2. Operation principle 
 
 
Fig. 1. Schematic diagram of the experimental setup (Insets show the interferometer structure 
and the sensing structure, respectively). 
 
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19292
    As shown in Fig. 1, the core-offset MMF interferometer is a three-segment fiber 
structure, where a segment of MMF of length L  is connected to two standard communication 
SMFs. The MMF was originally designed for dispersion compensation applications, with a 
large dispersion parameter of −270 ps/nm/km at 1550 nm and a cutoff wavelength of 1663 
nm. The core/cladding diameter of the MMF is 1.9μm/115.7μm. The SMF-MMF-SMF 
structure can act as an M-Z interferometer, based on intermodal interference. Many modes 
with different effective refractive indices can be excited when the light is coupled into the 
MMF from SMF1. When these modes are re-coupled back into the SMF2, they will interfere 
with each other. If only considering two dominant modes, the transmission spectrum is 
approximately a periodic function, given by  
2 1
1 2 1 2
2 ( )2 cos[ ],n n LI I I I I π λ
−
= + +                                       (1) 
where 1I and 2I  are the power distributed in the lower-order and higher-order dominant 
modes, respectively, with 2I < 1I ; 2n  and 1n are the effective refractive indices of the two 
modes respectively, and λ  is the wavelength of light in vacuum. The extinction ratio ER  of 
the interferometer can be given by 2 1 2
2 1
1
10lg( )
1
I I
ER
I I
+
=
−
. Figure 2 shows the extinction 
ratio as a function of the power ratio 2 1/I I of the two interference modes. It can be seen that 
bigger power ratio of 2 1/I I gives rise to higher extinction ratio. The extinction ratio for the  
 
         
 
 
 
 
 
 
directly fused 1.9μm/115.7μm MMF interferometer without core-offset is generally lower 
than 4 dB, corresponding to a power ratio of 0.01. In order to obtain a high extinction ratio, 
we have to increase the power ratio 2 1/I I , which can be realized by manually offsetting the 
cores between the SMF2 and MMF at splicing section 2. The core-offset splicing is an 
effective method to control the modes coupling [15]. The offset dependent loss characteristic 
was firstly studied with a MMF about 24cm in length. The splicing section 1 is fused 
automatically without core-offset. Using a broadband source (BBS) with the transmission 
power spectrum shown as the dotted line in Fig. 3, the transmission power spectra of the 
interferometer are shown in Fig. 3 for different core-offset distances of d at splicing section 2. 
It can be seen that there is a best offset position to obtain maximum extinction ratio. The 
homogeneous spectra in Fig. 3 confirm that the interference is mainly produced by two 
Fig. 2. Extinction ratio as a 
function of the power ratio 
2 1I I of the two 
interference modes 
Fig. 3. Transmission power 
spectra of the BBS and the MMF 
interferometer with core-offset d 
about 0, 4μm, 4.2μm and 5μm, 
respectively 
 
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19293
dominant modes. Because other higher-order modes are very weak, they have little influence 
on the interference. 
When a lateral force is applied to a short section of the MMF, deformation is produced in 
the MMF, which will lead to power loss of the two modes. For a given applied lateral force, 
the higher-order mode with power 2I  has more power loss than that of the lower-order mode. 
Moreover, the power of the higher-order mode decreases much faster than that of the lower- 
order mode when the force increases. Thus, the power ratio of the two interference modes 
2 1/I I  decreases accordingly with the increase of the lateral force, which will lead to a 
reduction of the extinction ratio (See Fig. 2). With a same lateral force applied to the MMF, 
the core-offset interferometer with higher extinction ratio will have a larger reduction in 
extinction ratio. The above phenomena can be applied to the measurement of the lateral force. 
When the lateral force is applied to a short section l of the MMF, the elongated length lΔ  
of the section is far less than L , producing negligible longitudinal strain ( / 0l LΔ ≈ ). Thus the 
phase in Eq. (1) is only determined by the difference of the two effective mode indices at a 
given value of λ . The birefringence variation nΔ  per unit length of the core refractive index 
under the lateral force can be expressed as [16] 
4kF
n
rlEπ
Δ =                                                                (2) 
where k is strain optical coefficient, F is the force acting on fiber of length l , and r , E  are 
the outer radius and Young’s Modulus of the fiber, respectively. Under the lateral force, the 
two interference modes approximately experience the same amount of variation according to 
Eq. (2). Thus the difference between two effective mode indices of 2 1n n− almost remains 
constant. As a result, the interference phase is independent of the lateral force, which can be 
applied to phase-independent force measurement.  
When the ambient temperature changes, the transmission spectrum of the MMF 
interferometer will shift, which is related to the thermal expansion and thermo-optic 
coefficients of the MMF material [9,11]. Although the extinction ratio varies with the applied 
lateral force, it does not change with the temperature variation. This feature can be applied to 
temperature-independent force measurement. 
3. Experimental results and discussions                        
The sensing structure is shown in Fig. 1. With the above fabrication method, a core-offset 
MMF interferometer sensor with the MMF length about 22 cm is fabricated. The extinction 
ratio reaches 8 dB, as shown in Fig. 4. A section of MMF identical to the sensing MMF is 
used as a supporting fiber. Rotation of the MMF will lead to inhomogeneous interference 
spectrum mainly because part of the power in the dominant interference modes is coupled into 
other higher-order modes. In order to avoid the rotation of the MMF, the interferometer is 
supported by two fiber holders placed on an optical table, and the supporting MMF and 
sensing MMF are fixed between two aluminum flakes with smooth surfaces. The width of the 
aluminum flake is about 1 cm. The transmission spectrum of the sensor is monitored by an 
optical spectrum analyzer (OSA). With different forces applied to the MMF, the extinction 
ratio changes accordingly, while the interference phase remains constant, as shown in Fig. 5. 
This can also be used as a tunable phase independent attenuator.  
 
     
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19294
       
 
 
     
 
 
Figure 6 shows the responses of the extinction ratio (See the extinction ratio between the 
two arrow marks in Fig. 5) to different lateral forces. It can be seen that there is a good 
quadratic relationship between the extinction ratio and the force for the 1.9μm/115.7μm 
MMF-based sensor, and the correlation coefficient square reaches 0.9944. In addition, another 
gradient index MMF of length 150 cm and core/cladding diameter of 50.7μm/125.3μm was 
used to measure the lateral force with the same sensing mechanism. Again, a good quadratic 
relationship between the extinction ratio and the applied force is found, and the correlation 
coefficient square reaches 0.999, as shown in Fig. 6. The extinction ratio of the 
50.7μm/125.3μm MMF-based sensor is more sensitive to the force than that of the 
1.9μm/115.7μm MMF-based sensor. However, the interferometer based on the 
50.7μm/125.3μm MMF needs a longer fiber, which is vulnerable to the influence of the 
ambient disturbance and is not suitable for smart sensing in actual measurement environment. 
The interferometer based on the 1.9μm/115.7μm MMF with shorter length is more suitable 
for the smart sensing in actual measurement environment.  
 
         
 
 
 
 
 
 
Figure 7 shows the transmission power spectra of the 1.9μm/115.7μm MMF-based sensor 
under different temperatures at a fixed force of 2.94 N. When the temperature increases, the 
spectrum has a red shift; a wavelength shift of 1.516 nm is observed when the temperature 
varies from 23°C to 50°C. However, the extinction ratio is unaffected when the ambient 
Fig. 6. Extinction ratio 
responses to different lateral 
forces 
 
 
Fig. 7. Measured 
transmission power spectra 
under different temperatures 
at a fixed force of 2.94 N 
 
Fig. 4. Transmission 
spectrum of the core-offset 
MMF interferometer sensor 
 
Fig. 5. Measured 
transmission power spectra 
under different lateral forces 
 
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19295
temperature changes. The above experimental results agree with the theoretical prediction of 
the temperature- and phase-independent features of the force sensor. Additional experimental 
results show that in the temperature range of 23°C ~ 60°C, the variation of the extinction ratio 
with the applied force can be well described by a quadratic relation. However, when the 
temperature is over 60°C, the extinction ratio and phase responses to temperature start to 
change erratically, which is attributed to the limitation of the thermal property of the MMF 
and aluminum flake materials. The operational temperature range may be extended by 
encapsulating temperature compensation materials with negative temperature coefficient to 
the sensor. In order to avoid breaking the MMF, the force is controlled in the range of 0~ 
5.88N. The operational force range of the sensor can be increased by encapsulating the MMF 
sensing head in materials with high Young’s modulus for practical applications. In addition, in 
order to avoid the rotation influence of the MMF on the interference spectrum of the sensor, 
the encapsulating model can adopt shape of a cuboid with a given force direction. 
4. Conclusion 
A novel and simple core-offset MMF interferometer force sensing mechanism has been 
presented and demonstrated experimentally. The MMF-based interferometer can be obtained 
by misaligning a fused cross section between the SMF and MMF. The advantages of the 
sensor include temperature- and phase-independency, high extinction ratio sensitivity, good 
repeatability, low cost, and simple structure. Moreover, the sensing mechanism shows that 
core-offset MMF-based interferometer can be applied to tunable phase-independent 
attenuators. Hence the core-offset MMF interferometer not only has the potential applications 
in fiber sensing but also in fiber filters and tunable phase-independent attenuators. 
Acknowledgment 
This work is supported by the Natural Science and Engineering Research Council of Canada 
(NSERC). The authors acknowledge Sumitomo Electric Industries, Ltd. for providing the 
1.9μm/115.7μm MMF. 
#102117 - $15.00 USD Received 29 Sep 2008; revised 1 Nov 2008; accepted 3 Nov 2008; published 6 Nov 2008
(C) 2008 OSA 10 November 2008 / Vol. 16,  No. 23 / OPTICS EXPRESS  19296


https://scholars.wlu.ca/cgi/viewcontent.cgi?article=1002&amp;context=phys_faculty

Temperature- and Phase-Independent Lateral Force Sensor based on a Core-Offset Multi-Mode Fiber Interferometer

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