LETTERIEICE Electronics Express, Vol.14, No.3, 1–9

Single-end-access strain andtemperature sensing basedon multimodal interference inpolymer optical ﬁbers
Tomohito Kawa1, Goki Numata1, Heeyoung Lee1, Neisei Hayashi2,
Yosuke Mizuno1a), and Kentaro Nakamura1
1

Institute of Innovative Research, Tokyo Institute of Technology,

Yokohama 226–8503, Japan
2

Research Center for Advanced Science and Technology, The University of Tokyo,

Tokyo 153–8904, Japana) ymizuno@sonic.pi.titech.ac.jp

Abstract: We develop a single-end-access strain/temperature sensor conﬁguration based on multimodal interference in a polymer optical ﬁber (POF)
with an extremely high sensitivity. The light Fresnel-reﬂected at the distal
open end of the POF is exploited. We obtain high strain and temperaturesensitivities of –122.2 pm/µε and 10.1 nm/°C, respectively, which are
shown to be comparable to those in two-end-access conﬁgurations.
Keywords: optical ﬁber sensors, multimodal interference
Classiﬁcation: Optical systems
References© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

[1] A. D. Kersey, et al.: “Fiber grating sensors,” J. Lightwave Technol. 15 (1997)
1442 (DOI: 10.1109/50.618377).
[2] J. Jung, et al.: “Fiber Bragg grating temperature sensor with controllable
sensitivity,” Appl. Opt. 38 (1999) 2752 (DOI: 10.1364/AO.38.002752).
[3] B. O. Guan, et al.: “Simultaneous strain and temperature measurement using a
superstructure ﬁber Bragg grating,” IEEE Photonics Technol. Lett. 12 (2000)
675 (DOI: 10.1109/68.849081).
[4] Y. Zhang and W. Yang: “Simultaneous precision measurement of hightemperature and large strain based on twisted FBG considering nonlinearity
and uncertainty,” Sens. Actuators A Phys. 239 (2016) 185 (DOI: 10.1016/j.sna.
2016.01.012).
[5] V. Bhatia and A. M. Vangsarkar: “Optical ﬁber long-period grating sensors,”
Opt. Lett. 21 (1996) 692 (DOI: 10.1364/OL.21.000692).
[6] Y. P. Wang, et al.: “Highly sensitive long-period ﬁber-grating strain sensor with
low temperature sensitivity,” Opt. Lett. 31 (2006) 3414 (DOI: 10.1364/OL.31.
003414).
[7] P. Wang, et al.: “Fabrication of phase-shifted long-period ﬁber grating and its
application to strain measurement,” IEEE Photonics Technol. Lett. 27 (2015)
557 (DOI: 10.1109/LPT.2014.2385067).
[8] T. Kurashima, et al.: “Brillouin optical-ﬁber time domain reﬂectometry,” IEICE
Trans. Commun. E76-B (1993) 382.
[9] Y. Dong, et al.: “High-spatial-resolution fast BOTDA for dynamic strain

1

IEICE Electronics Express, Vol.14, No.3, 1–9© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

measurement based on diﬀerential double-pulse and second-order sideband of
modulation,” IEEE Photon. J. 5 (2013) 2600407 (DOI: 10.1109/JPHOT.2013.
2267532).
[10] D. Garus, et al.: “Distributed sensing technique based on Brillouin optical-ﬁber
frequency-domain analysis,” Opt. Lett. 21 (1996) 1402 (DOI: 10.1364/OL.21.
001402).
[11] K. Hotate and T. Hasegawa: “Brillouin optical-ﬁber time domain reﬂectometry,” IEICE Trans. Electron. E83-C (2000) 405.
[12] Y. Mizuno, et al.: “Proposal of Brillouin optical correlation-domain
reﬂectometry (BOCDR),” Opt. Express 16 (2008) 12148 (DOI: 10.1364/OE.
16.012148).
[13] Y. Mizuno, et al.: “Ultrahigh-speed distributed Brillouin reﬂectometry,” Light
Sci. Appl. 5 (2016) e16184 (DOI: 10.1038/lsa.2016.184).
[14] M. A. Farahani and T. Gogolla: “Spontaneous Raman scattering in opticalﬁbers with modulated probe light for distributed temperature Raman remotesensing,” J. Lightwave Technol. 17 (1999) 1379 (DOI: 10.1109/50.779159).
[15] M. N. Alahbabi, et al.: “Simultaneous temperature and strain measurementwith combined spontaneous Raman and Brillouin scattering,” Opt. Lett. 30(2005) 1276 (DOI: 10.1364/OL.30.001276).
[16] M. K. Saxena, et al.: “Raman optical ﬁber distributed temperature sensor using
wavelet transform based simpliﬁed signal processing of Raman backscatteredsignals,” Opt. Laser Technol. 65 (2015) 14 (DOI: 10.1016/j.optlastec.2014.06.
012).
[17] Y. J. Rao, et al.: “Dual-cavity interferometric wavelength-shift detection for inﬁber Bragg grating sensors,” Opt. Lett. 21 (1996) 1556 (DOI: 10.1364/OL.21.
001556).
[18] O. Frazão, et al.: “Optical ﬁber refractometry based on multimodeinterference,” Appl. Opt. 50 (2011) E184 (DOI: 10.1364/AO.50.00E184).
[19] Y. Liu and L. Wei: “Low-cost high-sensitivity strain and temperature sensing
using graded-index multimode ﬁbers,” Appl. Opt. 46 (2007) 2516 (DOI: 10.
1364/AO.46.002516).
[20] S. M. Tripathi, et al.: “Strain and temperature sensing characteristics of singlemode–multimode–single-mode structures,” J. Lightwave Technol. 27 (2009)
2348 (DOI: 10.1109/JLT.2008.2008820).
[21] J. Huang, et al.: “Polymer optical ﬁber for large strain measurement based on
multimode interference,” Opt. Lett. 37 (2012) 4308 (DOI: 10.1364/OL.37.
004308).
[22] G. Numata, et al.: “Ultra-sensitive strain and temperature sensing based onmodal interference in perﬂuorinated polymer optical ﬁbers,” IEEE Photon. J. 6
(2014) 6802306 (DOI: 10.1109/JPHOT.2014.2352637).
[23] G. Numata, et al.: “Strain and temperature sensing based on multimodeinterference in partially chlorinated polymer optical ﬁbers,” IEICE Electron.
Express 12 (2015) 20141173 (DOI: 10.1587/elex.12.20141173).
[24] G. Numata, et al.: “Drastic sensitivity enhancement of temperature sensing
based on multimodal interference in polymer optical ﬁbers,” Appl. Phys.
Express 8 (2015) 072502 (DOI: 10.7567/APEX.8.072502).
[25] A. Kumar, et al.: “Transmission characteristics of SMS ﬁber optic sensor
structures,” Opt. Commun. 219 (2003) 215 (DOI: 10.1016/S00304018(03)01289-6).
[26] M. Kumar, et al.: “A comparison of temperature sensing characteristics of SMS
structures using step and graded index multimode ﬁbers,” Opt. Commun. 312(2014) 222 (DOI: 10.1016/j.optcom.2013.09.034).
[27] A. Mehta, et al.: “Multimode interference-based ﬁber-optic displacement
sensor,” IEEE Photonics Technol. Lett. 15 (2003) 1129 (DOI: 10.1109/LPT.

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IEICE Electronics Express, Vol.14, No.3, 1–9

2003.815338).
[28] E. Li, et al.: “Fiber-optic temperature sensor based on interference of selective
higher-order modes,” Appl. Phys. Lett. 89 (2006) 091119 (DOI: 10.1063/
1.2344835).
[29] R. M. Ribeiro and M. M. Werneck: “An intrinsic graded-index multimodeoptical ﬁbre strain-gauge,” Sens. Actuators A 111 (2004) 210 (DOI: 10.1016/
j.sna.2003.11.009).
[30] Y. Koike and M. Asai: “The future of plastic optical ﬁber,” NPG Asia Mater. 1(2009) 22 (DOI: 10.1038/asiamat.2009.2).
[31] T. Ishigure, et al.: “Optimum index proﬁle of the perﬂuorinated polymer-based
GI polymer optical ﬁber and its dispersion properties,” J. Lightwave Technol.
18 (2000) 178 (DOI: 10.1109/50.822790).
[32] Y. Mizuno and K. Nakamura: “Experimental study of Brillouin scattering in
perﬂuorinated polymer optical ﬁber at telecommunication wavelength,” Appl.
Phys. Lett. 97 (2010) 021103 (DOI: 10.1063/1.3463038).

1© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

Introduction

Fiber-optic strain and temperature sensors have been developed based on avariety of principles including ﬁber Bragg gratings [1, 2, 3, 4], long-period gratings[5, 6, 7], Brillouin scattering [8, 9, 10, 11, 12, 13], Raman scattering [14, 15, 16],and optical interference [17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. While many typesof interference-based strain and temperature sensors are reported, those based on
the interference of multiple guided modes in multimode ﬁbers (MMFs) havereceived a great deal of attention for the past two decades because of their system
simplicity, cost eﬃciency, and high sensitivity. As summarized in Table 1 inRef. [18], a number of conﬁgurations have been implemented; the most commonlyused conﬁguration of them is a so-called “single-mode-multimode-single-mode”(SMS) structure [19, 20, 21, 22, 23, 24, 25, 26], where an MMF is sandwiched
between two single-mode ﬁbers (SMFs).
Let us review the recent developments of SMS-based strain and temperature
sensors. Using a 1.8-m-long silica graded-index (GI-) MMF, a strain sensitivity of+18.6 pm/µε and a temperature sensitivity of +58.5 pm/°C were obtained at1550 nm [19]. Both the absolute values and the signs of the strain and temperaturesensitivities were found to be determined by “critical wavelengths” [20], which
depend on the core diameter and/or the dopant of silica MMFs. To extend themeasurable strain range, using a 0.16-m-long polymethyl methacrylate (PMMA)based step-index polymer optical ﬁber (POF) as an MMF, a strain sensitivity of−1.72 pm/µε and a temperature sensitivity of −56.8 pm/°C were obtained at
1570 nm [21]. However, the propagation loss of PMMA-based POFs at telecom
wavelength is so high ( 1  105 dB/km) that the measurable distance is intrinsically limited to several meters or less. To overcome this problem, we have recently
implemented SMS-based strain and temperature sensors using perﬂuorinated (PF)GI-POFs [22, 23, 24], which are the only POFs with a relatively low loss of∼250 dB/km even at 1550 nm (or ∼50 dB/km at 1300 nm). When the POF length
was 1.0 m and the core diameter was 62.5 µm, we obtained a strain sensitivity of−111.8 pm/µε and a temperature sensitivity of +49.8 nm/°C at room temperature
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at 1300 nm; these values are by far larger than those previously reported using other
MMFs [22].
Thus, substantial eﬀorts have been made to improve the performance of SMSbased strain and temperature sensors, but almost all the SMS-based sensors
reported thus far are two-end-access systems, in which both ends of the MMF
are physically connected to SMFs. From a practical viewpoint, single-end-access
conﬁgurations with an enhanced degree of freedom in embedding the sensors into
structures are preferable. There are only three examples of such single-end-access
conﬁgurations; the ﬁrst is a displacement sensor reported by Mehta et al. [27],which comprises an SMF-MMF-airgap-mirror structure. It is, however, diﬃcult
to directly employ this structure to measure strain and temperature; in addition, useof the mirror reduces the ease of handling. The second is a temperature sensor
reported by Li et al. [28], in which no descriptions on strain sensing capability havebeen provided at all. The third is a strain sensor reported by Ribeiro et al. [29], inwhich strain is measured based on modulated power; its operating principle is quite
diﬀerent from that of other frequency-based SMS sensors.
In this work, by using Fresnel reﬂection at the distal open end of the MMF, wedevelop a single-end-access conﬁguration of SMS-based strain and temperaturesensing systems, in which PFGI-POFs were employed as MMFs to obtain highsensitivities. We experimentally show that when the MMF length is the same, thestrain and temperature sensitivities do not largely change regardless of the conﬁgurations (i.e., either single- or two-end access).
2

Principle

A conceptual setup of the conventional two-end-access (or transmissive) conﬁguration is depicted in Fig. 1(a). When light is injected from an SMF to an MMF,
a few lower modes are excited in the MMF owing to the spot-size diﬀerence
between the fundamental (or 0th) modes in the SMF and the MMF. They propagate
along the MMF with their respective propagation constants and reach the other
MMF-to-SMF interface, at which the net ﬁeld coupled to the SMF is determined by
the relative phase diﬀerences among the multiple modes guided in the MMF. Under
the assumption that the MMF and SMFs are axially aligned, the modes excited in
the MMF are axially symmetric, and the optical power Pout output from the SMS
structure is expressed as [25]Pout ¼ ja0 2 þ a1 2 exp ið0  1 ÞL þ a2 2 exp ið0  2 ÞL þ    j2 ;© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

ð1Þ

where ai is the ﬁeld amplitude of the i-th mode at the ﬁrst SMF-to-MMF interface,i is the propagation constant of the i-th mode, and L is the MMF length. Thisequation indicates that the optical output power is inﬂuenced by physical changes(especially, the changes in the propagation constants and in the MMF length)
caused by strain and temperature. Thus, by measuring the shift of spectral dips (orpeaks), strain and temperature sensing can be performed.
Subsequently, a conceptual setup of the single-end-access (or reﬂectometric)
conﬁguration is shown in Fig. 1(b). The light injected from an SMF into an MMF
via an optical circulator is Fresnel-reﬂected at the distal open end of the MMF
and then propagates back along the MMF and the SMF; the output spectrum is
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IEICE Electronics Express, Vol.14, No.3, 1–9(a)Fig. 1.

(b)Conceptual setups of (a) transmissive conﬁguration and (b)reﬂectometric conﬁguration. MMF, multimode ﬁber; SMF,
single-mode ﬁber.

ﬁnally observed at the third port of the circulator. In this reﬂectometric conﬁguration, the optical path length in the MMF becomes twice as long as that in thetransmissive one; the purpose of this work includes clariﬁcation of this eﬀect on
the sensitivities.
3

Experimental setup

The MMFs used in the experiment are PFGI-POFs [30] with a core diameter of
62.5 µm and a cladding diameter of 72.5 µm. Their core and cladding layers arecomposed of doped and undoped polyperﬂuorobutenylvinyl ether, respectively. The
POF length is 0.7 m (except for the experiment of the length dependence measurement). The refractive indices at the center of the core and in the cladding layer areapproximately 1.35 and 1.34, respectively, irrespective of the optical wavelength[31]. An overcladding layer (diameter: 750 µm) composed of polycarbonate iscoated outside the cladding layer to lower microbending loss and to improve theload-bearing capability.
The actual experimental setups of transmissive (for comparison) and reﬂectometric conﬁgurations are shown in Fig. 2(a) and 2(b), respectively. In both
conﬁgurations, a swept-source laser with a 20-kHz sweep rate was employed asa broadband light source with a central wavelength of 1320 nm and a bandwidthof 110 nm. The laser output was ﬁrst input to a polarization controller to suppress
the polarization-dependent spectral ﬂuctuations, and then injected into the POF. In
Fig. 2(a), both ends of the POF were butt-coupled to silica SMFs via “SC/PC-FC/
PC” adaptors [32], and the spectrum of the transmitted light was monitored using
an optical spectrum analyzer (OSA). In contrast, in Fig. 2(b), one end of the POF(a)Fig. 2.
© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017(b)

Actual experimental setups of (a) transmissive conﬁgurationand (b) reﬂectometric conﬁguration. OSA, optical spectrum
analyzer; PFGI-POF, perﬂuorinated graded-index polymer
optical ﬁber; PSCR, polarization scrambler; SSL, swept-source
laser. The yellow lines indicate silica single-mode ﬁbers.

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IEICE Electronics Express, Vol.14, No.3, 1–9

Fig. 3.

(a)

(b)

(c)

(d)

Measured spectral dependences on strain in (a) transmissive
conﬁguration and (b) reﬂectometric conﬁguration. The dip
wavelength dependences on strain in (c) transmissive conﬁguration and (d) reﬂectometric conﬁguration.

was butt-coupled to a silica SMF in the same way, but the other end was kept open
(ﬂatly polished); the spectrum of the reﬂected light was monitored using an OSA.
Note that the optical circulator used in Fig. 2(b) had an operating wavelength of1280 to 1340 nm and insertion losses of approximately 0.5 dB for both directions(i.e., port 1 to port 2 and port 2 and port 3). In both cases, the entire length of the
POF was strained or heated. The room temperature was approximately 28°C.
4© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

Experimental results

The measured dependences of the spectral dips on strain in transmissive andreﬂectometric conﬁgurations are shown in Fig. 3(a) and 3(b), respectively. In bothcases, a single relatively broad dip was observed in this range, which shifted toshorter wavelengths with increasing applied strain. The spectral power in Fig. 3(b)was approximately 20 dB lower than that in Fig. 3(a); this is valid considering theloss of Fresnel reﬂection at the POF end (∼2.2% reﬂection, corresponding to a
16.5 dB loss; by a simple calculation based only on the core refractive index
diﬀerence) and the additional POF propagation loss (if compared with the Fresnel
loss, negligibly low with this short POF (0.7 m)). In the reﬂectometric conﬁguration, if necessary, we could form a mirror at the open end of the POF to increase
the spectral power. Figs. 3(c) and 3(d) show the dip wavelengths plotted asfunctions of strain. The dependences were both almost linear with slopes of−1218 nm/% (¼ 121:8 pm/µε; transmissive) and −1222 nm/% (¼ 122:2
pm/µε; reﬂectometric). These values moderately agree with the previously reported

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value [22]; the discrepancy probably originates from the imperfect end faces,
asymmetric coupling to the SMFs, and longitudinal structural non-uniformity of
the POF.
Subsequently, the dependences of the dip on temperature were also measured(Figs. 4(a) (transmissive) and 4(b) (reﬂectometric)). The dips shifted to shorter
wavelengths as temperature increased. The dip wavelengths plotted as functions oftemperature (Figs. 4(c) and 4(d)) indicate that the temperature-dependence coefﬁcients were 9.63 nm/°C (transmissive) and 10.1 nm/°C (reﬂectometric); thesevalues are also consistent with those previously reported [22]. Thus, the reﬂectometric conﬁguration was experimentally proved to possess almost the same strain
and temperature sensitivities as those of transmissive conﬁguration with an advantage of single-end accessibility (see Appendix). One concern is that when the
POF length is longer than several dozen meters, the additional propagation loss
may result in the reﬂected spectrum buried by the noise ﬂoor. This problem could
be mitigated by attaching a mirror at the end of the POF.

Fig. 4.

5© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

(a)

(b)

(c)

(d)

Measured spectral dependences on temperature in (a) transmissive conﬁguration and (b) reﬂectometric conﬁguration. The
dip wavelength dependences on temperature in (c) transmissive
conﬁguration and (d) reﬂectometric conﬁguration.

Conclusion

A single-end-access conﬁguration of SMS-based strain and temperature sensing
systems exploiting Fresnel reﬂection at the distal open end of the MMF (PFGIPOF) was developed. High strain and temperature sensitivities of −122.2 pm/µε7IEICE Electronics Express, Vol.14, No.3, 1–9

and 10.1 nm/°C, respectively, were obtained. These values were comparable tothose in the two-end-access conﬁguration. We anticipate that our method will
drastically enhance the ease of handling of SMS-based ﬁber-optic sensors.
Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers 25709032,
26630180, and 25007652, and by research grants from the Japan Gas Association,
the ESPEC Foundation for Global Environment Research and Technology, and the
Association for Disaster Prevention Research.
Appendix© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 2017

The experimental results may raise the question as to why, although the optical path
length in the POF in the reﬂectometric conﬁguration becomes twice the value in thetransmissive conﬁguration, the strain and temperature sensitivities are not doubled.
This question leads to a fundamental discussion whether the strain and temperaturesensitivities of SMS-based sensors are dependent on the MMF lengths or not.
Suppose the whole length of the MMF is strained or heated. As for thetemperature sensitivity, in some references [20, 22, 23, 24], it was assumed to be
in proportion to the MMF lengths and the units of “nm/°C/m”, “pm/°C/cm”, etc.
were used, where the values expressed with “m” and “cm” are the MMF lengths.
This way of using the units originates from the following theory: “for simplicity,
suppose the interference of the lights only of the two modes (fundamental and ﬁrstorder higher modes [24] or LP06 and LP07 modes [28]) propagating along the MMF.
A longer MMF then leads to their longer optical-path diﬀerence (due to the thermal
expansion, etc.), resulting in a larger temperature-dependence coeﬃcient of the dip
wavelength. Thus, the temperature sensitivity is linearly dependent on the MMF
length”. In the meantime, there has been a hot discussion on what units should be
used for the strain sensitivity. In some references [20, 22, 23, 24], researchers used
“pm/µε”, “nm/%”, etc. probably considering that the strain sensitivity does notdepend on the MMF length because strain in itself is the value divided by the MMF
length. Nevertheless, from the standpoint of the aforementioned two-mode-interference theory, the induced optical path length diﬀerence between the two modes
should be determined not by strain but by displacement. When the MMF is longer,
larger displacement can be obtained with the same strain. Therefore, in this sense,
the units for the strain sensitivity should be “pm/µε/cm”, “nm/%/m”, etc.
However, if this conventional theory does hold true, our experimental results in
the reﬂectometric conﬁguration cannot be elucidated. To refute this theory, wemeasured the POF length dependences of the strain and temperature sensitivities, as
shown in Figs. A1(a) and A1(b), respectively. POFs with lengths of 0.3, 0.7, 1.0,
and 2.0 m were used. Although considerable ﬂuctuations of the values probably
caused by the modal instability were observed, it was clear that neither the strain
sensitivity nor the temperature sensitivity was proportional to the POF lengths. This
result indicates that in theoretical analysis of the performance of the SMS-based
sensors, not only two modes but also many other modes need to be simultaneously
considered. The details of the analysis is out of the scope of this paper, and will

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IEICE Electronics Express, Vol.14, No.3, 1–9(a)Fig. A1.

(b)

Measured POF length dependences of (a) strain and (b)temperature sensitivities.

be discussed elsewhere. Hence, the practically important ﬁnding concerning theunits is that we should use “pm/µε”, “nm/%”, etc. for the strain sensitivity and“nm/°C”, “pm/°C”, etc. for the temperature sensitivity.

© IEICE 2017
DOI: 10.1587/elex.14.20161239
Received December 14, 2016
Accepted December 16, 2016
Publicized January 13, 2017
Copyedited February 10, 20179