JOURNAL OF APPLIED PHYSICS 119, 223102 (2016)

Dependence of Brillouin frequency shift on water absorption ratio
in polymer optical fibers
Kazunari Minakawa,1,a) Kotaro Koike,2 Neisei Hayashi,3 Yasuhiro Koike,2 Yosuke Mizuno,1
and Kentaro Nakamura1,a)1
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology,
4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, Japan
2
Keio Photonics Research Institute, Keio University, 7-1 Shinkawasaki, Saiwai-ku, Kawasaki 212-0032, Japan
3
Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1, Komaba, Meguro-ku,
Tokyo 153-8904, Japan(Received 29 March 2016; accepted 24 May 2016; published online 9 June 2016)
We studied the dependence of the Brillouin frequency shift (BFS) on the water-absorption ratio inpoly(methyl methacrylate)-based polymer optical fibers (POFs) to clarify the effect of the humidity
on POF-based Brillouin sensors. The BFS, deduced indirectly using an ultrasonic pulse-echo technique, decreased monotonically as the water absorption ratio increased, mainly because of thedecrease in the Young’s modulus. For the same water absorption ratio, the BFS change was larger
at a higher temperature. The maximal BFS changes (absolute values) at 40, 60, and 80  C were158, 285, and 510 MHz, respectively (corresponding to the temperature changes of 9  C, 16  C,
and 30  C). Thus, some countermeasure against the humidity is indispensable in implementing
strain/temperature sensors based on Brillouin scattering in POFs, especially at a higher temperature. On the other hand, Brillouin-based distributed humidity sensors might be developed by
exploiting the BFS dependence on water absorption in POFs. Published by AIP Publishing.
[http://dx.doi.org/10.1063/1.4953388]
I. INTRODUCTION

Distributed strain/temperature sensing techniques havebecome increasingly important in a variety of application
fields, including structural health monitoring and thermal
management. Among them, strain/temperature sensing basedon Brillouin scattering in optical fibers has attracted significant attention because it offers completely distributed sensing with high stability. Sensor heads of conventional
Brillouin sensors are made of glass optical fibers (GOFs),
which cannot withstand strains exceeding 3%.1–9 To
improve the measurable strain limit, Brillouin sensors basedon polymer optical fibers (POFs) have been extensively studied,10–16 because they generally have high flexibility and canwithstand significantly larger strains exceeding 50%.17,18
To date, some of the fundamental properties of Brillouinscattering in POFs have been investigated, such as theBrillouin gain coefficient, the Brillouin threshold power, theBrillouin frequency shift (BFS), and its strain and temperature dependences.10–16,19–23 The POF-based Brillouin sensing of strain and temperature distributions has also been
demonstrated.14–16 However, no reports have been provided
on the effect of the humidity on the Brillouin properties of
POFs. In standard silica GOFs, as reported, the BFS measured at 1500 nm increases by 0.3 MHz when the relative humidity is increased from 60% to 98%,24 corresponding to astrain change of 6.6 le1 or a temperature change of0.3  C.2,24 This result indicates that the accuracy of
Brillouin sensing is deteriorated by the ambient humidity. As
polymers absorb larger amount of water,25 the accuracy ofa)Authors to whom correspondence should be addressed. Electronic addresses:
kminakawa@sonic.pi.titech.ac.jp and knakamur@sonic.pi.titech.ac.jp

0021-8979/2016/119(22)/223102/5/$30.00

POF-based Brillouin sensors is also expected to be loweredby the humidity. Thus, it is of paramount importance toreveal the effect of water absorption on the Brillouin properties of POFs.
In this work, we evaluate the BFS dependence on thewater absorption ratio in poly(methyl methacrylate)-based(PMMA-) POFs, which are most widely used for POF-based
sensing and are reported as potentially applicable to
Brillouin sensors.21 The BFS decreased monotonically as thewater absorption ratio increased. For the same water absorption ratio, the BFS change increased with the temperature.
The maximal BFS changes (absolute values) caused by thewater absorption at 40, 60, and 80  C were 158, 285, and
510 MHz, respectively (corresponding to temperaturechanges of 9  C, 16  C, and 30  C).21 Therefore, somepreventive steps should be taken to mitigate the influence ofthe humidity and to develop accurate strain/temperature sensors based on Brillouin scattering in POFs.
II. PRINCIPLE

Light transmitted through an optical fiber interacts withacoustic phonons in the core and is backscattered with a frequency downshift of several gigahertz. This phenomenon is
known as Brillouin scattering, and the extent of the frequency downshift is termed the BFS.26 The BFS can be
expressed by1,26,27
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2nva 2n
1r
E
;
(1)
BFS ¼
¼
kp
kp ð1  2rÞð1 þ rÞ q
where n is the refractive index, va is the acoustic velocity, r
is the Poisson’s ratio, E is the Young’s modulus, and q is the119, 223102-1

Published by AIP Publishing.

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223102-2

Minakawa et al.

density of the fiber core; kp is the wavelength of the incident
light. Since n, r, E, and q depend on the fiber strain and theambient temperature,28–36 the BFS has the strain/temperaturedependence.1,2 Thus, by measuring the BFS, the strain- or
temperature-related information, which is the foundation of
Brillouin-based fiber-optic sensing of strain and temperature,
can be derived.26
III. METHODS

The direct observation of Brillouin scattering in
PMMA-POFs is difficult because the low-loss window of thefibers is in the visible range, in which some of the opticaldevices required for fiber-optic Brillouin measurements are
not available (note that Brillouin scattering has been
observed at visible wavelength in bulk materials).37–39
Therefore, we indirectly calculated the BFS dependence on
the water-absorption ratio. Using a PMMA bulk sample (theBrillouin properties of PMMA-POFs with relatively large
core diameters are reported to be almost the same as those of
PMMA bulk samples),40 we measured the acoustic-velocitychange caused by water absorption, and then calculated the
BFS dependence on the water absorption ratio using Eq. (1).
A. Preparation of the PMMA bulk sample

We prepared the PMMA bulk sample by free-radical polymerization. Methyl methacrylate (MMA) and di-tert-butyl
peroxide (DTBP; used as an initiator) were purchased from
Sigma Aldrich. The monomer was distilled using a spinningband column, and DTBP was used as received. The monomer
mixture containing the initiator was transferred into a glass
ampoule and subjected to repeated freeze-pump-thaw cycles.
The ampoule was then flame-sealed in vacuum. The polymerization was conducted at 90  C for 19 h and subsequently at
110  C for 27 h to allow for complete polymerization of themonomers. After the polymerization, we measured the refractive index and the glass transition temperature (Tg).
The refractive index was measured using a prism coupler with an accuracy of 60.0005 at room temperature. The
probe wavelengths were 532.0, 632.8, 839.0, and 1544 nm.
The measured values were fitted to the three-term Cauchy’s
equation.41 Considering that PMMA-POFs will be used as
Brillouin sensors at 650 nm (low-loss window),42 the refractive index at this wavelength was used (calculated to be
1.489).
The Tg value was determined using a differential scanning calorimeter at a scan rate of 10  C/min under dry nitrogen. To avoid the measurement error caused by enthalpy
relaxation, the Tg measurement was performed during thesecond heating scan at the midpoint of the heat capacity transition between the upper and lower points of the deviationfrom the extrapolated rubber and glass lines. The Tg value
was then estimated to be 124  C.

J. Appl. Phys. 119, 223102 (2016)

sample was dried and immersed in pure water at a constanttemperature to measure the water absorption ratio as a function of the immersion time. The water absorption ratio wasdefined as the increase in weight as a percentage of the original weight.
After the measurement, the sample was dried again, andwe investigated its BFS with respect to the immersion timeusing an ultrasonic pulse-echo technique.40 First, as shownin Fig. 1, the sample was placed in degassed pure water ofthe same temperature as was used during the waterabsorption ratio measurement. Next, ultrasonic pulses with acentral frequency of 20 MHz were delivered to the sample
by an ultrasonic transducer, and the reflected signals fromthe top and bottom of the sample were recorded using thesame transducer. By measuring the temporal delay Dtbetween the two reflected waves using an oscilloscope, we
calculated the acoustic velocity va in the PMMA sample as
va ¼

2l
;
Dt

(2)

where l is the sample thickness (¼1.50 mm). Next, we calculated the BFS at kp ¼ 650 nm by substituting the acoustic velocity and the refractive index n into Eq. (1). Here, as ndecreased only by 0.1% (corresponding to 0.1% decreasein the BFS), we assumed the n value to be constant (¼1.489)
during the measurement. These procedures were repeated
while the sample was immersed for 72–96 h, yielding the
BFS dependence on the immersion time.
Finally, by combining the aforementioned two measurement results (water absorption ratio vs. immersion time; BFS
vs. immersion time), we derived the BFS dependence on thewater absorption ratio.
IV. EXPERIMENTAL RESULTS

Figure 2(a) shows the water-absorption ratio at three different temperatures (40, 60, and 80  C, respectively) plottedwith respect to the water-immersion time. This temperature
range was set by considering that glass-rubber phase transitions generally occur at temperatures lower than Tg by several dozen degrees43,44 and that the transition to the rubbery
state caused the physical deformation of the sample, making
the sample thickness difficult to measure accurately. The
measured data were fitted using the following equation:45

B. Estimation of the BFS dependence
on the water-absorption ratio

We cut the PMMA bulk (polymerized as described in
Section III A) into a 1.50 mm thick cylindrical sample. The

FIG. 1. Experimental setup for the estimation of the BFS in the PMMA
sample.

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Minakawa et al.

J. Appl. Phys. 119, 223102 (2016)

FIG. 2. (a) Water-absorption ratio and(b) BFS change vs. water-immersion
time for the PMMA sample. The data
were fitted using Eq. (3).

!
20
ð2k  1Þ2 Dp2
8cs X
1cðtÞ ¼ cs  2
exp t ; (3)p k¼1 ð2k  1Þ2
l2
where c(t) is the water-absorption ratio at immersion time t,
cs is the saturated water-absorption ratio, and D is the diffusion coefficient of the bulk sample. The water-absorption ratio increased with the water-immersion time. The change
was most pronounced at <24 h and nearly leveled off at>96 h. As the temperature increased, the saturation timeshortened and the water-absorption ratio at the steady stateincreased. The saturated water absorption ratios at 40, 60,
and 80  C were 1.9, 2.0, and 2.5%, respectively.
Figure 2(b) shows the BFS dependence on the immersion time at 650 nm at 40, 60, and 80  C. The BFS changes
were observed after the sample was immersed for 40 s(note that the sample absorbs almost no water at the immersion time of 40 s) to exclude the BFS change caused byheating.21 We fitted the obtained BFS values using Eq. (3),considering that the BFS change will roughly follow thechange in the water-absorption ratio (this assumption appears
to be valid because the temporal variations of the BFS
changes in Fig. 2(b) showed similar trends to those in Fig.
2(a)). When the immersion time increased, the BFS
decreased, opposite to GOFs.24 The BFS changes (absolutevalues) at the steady state were 158, 285, and 510 MHz corresponding to temperature changes of 9, 16, and 30  C,
respectively.21
By combining the observations in Figs. 2(a) and 2(b),we calculated the BFS dependence on the water-absorption
ratio (Fig. 3). The BFS monotonically decreased as thewater-absorption ratio increased. For the same waterabsorption ratio, the BFS change (absolute value) was larger
when the temperature was higher. At <1.5%, the BFS dependence on the water-absorption ratio was almost linearwith the coefficients of approximately 47, 124, and225 MHz at 40, 60, and 80  C, respectively.
These results indicate that measurements should betaken to assuage the effect of the humidity to maintain theaccuracy of strain/temperature sensing based on Brillouinscattering in PMMA-POFs, especially at a higher temperature. One such method is based on coating POFs with waterproof materials such as polypropylene46 and polyethylene.47
The use of perfluorinated graded-index POFs, which arereported to absorb no quantifiable water,48 is also a promising solution. However, this disadvantage becomes an advantage for humidity sensing. For example, using the BFS
dependence on the humidity in POFs, distributed Brillouinhumidity sensing might be implemented by exploiting conventional time-,3,4,7 frequency-,8 and correlation-domain
techniques.5,6
V. DISCUSSION

Here, we discuss which of the four parameters (refractive index n, the Poisson’s ratio r, the Young’s modulus E,
and the density q; see Eq. (1)) most dominantly causes the
BFS change when the PMMA sample is immersed in water.
To clarify this, we compared their values before and after
saturated water absorption at 60  C.
When the water absorption ratio is saturated, the refractive index n decreased by 0.1%, which corresponds to0.1% decrease in the BFS, as described in Sec. III A.
Likewise, the density q, measured using the water displacement method with a density determination kit (AD-1653,
A&D), decreased by 0.3%, which corresponds to 0.2%
increase in the BFS. The Poisson’s ratio r and the Young’s
modulus E of the PMMA sample were measured using acompression tester described in Fig. 4. We attached two

FIG. 3. BFS dependence on the water absorption ratio for PMMA; the dependence was calculated using the fitted curves presented in Figs. 2(a) and2(b).

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223102-4

Minakawa et al.

J. Appl. Phys. 119, 223102 (2016)

strain gauges to measure the vertical strain ev and lateralstrain el, and then calculated r using the following
equation:49
r¼

el
:
ev

strain and temperature, the humidity can be measured by distributed Brillouin sensing. We hope that the results describedin this work will be an important step towards future development of next-generation Brillouin sensors.

(4)
ACKNOWLEDGMENTS

On the other hand, the E value was calculated as the slope ofthe stress-strain curve in the elastic region.49 When the
PMMA sample absorbed water, the E value decreased by11%, which corresponds to 6% decrease in the BFS,
whereas the r value was 0.40 and showed no dependence on
the water-absorption ratio in this measurement (with a maximal measurement error of 0.01). Although there should be acorrelation between r and E,49,50 the change rate of r is usually negligibly small compared to that of E. Thus, we deducethat the reduction in the Young’s modulus is the major cause
for the BFS reduction by water absorption.

The authors are indebted to Masaki Tahara, Hideki
Hosoda, Minoru Kuribayashi Kurosawa, Wei Qiu, and Jiang
Wu, Tokyo Institute of Technology, Japan, for theirexperimental assistance. They also acknowledge the staff ofthe Technical Department, Tokyo Institute of Technology,
Japan, for fabricating the stage used in the experiments. This
work was supported by the JSPS KAKENHI Grant Numbers
25709032, 26630180, 25007652, and 15J11445, and byresearch grants from the Iwatani Naoji Foundation, theSCAT Foundation, and the Konica Minolta Science andTechnology Foundation.

VI. CONCLUSION

1

We investigated the BFS dependence on the water
absorption ratio in PMMA to clarify the effect of the humidity on POF-based Brillouin sensors. The BFS decreased
monotonically as the water-absorption ratio increased,
mainly because of the decrease in the Young’s modulus. For
the same water-absorption ratio, the BFS change (absolutevalue) became larger with the increase in the temperature.
The maximal BFS changes (absolute values) caused by thewater absorption at 40, 60, and 80  C were 158, 285, and
510 MHz, respectively (corresponding to temperaturechanges of 9  C, 16  C, and 30  C).21 The dependenceswere almost linear when the water-absorption ratio was<1.5%. The coefficients at 40, 60, and 80  C were approximately 47, 124, and 225 MHz, respectively. Thus, todevelop accurate strain/temperature sensors based on
Brillouin scattering in PMMA-POFs, especially for using
them at a higher temperature, we need to take some actions
to reduce the effect of the humidity, either by coating
PMMA-POFs with waterproof materials or by using special
POFs with almost no water absorption. However, for humidity sensing, the monotonic BFS dependence on the humidity
in PMMA-POFs becomes an advantage. Along with the

FIG. 4. Compression tester for measuring the Poisson’s ratio and theYoung’s modulus in the PMMA sample (dimension: 6.0  6.0  20.0 mm3).

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