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Cross Effect of Strain and Temperature on BrillouinFrequency Shift in Polymer Optical Fibers
Kazunari Minakawa, Yosuke Mizuno, Senior Member, IEEE, and Kentaro Nakamura, Member, IEEE

Abstract—The strain–temperature cross-sensitivity effect on the
Brillouin frequency shift (BFS) in polymer optical fibers (POFs)
is fully investigated. First, we show that the strain coefficient of
the BFS is dependent on the temperature. In the strain ranges of
0–1.2% and 4.0–9.0%, the temperature dependence is linear withcoefficients of 1.5 and – 0.3 MHz/(%·°C), respectively. We then findthat the temperature coefficient of the BFS is linearly dependent on
the strain with a coefficient of 1.5 MHz/(%·°C) in the strain range
of 0–1.2%. For strains of 4.0–9.0%, the BFS basically decreases
with increasing temperature. These results indicate that temperature (and strain) compensation for the strain (and temperature)sensitivity of the BFS is required to correctly detect the magnitudesof the strain and temperature in POF-based Brillouin sensing. For
strains >13%, we show that temperature sensing with no sensitivity to strain is potentially feasible using the BFS in POFs. The
height of the Brillouin gain spectrum is also evaluated.
Index Terms—Brillouin frequency shift, Brillouin scattering,
polymer optical fibers, strain and temperature measurement.

I. INTRODUCTION
IBER-OPTIC strain and temperature sensing techniques
have been extensively studied and used in many application fields including structural health monitoring. Among thevarious types of fiber-optic sensors, those exploiting Brillouinscattering have attracted a considerable amount of attention owing to their capability of completely distributed measurement
based on frequency information [1]–[9]. Their sensor heads areconventionally composed of glass optical fibers, which are easily broken when a strain of only ∼3% is applied. To extend themeasurable maximum strain, polymer optical fibers (POFs) havebeen vigorously studied recently as alternatives to glass fibers
because POFs are generally so flexible that they can withstandstrains >50% [10]–[19].
Brillouin scattering in POFs was first observed in 2010 [10],and since then, its properties have been evaluated from a varietyof aspects. For instance, the Brillouin frequency shift (BFS) dependencies on the strain (a relatively small strain [11] and large

F

Manuscript received December 19, 2016; revised March 7, 2017; accepted
March 24, 2017. Date of publication March 28, 2017; date of current version
May 5, 2017. This work was supported in part by JSPS KAKENHI under Grants
25709032, 26630180, and 15J11445, and in part by research grants from Japan
Gas Association, in part by the ESPEC Foundation for Global Environment
Research and Technology, and in part by the Association for Disaster Prevention
Research. (Corresponding author: Kazunari Minakawa.)
The authors are with the Institute of Innovative Research, Tokyo Institute ofTechnology, Yokohama 226-8503, Japan (e-mail: kminakawa@sonic.pi.titech.
ac.jp; ymizuno@sonic.pi.titech.ac.jp; knakamur@sonic.pi.titech.ac.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2017.2689331

strain [12]) and temperature (a relatively narrow range [11]and wide range [13]) have been clarified to be much different
from those in silica glass fibers. Other unique features of Brillouin scattering in POFs, such as the BFS hopping phenomenon[14] and the strain and thermal memory functions [20]–[22],have also been investigated, and distributed strain and temperature measurements have been recently demonstrated [15]–[17].
However, no reports have been provided regarding the cross effect of the strain and temperature on the BFS in POFs. As thesetwo parameters generally change simultaneously in practicalapplications, clarification of this effect is of crucial importance.
Although the cross effect has been shown to be negligibly small
in the temperature range of 35–83 °C for standard silica singlemode fibers (SMFs) [23], it does not necessarily hold true for
POFs with a much lower glass-transition temperature.
In this work, we investigate the strain-temperature cross effecton the BFS in POFs. First, we measure the BFS dependence on
the strain at different temperatures and that on the temperature
at different strains in the temperature range of 32–60 °C. For
strains ranging from 0 to 1.2%, we find that the strain coefficientof the BFS is linearly dependent on the temperature with acoefficient of 1.5 MHz/(%·°C). The temperature coefficient of
the BFS is also experimentally confirmed to have a linear strain
dependence with a coefficient of 1.5 MHz/(%·°C) (these twovalues are theoretically identical). For strains ranging from 4.0
to 9.0%, the temperature dependence of the BFS coefficient on
the strain is linear with a coefficient of –0.3 MHz/(%·°C). The
BFS is found to basically decrease as the temperature increases,
and its temperature coefficient is confirmed to be dependent
on the strain with a coefficient of –0.3 MHz/(%·°C) (these twovalues are also theoretically equal). These results indicate that
we need temperature (or strain) compensation for the strain (ortemperature) sensitivity of the BFS to perform accurate strain
and temperature sensing using the BFS. For strains >13%, weshow that Brillouin-based temperature sensors with no strain
sensitivity can be potentially implemented using POFs. Afterthe BFS measurement, we measure the dependence of the BGS
height (i.e., the power difference between the BGS peak and thenoise floor) on the strain at different temperatures.

II. PRINCIPLES
Incident light into an optical fiber interacts with acoustic
phonons and generates backscattered light accompanying a frequency downshift of several gigahertz (called the BFS). Thisphenomenon is Brillouin scattering [24], and the spectrum of0733-8724 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

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Fig. 2.
Fig. 1. Experimental setup for measuring the BFS dependence on the strain(or temperature) at different temperatures (or strains). BPF, band-pass filter;
EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer; LD,laser diode; PD, photodetector; PSCR, polarization scrambler. The orange andgreen lines indicate silica SMFs and electrical cables, respectively.

the backscattered light is known as the Brillouin gain spectrum(BGS). The BFS is expressed by [1], [24], [25]

1−σ
E
2n
2nva
,
(1)
=
BF S =λp
λp (1 − 2σ) (1 + σ) ρwhere n is the refractive index, va is the acoustic velocity, σ isthe Poisson’s ratio, E is the Young’s modulus, ρ is the density of
the core material, and λp is the wavelength of the incident light.
As all of these parameters excluding λp are dependent on thestrain and temperature [26]–[34], the BFS also shows strain andtemperature dependencies, which serve as the fundamental principle of Brillouin-based sensing. In perfluorinated graded-index(PFGI) POFs (the only POFs in which Brillouin scattering has
been experimentally observed) [10], [35], the BFS dependence
on the strain at room temperature is reported to be nonmonotonic, i.e., its coefficient varies, including the sign, dependingon the strain (for a strain less than 1.0%, the coefficient is constantly −121 MHz/%) [11]. Moreover, the BFS dependence on
the temperature in PFGI-POFs is reported to be monotonic but
not completely linear (in the limited temperature range from–160 to ∼85 °C at 0% strain, the coefficient is constantly –3.2 MHz/°C) [13].
III. EXPERIMENTAL PROCEDURES
We used ∼440-mm-long PFGI-POF samples (FONTEX,
Asahi Glass Co. Ltd.) with a core diameter of 50 μm, a cladding
diameter of 70 μm, an overcladding diameter of 490 μm,
a core refractive index of ∼1.35, and a propagation loss of∼250 dB/ km at 1.55 μm. The experimental setup for measuring the BFS dependence on the strain (or temperature) atdifferent temperatures (or strains) is depicted in Fig. 1. A
Fresnel-assisted self-heterodyne technique was exploited to acquire the BGS with a high signal-to-noise ratio (SNR) [36].
First, the continuous-wave output from a laser diode (LD) witha central wavelength of 1.55 μm and a bandwidth of ∼1 MHz
was guided to a polarization scrambler (PSCR) to randomize its
polarization state and thus suppress the polarization-dependent

BFS dependence on the strain at four different temperatures.

fluctuations in the signal. The light was then boosted to 30 dBm
using an erbium-doped fiber amplifier (EDFA) and, via an optical circulator, injected into a POF sample fixed on an automatictranslation stage in a thermostatic chamber. Both ends of the
POF were polished to an angle (8°) using a polishing disc, which
was optimally designed so that the angled surfaces of a POF anda silica SMF become parallel when they are connected. One of
the POF ends (SC connector) was connected to an SMF (FCconnector; the port 2 of the circulator) using an SC-FC adaptor;
thus, the Fresnel reflection at the open end of the POF was suppressed. The Brillouin-scattered light from the POF, along with
the Fresnel-reflected light from the SMF-to-POF boundary, wasamplified again to a total power of approximately –4.5 dBm using another EDFA, the amplified spontaneous emission noise ofwhich was suppressed by an optical band-pass filter (BPF). The
light was then guided to a photodetector (PD), which generated
an electrical Brillouin signal because of the beating between
the Brillouin-scattered light and the Fresnel-reflected light. The
Brillouin signal was amplified by 20 dB, observed as a BGS
using an electrical spectrum analyzer (ESA), and sent to a computer for data processing. By fitting the BGS with a Lorentzian
curve [10], [13], the relevant parameters (the BFS, peak power,
and noise floor) were extracted. By changing the strain from
0% to 16% using an automatic translation stage with a speedof 100 μm/s, the strain dependencies of each parameter were
measured. Furthermore, this procedure was repeated at different
temperatures of 32, 40, 51, and 60 °C, and the temperature (andstrain) dependencies of the strain (and temperature) coefficientsof each parameter were derived.
IV. EXPERIMENTAL RESULTS
A. Brillouin Frequency ShiftFig. 2 shows the BFS dependence on the strain measured
at 32, 40, 51, and 60 °C. Irrespective of the temperature, withincreasing strain, the BFS first decreased (for strains from 0
to ∼2%), then increased (for strains from ∼2 to ∼13%), andfinally became constant (for strains >13%). This behavior has
already been reported at room temperature [12]. We measured
the measurement errors (defined here as the standard deviationsof tens of data obtained with 30-times averaging) at 60 °C, atwhich the highest errors are anticipated. The errors in 0–1.2,

MINAKAWA et al.: CROSS EFFECT OF STRAIN AND TEMPERATURE ON BRILLOUIN FREQUENCY SHIFT IN POLYMER OPTICAL FIBERS

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the temperature sensitivity depending on the strain to accurately
measure the temperature using the BFS.
Using these results, the BFS in this strain range (0–1.2%) andin this temperature range (32–60 °C) can be expressed by thefollowing equation:
BF S (ε, T ) = Cε (T )ε + CT (ε) T + BF S (0, 0)= (Cε,T T + Cε (0)) ε + (CT,ε ε + CT (0)) T+ BF S (0, 0)
Fig. 3.

Temperature dependence of the BFS coefficient on the strain (0–1.2%).

Fig. 4. (a) BFS dependence on the temperature and (b) the temperature coefficient of the BFS for strains of 0–1.2%.

∼2.0–9.0, and ∼9.0–16.0% strains were about ±8, 11, and
10 MHz, respectively, in this experiment. In the following, weanalyze the BFS in detail for three strain ranges: 0–1.2%, ∼2.0–
9.0%, and ∼9.0–16.0%.
1) Strains of 0–1.2%: The strain dependence was almost
linear, and its coefficient was plotted as a function of temperature (see Fig. 3). The strain coefficient was shown tobe linearly dependent on the temperature with a coefficientof 1.5 MHz/(%·°C). This indicates that the absolute valueof the strain coefficient (which has negative values) becomes
smaller with increasing temperature, resulting in a deterioration in the strain sensitivity at higher temperature (the value of–121 MHz/% reported in Ref. [11] was obtained at room temperature lower than 32 °C). Therefore, we clarified that we needto select the specific value of the strain sensitivity depending on
temperature to correctly detect the strain magnitude using POFbased Brillouin sensors, especially at higher temperatures. Notethat such compensation is not required when standard silica
SMFs are used at temperatures less than 83 °C [23].
The temperature dependence of the BFS was linear regardlessof the strain [see Fig. 4(a)]. Further, the temperature coefficientof the BFS was linearly dependent on the strain with a coefficientof 1.5 MHz/(%·°C) [see Fig. 4(b)]; it is natural that this value isthe same as the temperature coefficient of the strain coefficientmentioned in the preceding paragraph. Note that the value of–3.2 MHz/°C at zero strain reported in Ref. [13] was obtainedusing another type of PFGI-POF sample (GINOVER, Sekisui
Chemical Co. Ltd.); different dopants and their concentration
could strongly affect the BFS dependence on temperature [37].
As the absolute value of the coefficient is lowered with increasing strain, the temperature sensitivity of the BFS deteriorates
at a larger strain. Thus, we need to use the specific value of(2)

where ε is strain (%), T is temperature (°C), Cε (T ) is the strain
coefficient of the BFS (MHz/%) at the temperature T, CT (ε) isthe temperature coefficient of the BFS (MHz/°C) at the strainε, Cε,T is the temperature coefficient of Cε (T ) (MHz/(%·°C)),
CT,ε is the strain coefficient of CT (ε) (MHz/(%·°C)). As mentioned above, the value of Cε,T is the same as that of CT,ε .
Eq. (2) should be practically used to measure the strain andtemperature accurately using the BFS in PFGI-POFs.
2) Strains of ∼2.0–9.0%: In Fig. 2, by exploiting the BFS
dependence in this strain range, strain sensing exploiting the socalled strain memory effect with a wider dynamic strain range
appears to be feasible [20], [21] unlike strain sensing in the range
of 0–1.2%. In that case, we need to apply ∼2% strain beforehand. We calculated the strain coefficients of the BFS at eachtemperature using the measured data in the range of 4.0–9.0%(where the strain dependence was almost linear irrespective ofthe temperature) and plotted them as a function of the temperature (see Fig. 5). The strain coefficient (or strain sensitivity)
decreased with a coefficient of –0.3 MHz/(%·°C) with increasing temperature, indicating that the temperature compensationof the coefficient is also required for BFS-based strain sensing
in this strain range. The absolute values of the coefficients inthis range were, regardless of the temperature, <1/5 of those forstrains of 0–1.2%, resulting in a lower strain sensitivity.
The temperature dependence of the BFS was calculated at
different strains [see Fig. 6(a)]. The trends were not completely
linear partially due to the thermal instability of the thermostaticchamber. The BFS tended to decrease with increasing temperature. The temperature coefficient, calculated by a rough linear
approximation, exhibited a linear strain dependence with a coefficient of –0.3 MHz/(%·°C) [see Fig. 6(b)], which was also
the same as the value derived in the preceding paragraph. As
the absolute value of the temperature coefficient increased withincreasing strain, the temperature sensitivity of the BFS became
higher at a larger strain. Therefore, in this strain range, the strain
compensation of the BFS coefficient on temperature is also required for accurate temperature sensing. Note that Eq. (2) is stillvalid because the temperature (and strain) dependencies of the
BFS coefficients on the strain (and temperature) were linear.
3) Strains of ∼9.0–16.0%: The BFS slightly increased as thestrain increased and became almost independent of the strain.
The critical strain at which the BFS became almost constant
was plotted as a function of the temperature (see Fig. 7). Suchcritical strains were calculated as the intersection of (i) the regression line of the strain dependence of the BFS in the range of
4.0–9.0% and (ii) the horizontal line indicating the BFS value
averaged for strains >13%. The dependence on the temperature

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Fig. 8.

Temperature dependence of the BFS for strains of 13.0–16.0%.

Fig. 5. Temperature dependence of the BFS coefficient on the strain(4.0–9.0%).

Fig. 6. (a) BFS dependence on the temperature and (b) the temperature coefficient of the BFS for strains of 4.0–9.0%.

Fig. 9. Strain dependence of the BGS height measured at four different temperatures.

B. BGS HeightFig. 7. Critical strain (at which the BFS becomes almost constant) plotted asa function of the temperature.

exhibited a monotonic increase with a roughly linear coefficientof 0.11%/°C. This result indicates that the dynamic strain range
for strain sensing (which exploits the BFS dependence in therange of ∼2–9%) is widened at higher temperatures, which isa trade-off with the strain sensitivity (refer to the preceding
paragraph). Moreover, as the critical strain corresponds to thestrain at which the POF partially starts to slim down [14], thistemperature dependence may explain the reason why this slimdown phenomenon does not occur in the case of POF tapering
performed at high temperatures [38], [39].
For strains >13%, the BFS became almost constant. The
temperature dependence of the BFS (averaged in the range of
13–16%) is shown in Fig. 8. The BFS decreased with increasing
temperature, and the rough linear approximation led to a coefficient of –1.8 MHz/°C. By using POFs prestrained at strains>13%, temperature sensors with no sensitivity to strain appear
to be implementable.

Fig. 9 shows the strain dependence of the change in the BGS
height measured at 32, 40, 51, and 60 °C. Here, the BGS heightwas defined as the difference between the peak power and thenoise floor. At 32 and 40 °C, the BGS height slightly decreased
with increasing strain, and its change reached approximately–1 dB at ∼16% strain. The slopes of the strain dependencies
for strains >8% measured at 32 and 40 °C were approximately–0.14 and –0.12 dB/%, respectively. In contrast, when the temperature was greater than 51 °C, the BGS height was almost
constant. Thus, strain sensing using the BGS height, which canbe potentially used to implement simultaneous strain and temperature sensing [40], appears difficult at temperatures >51 °C(although the SNR is insufficient even at temperatures <40 °C
at present).
V. CONCLUSION
In the temperature range of 32–60 °C and in the strain range
of 0–16%, we investigated the BFS and BGS height dependencies on the strain (and temperature) at different temperatures(and strains) in POFs. First, the strain coefficient of the BFS
was shown to be linearly dependent on the temperature witha coefficient of 1.5 MHz/(%·°C) for strains of 0–1.2% and –0.3 MHz/(%·°C) for strains of 4.0–9.0%, indicating degradedstrain sensitivity at higher temperatures. The absolute value ofthe strain coefficient for strains of 4.0–9.0% was then foundto be <1/5 of that for strains of 0–1.2% at the same temperature. Subsequently, the temperature coefficient of the BFS was
found to be linearly dependent on the strain with a coefficientof 1.5 MHz/(%·°C) for strains of 0–1.2%. For strains of 4.0–

MINAKAWA et al.: CROSS EFFECT OF STRAIN AND TEMPERATURE ON BRILLOUIN FREQUENCY SHIFT IN POLYMER OPTICAL FIBERS

9.0%, the BFS tended to decrease with increasing temperature.
The temperature coefficient showed a linear strain dependencewith a coefficient of –0.3 MHz/(%·°C). In addition, temperature sensing that is not susceptible to the strain was shown to
be potentially feasible by using the BFS in POFs prestrained
at strains >13%. Further, we found that strain sensing using
the BGS height appears to be difficult at least at temperatures>51 °C. The most important finding is that temperature (andstrain) compensation for the strain (and temperature) dependence of the BFS needs to be conducted to correctly detect thestrain and temperature values in POF-based Brillouin sensing.
We hope that this paper will be an important archive in developing distributed strain and temperature sensors based on Brillouinscattering in POFs.

ACKNOWLEDGMENT
The authors are indebted to Neisei Hayashi, the University ofTokyo, Japan, for his experimental assistance.

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Kazunari Minakawa was born in Ibaraki, Japan, on September 3, 1989. Hereceived the B.E. degree from Ibaraki University, Ibaraki, Japan, in 2012, andthe M.E. degree from Tokyo Institute of Technology, Tokyo, Japan, in 2014. In
2011, he studied 3D-shape and refractive-index measurement of a transparent
object for his B.E. degree at the Ibaraki University. From 2012 to 2014, heworked on nonlinear optics in polymers for his M.E. degree at Tokyo Instituteof Technology. Since 2015, he has been continuing to study polymer optics for
his Dr.Eng. degree at Tokyo Institute of Technology.
In 2015, he became a Research Fellow (DC2) of the Japan Society for the
Promotion of Science. His research interests include fiber-optic sensors andpolymer optics.
Mr. Minakawa is a member of the Japan Society of Applied Physics.

Yosuke Mizuno (M’14–SM’17) was born in Hyogo, Japan, on October 13,
1982. He received the B.E., M.E., and Dr.Eng. degrees in electronic engineeringfrom the University of Tokyo, Japan, in 2005, 2007, and 2010, respectively.
From 2007 to 2010, he was involved in Brillouin optical correlation-domainreflectometry for his Dr.Eng. degree at the University of Tokyo.
From 2007 to 2010, he was a Research Fellow (DC1) of the Japan Society
for the Promotion of Science (JSPS). From 2010 to 2012, as a Research Fellow(PD) of JSPS, he worked on polymer optics at Tokyo Institute of Technology,
Japan. In 2011, he stayed at BAM Federal Institute for Materials Research andTesting, Germany, as a Visiting Research Associate. Since 2012, he has beenan Assistant Professor in the Precision and Intelligence Laboratory (presently,
Institute of Innovative Research), Tokyo Institute of Technology, where he isactive in fiber-optic sensing, polymer optics, and ultrasonics.
Dr. Mizuno is the winner of the Funai Research Award 2010, the Ando
Incentive Prize for the Study of Electronics 2011, the NF Foundation R&D
Encouragement Award 2012, the Tokyo Tech Challenging Research Award
2013, the Konica Minolta Imaging Science Award 2014, the Japanese Societyof Applied Physics (JSAP) Young Scientist Presentation Award 2015, and the
ESPEC Prize for the Encouragement of Environmental Studies 2016. He is a
Senior Member of the IEEE Photonics Society, the JSAP, and the Institute ofElectronics, Information, and Communication Engineers of Japan.

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 12, JUNE 15, 2017

Kentaro Nakamura (M’00) was born in Tokyo, Japan, on July 3, 1963. Hereceived the B.E., M.E., and Dr.Eng. degrees from Tokyo Institute of Technology, Japan, in 1987, 1989, and 1992, respectively.
Since 2010, he has been a Professor in the Precision and Intelligence Laboratory (presently, Institute of Innovative Research), Tokyo Institute of Technology. His research field is the applications of ultrasonic waves, measurement ofvibration and sound using optical methods, and fiber-optic sensing.
Dr. Nakamura is the winner of the Awaya Kiyoshi Award for Encouragementof Research from the Acoustical Society of Japan (ASJ) in 1996, and the Best
Paper Awards from the Institute of Electronics, Information and Communication
Engineers (IEICE) in 1998 and from the Symposium on Ultrasonic Electronics
in 2007 and 2011. He also received the Japanese Journal of Applied Physics
Editorial Contribution Award from the Japan Society of Applied Physics (JSAP)in 2007. He is a member of the ASJ, the JSAP, the IEICE, and the Institute ofElectrical Engineers of Japan.