BRIEF NOTEJapanese Journal of Applied Physics 57, 058002 (2018)https://doi.org/10.7567/JJAP.57.058002

Displacement sensing based on modal interferencein polymer optical ﬁbers with partially applied strain
Yosuke Mizuno*, Sonoko Hagiwara, Tomohito Kawa, Heeyoung Lee, and Kentaro Nakamura
Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan*E-mail: ymizuno@sonic.pi.titech.ac.jp
Received January 22, 2018; accepted March 5, 2018; published online April 13, 2018
Strain sensing based on modal interference in multimode ﬁbers (MMFs) has been extensively studied, but no experimental or theoretical reports
have been given as to how the system works when strain is applied not to the whole MMF but only to part of the MMF. Here, using a perﬂuorinatedgraded-index polymer optical ﬁber as the MMF, we investigate the strain sensing characteristics of this type of sensor when strain is partiallyapplied to ﬁber sections with different lengths. The strain sensitivity dependence on the length of the strained section reveals that this strain sensor
actually behaves as a displacement sensor. © 2018 The Japan Society of Applied Physics

To develop smart materials and structures, strain sensing using
optical ﬁbers has been regarded as one of the major researchtargets, and its various conﬁgurations have been reported thus
far. Their operating principles include ﬁber Bragg gratings,1–4)
long-period gratings,5–7) Brillouin scattering,8–13) Raman
scattering,14–16) optical interference,17–30) and many others.
Among numerous types of interference-based strain sensors,
those based on the interference of multiple guided modes in
multimode ﬁbers (MMFs) have recently attracted considerable
attention because they generally oﬀer system simplicity, costeﬃciency, and high sensitivity. Many multimode-interferencebased conﬁgurations have been developed, as listed in Table I
in Ref. 18. Here, we focus on the most widely used simple
conﬁguration, which is often referred to as a “single-modemultimode-single-mode” (SMS) structure.19–28) This meansthat an MMF, which works as a sensing ﬁber, is placed
between two single-mode ﬁbers (SMFs).
The ﬁrst demonstration of SMS-based strain sensing was
given by Liu et al.19) Using a 1.8-m-long silica graded-index(GI-) MMF, they reported a strain sensitivity of −18.6 pm=µε
at 1550 nm. Then, Tripathi et al.20) clariﬁed that not only
the absolute value but also the sign of the strain sensitivity
is determined by a so-called “critical wavelength”, which
depends on the structural and material properties of the MMF.
In order to extend the strain dynamic range, Huang et al.21)
used a 0.16-m-long poly(methyl methacrylate) (PMMA)based step-index polymer optical ﬁber (POF) as an MMF
and obtained a strain sensitivity of −1.72 pm=µε at 1570 nm.
The propagation loss of PMMA-based POFs is, however, sohigh at telecommunication wavelength (≫100 dB=m) that themeasurement range is inherently limited to ≪1 m. One solution to tackle this issue is to employ a perﬂuorinated (PF) GIPOF31–36) as an MMF, which is the only POF with a relatively
low loss of ∼0.25 dB=m even at 1550 nm (or ∼0.05 dB=m at
1300 nm). Numata et al.22) implemented an SMS-based strain
sensor using a 1.0-m-long PFGI-POF and obtained a strain
sensitivity of −112 pm=µε (core diameter: 62.5 µm) at 1300
nm. Its absolute value is much larger than those of previous
reports using other MMFs.
In addition to these advances, to date, signiﬁcant eﬀorts
have been made to improve the performance of SMS-based
strain sensors.23,24,26–28) One report has clariﬁed that the strain
sensitivity of an SMS-based sensor does not depend on thelength of the MMF to be strained.27) This fact indicates that
not only two fundamental modes but also many other modes
need to be simultaneously considered to elucidate theperformance of this type of sensor (as is also inferred by
the existence of the critical wavelength).20) In the meantime,
no reports have been published to clarify the operation of thesystem when strain is applied not to the whole length of the
MMF but only to part of the MMF. It is highly conceivable
that, when we monitor the distortion of a structure in whichan MMF is embedded, strain is partially applied to the MMF.
Thus, it is of paramount importance to clarify this point.
In this work, using a PFGI-POF as an MMF, we investigate the performance of the SMS-based strain sensor whenstrain is partially applied to ﬁber sections with diﬀerent
lengths. The strain sensitivity plotted as a function of thelength of the strained section reveals that, whether strain isapplied to the whole length of the MMF or only to part of
the MMF, the SMS-based strain sensors can be treated as
displacement sensors.
Here, we present a simpliﬁed explanation of the operating
principle of SMS-based strain sensing. When light is injectedfrom the ﬁrst SMF into the MMF, multiple guided modes are
excited and travel along the MMF with their respective
propagation constants. At the other MMF-to-SMF boundary,
the net ﬁeld coupled to the second SMF is determined by the
relative phase diﬀerences among all the guided modes. If we
simply assume that the MMF and the two SMFs are perfectly
axially aligned, the optical output power from the second
SMF, Pout, can be given as25)
Pout ¼ ja20 þ a21 exp ið 0  1 ÞLþ a22 exp ið 0  2 ÞL þ    j2 ;

ð1Þwhere aj is the ﬁeld amplitudes of the j-th modes at the ﬁrst
SMF-to-MMF boundary, βj is the propagation constants of thej-th modes, and L is the length of the MMF. It is clear that Poutis inﬂuenced by strain applied to the MMF (which causes
some change in βj and L), and it is thus feasible to performstrain sensing by measuring the shift of spectral dips or peaks.
The MMF used in the experiment is a 1.0-m-long PFGIPOF.31–36) It has a core diameter of 62.5 µm, a cladding
diameter of 72.5 µm, and an overcladding diameter of 750 µm.
The core and cladding layers are made up of doped andundoped polyperﬂuorobutenylvinyl ether [refractive indices:
1.356 (center) and 1.342], respectively, while the overcladding layer for protecting the core and cladding layers is
composed of polycarbonate.
The experimental setup of the SMS-based strain sensing
using the PFGI-POF is depicted in Fig. 1. The output of asupercontinuum source (SCS) with a bandwidth of 460–

058002-1© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 058002 (2018)

Y. Mizuno et al.

Fig. 1. (Color online) Experimental setup. OSA: optical spectrum
analyzer; PFGI-POF: perﬂuorinated graded-index polymer optical ﬁber;
SCS: supercontinuum source; SMF: single-mode ﬁber.

(a)Fig. 2. (Color online) Optical spectra measured before and after thetransmission through the POF. The spectral dip in the green circle was usedin the subsequent measurements.

2000 nm was injected into one end of the PFGI-POF. The
SMF-to-POF coupling was performed using so-called buttcoupling.32) The transmitted light was injected into an SMF
and then guided to an optical spectrum analyzer (OSA) witha bandwidth of 600–1700 nm. The whole setup was ﬁxed
during all measurements, which led to a negligible change inthe polarization state (guaranteed by the fact that almost thesame spectral patterns were constantly observed). Strain
was applied partially to the middle of the PFGI-POF usingtranslation stages. The lengths of the strained sections were set
to 0.1, 0.2, 0.4, 0.6, 0.8, and 0.93 m (note that 0.93 m is thelength of the whole POF excluding the connectors at bothends). Regardless of the lengths of the strained sections, thesame amount of displacement of up to 500 µm was applied.
We ﬁrst measured and compared the optical spectra before
and after the transmission through the POF, namely, those of
the SCS output and the OSA input (Fig. 2). The optical powerat each wavelength was reduced by ∼7.7 dB mainly becauseof the propagation loss of the POF. The spectrum after the
POF transmission exhibited some dips; as these dips were notobserved in the spectrum before the POF transmission, it isclear that they were induced by the modal interference in
the POF. Considering that the extremely clear dips around1300 nm are caused not by the modal interference but by theinherent property of the SCS, we used the relatively clear
dip at 1470 nm in the following measurements.
Subsequently, we measured the spectral change around1470 nm when a displacement of up to 500 µm was applied toa 0.1-m-long section in the middle of the POF (corresponding
to partially applied strain of up to 0.5%). As shown in
Fig. 3(a), with increasing displacement, the dip shifted toshorter wavelength. The dip wavelength dependence on displacement was almost linear [Fig. 3(b)], and its dependence
coeﬃcient (with displacement converted into strain) was(b)
Fig. 3. (Color online) (a) Applied displacement dependence of thespectral dip at 1470 nm when the length of the strained section was 0.1 m.
(b) Corresponding dip wavelength plotted as a function of displacement.
The solid line is a linear ﬁt.

−3.1 pm=µε. We also measured the spectral change whendisplacement was applied to POF sections with diﬀerent
lengths. The example results, i.e., the spectral dependence anddip wavelength dependence on displacement when the lengthof the strained section was 0.93 m, are shown in Figs. 4(a) and
4(b), respectively. As displacement was increased, the dip
shifted to shorter wavelength with a dependence coeﬃcient of−48 pm=µε. Its absolute value is 2.3 times smaller than that ofour previous report 22) because not only the strained length but
also the measured wavelength region was largely diﬀerent.
Finally, the absolute value of the measured strain sensitivity
was plotted as a function of the length of the strained section(Fig. 5). The sensitivity was almost proportional to thestrained length with a coeﬃcient of 51.7 pm=µε=m. This
result indicates that, regardless of the strain magnitude or thestrained length, the spectral dip shifts for the same amountof wavelength, as long as the displacement of the POF isconstant. This feature is not a matter of course, consideringthat the strain sensitivity does not explicitly depend on the
POF length (when strain is applied to the whole length) andthat all the guided modes in the POF need to be simultaneously considered to explain the behavior of this sensor.
Additional discussion based on a “refocusing length” of a
GI-MMF37) is provided in the online supplementary data
at http://stacks.iop.org/JJAP/57/058002/mmedia. Thus, we
proved that, even including the case where strain is applied
only to part of the POF, SMS-based “strain” sensing can be

058002-2© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 058002 (2018)

Y. Mizuno et al.

SMS-based strain sensors can be treated as displacement
sensors. We believe that this ﬁnding will be a basic but
important guideline when we practically use SMS-based
strain sensors to monitor the conditions of civil structures in
the future.
Acknowledgments This work was supported by JSPS KAKENHI Grant
Numbers 17H04930 and 17J07226, and by research grants from the Japan Gas
Association, the ESPEC Foundation for Global Environment Research andTechnology, the Association for Disaster Prevention Research, the Fujikura
Foundation, and the Japan Association for Chemical Innovation.

(a)

(b)
Fig. 4. (Color online) (a) Applied displacement dependence of thespectral dip at 1470 nm when the length of the strained section was 0.93 m.
(b) Corresponding dip wavelength plotted as a function of displacement. The
solid line is a linear ﬁt.

Fig. 5. (Color online) Measured strain sensitivity (absolute value) plotted
as a function of the length of the strained section. The solid line is a linear ﬁt.

treated as “displacement” sensing; note that a strain sensor
using the whole length of the ﬁber is naturally treated asa displacement sensor, as strain and displacement are in oneto-one correspondence in this case.
In conclusion, we characterized the SMS-based strain
sensor using a PFGI-POF when strain was partially applied toﬁber sections with diﬀerent lengths, and the strain sensitivity
was found to be proportional to the length of the strained
section. This result indicates that, whether strain is applied to
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058002-3© 2018 The Japan Society of Applied Physics

Supplementary Information

Displacement sensing based on modal interference inpolymer optical fibers with partially applied strain
Yosuke Mizuno*, Sonoko Hagiwara, Tomohito Kawa, Heeyoung Lee, and Kentaro Nakamura
Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan*

E-mail: ymizuno@sonic.pi.titech.ac.jp

Discussion
We discuss how we can reasonably explain the apparently contradictory results of theprevious report (the strain sensitivity (and the dip shift as well) does not explicitly depend on
the MMF length)27) and this paper (the dip shift clearly depends on the MMF length (because
the dip shift is proportional to the displacement)). What is important here is a “refocusing
length” of a GI-MMF, which is the period of the continual refocusing of the rays in the core.
The refocusing length Lref can be calculated using the core radius a (62.5 μm / 2) and therefractive indices of the core (center) n1 and the cladding n2 (which are 1.356 and 1.342,
respectively) as:37) Lref = πa√2/(1 − 𝑛2 /𝑛1 ), which is 1366 μm in this experiment. In the
SMS-based measurement, similar transmitted spectra are repeatedly obtained when the MMF
is elongated by multiples of the refocusing length, as experimentally shown in Figs. S1(a)–(d)and S2. In the measurements in this paper, displacements (changed continuously from 0 up to
500 μm) were applied to part of the GI-MMF. As a result, an identical spectral dip(corresponding to the same modal conditions) around 1470 nm was tracked, leading to theclear dependence of the dip shift on the MMF length. In contrast, in the measurements in theprevious report,27) the strain sensitivity around 1310 nm was investigated when the MMF
length was discontinuously set to 0.3, 0.7, 1.0, and 2.0 m (note that each difference is much
longer than the refocusing length). Considering that similar spectra are repeatedly obtained
when the MMF length is changed by multiples of the refocusing length, even when spectral
dips are observed in the same wavelength region, they may not correspond to the same modal
conditions. In general, the dips corresponding to different modal conditions have different
strain sensitivities even when observed in the same wavelength region (see Figs. S3(a),(b)).
Therefore, it is reasonable that, in the previous report,27) the strain sensitivity did not
explicitly depend on the MMF length, unlike in this paper.
1Supplementary Figures

Supplementary Figure S1 | Transmitted optical spectra when displacements ΔL of (a) 0, (b)440, (c) 880, and (d) 1320 μm were applied to the whole length of a 0.5-m-long PFGI-POF.
Note that the spectrum of (a) has a marked similarity to that of (d).

Supplementary Figure S2 | Pearson correlation coefficient (calculated using the data in the
wavelength range from 800 to 1600 nm) plotted as a function of displacement. This clearlyshows that similar spectra were repeatedly observed when the MMF was elongated bymultiples of approximately 1320 μm (which is close to the refocusing length).
2

Supplementary Figure S3 | (a,b) Examples of the spectral dependences on strain.

3