JOURNAL OF APPLIED PHYSICS 117, 144505 (2015)

Temperature dependence of Brillouin frequency shift in polymers controlled
by plasticization effectKazunari Minakawa,1,a) Kotaro Koike,2 Qiming Du,3 Neisei Hayashi,1 Yasuhiro Koike,2
Yosuke Mizuno,1 and Kentaro Nakamura1,a)1
Precision and Intelligence Laboratory, 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
Polytechnic School of Engineering, New York University, 6 MetroTech Center, Brooklyn,
New York 11201, USA(Received 30 October 2014; accepted 2 April 2015; published online 14 April 2015)
The temperature-dependence coefficient of Brillouin frequency shift (BFS) in perfluorinatedgraded-index polymer optical fibers is known to change drastically, because of the glass transition,
at a certain critical temperature (Tc), above which the BFS becomes more sensitive to temperature.
In this paper, we demonstrate that the Tc value can be adjusted by varying the dopant concentration,
which is originally used to form the graded-index profile in the core region. Furthermore, we showthat the temperature sensitivity of the BFS is enhanced in the presence of dopant probably because
the temperature sensitivity of Young’s modulus is increased. The results indicate a big potential of
the temperature sensors based on Brillouin scattering with an extremely high sensitivity in a speC 2015 AIP Publishing LLC.
cific desired temperature range. V[http://dx.doi.org/10.1063/1.4917533]

I. INTRODUCTION

Temperature sensors based on Brillouin scattering in
optical fibers have attracted a great deal of attention in fields
such as structural heath monitoring and thermal management, because the sensors can easily be distributed for measurement and maintain a high stability based on frequency
information.1–6 Conventionally, the sensing heads have been
primarily composed of glass optical fibers, which cannot
withstand strains over 3%. To overcome this restriction,
we have been studying Brillouin-based distributed temperature sensors comprising polymer optical fibers (POFs).7–10
To date, we have succeeded in observing Brillouinscattering in perfluorinated graded-index (PFGI-) POFs,
which are composed of cyclic transparent optical polymer(CYTOPV),11 and found that the temperature-dependent
coefficient of the Brillouin frequency shift (BFS) in PFGIPOFs at room temperature is 4.09 MHz/K at 1550 nm.8
The absolute value is approximately 3.5 times that for silica
single-mode fibers (SMFs), indicating that PFGI-POFs arepotentially applicable for temperature sensors with higher
sensitivity. A more interesting result is that with an increasein temperature, the temperature-dependent coefficient of
BFS in PFGI-POFs abruptly decreases at 80  C (hereafter
called the Brillouin critical temperature Tc) and the temperature sensitivity considerably increases above Tc.10
This phenomenon is known to be related to the glasstransition of polymer. Several previous works have shownthat the temperature dependence of the BFS in polymer
materials significantly changes at around the glass-transition
temperatures Tg.12–15 Thus, if the fiber core has a lower Tg
Ra)

Authors to whom correspondence should be addressed. Electronic addresses:
kminakawa@sonic.pi.titech.ac.jp and knakamur@sonic.pi.titech.ac.jp

0021-8979/2015/117(14)/144505/5/$30.00

value than the target temperature range, it should work as an
excellent temperature sensor with a higher sensitivity.
Although one may concern about the thermal stability of
POFs under such conditions, we recently demonstrated thatthe core layer of POFs is not necessarily required to be in a
glassy state to maintain its optical transmission loss as longas the cladding layer is in a glassy state.16
To obtain a desired Tc (or Tg) value, the first choice is toemploy a different kind of polymer as the core. But unfortunately, at this moment, there is no alternative of CYTOP that
can transmit light at 1550 nm, where various optical devices
required to study the BFS properties are available. Thus, inthis study, we focus on another possibility, i.e., addition of
dopant. The parabolic refractive index profile of GI-POF isformed by a gradient of dopant concentration. Here, as the
dopant, low-molecular-weight organic compounds are utilized so that the dopant is compatible with the base polymer
and is diffusible during the fiber fabrication process. In otherwords, the dopant not only forms the GI profile but also performs as plasticizer. As mentioned above, although the BFS
behaviors against the temperature change in different kindsof polymers have been reported, almost no attention has
been given to the effect of “plasticizer” on Tc. In addition,
the influence of the concentration on the temperaturedependence coefficient of the BFS has never been studied,either.
In this paper, we demonstrate that the Tc values follow
the Tg changes caused by the plasticization and clarify the
influence of the dopant concentration on the coefficient. The
best way would be to directly measure the PFGI-POFs withdifferent known dopant concentrations. However, as suchfibers or the raw materials are not commercially available,
wepreparedpoly(2,2,2-trifluoroethyl
methacrylate)117, 144505-1

C 2015 AIP Publishing LLC
V[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
131.112.174.59 On: Thu, 16 Apr 2015 09:11:03

144505-2

Minakawa et al.

(PTFEMA)17 doped with benzyl benzoate (BB) instead, andestimated the BFS at 1550 nm from the acoustic velocity andrefractive index. Although the dopant concentration of
GI-POF is generally specified by the refractive index difference between the dopant and core base polymer, this time
we changed the dopant concentration from the perspective ofTg control.
II. PRINCIPLES
A. Differential scanning calorimetry andglass-transition temperature

The Tg of a polymer material is generally evaluatedusing a differential scanning calorimeter (DSC),18–20 whichis also used to characterize various thermal properties. The
DSC records the difference in the heat flow rate to thesample and to the reference, which are placed in identical
furnaces, as a function of the furnace temperature. In DSC
measurements, both the sample and reference cell are heatedat a constant temperature rate, and their temperature difference is measured with two thermocouples. The temperature
difference is converted into a differential heat flow
rate, which is then plotted as a function of the furnace
temperature.
The obtained curve, referred to as a DSC curve, is used
to determine the Tg of the sample. In the temperature region
with no phase transition, the differential heat flow rate does
not significantly change. However, while the polymer showsa phase transition to a rubbery state, the temperature ceases
to increase because the heat energy is used for the phasetransition, resulting in a drastic drop in the DSC curve. The
Tg is defined as the midpoint of the heat capacity transition
between the upper and lower points of the deviation from theextrapolated rubber and glass lines.
B. Estimation of Brillouin frequency shift in polymer
optical fibers

The incident pump light propagating through an optical fiber undergoes an interaction with acoustic phonons,
generating backscattered light with a frequency downshift.
This phenomenon is known as Brillouin scattering,21 andthe amount of the frequency downshift (2.8 GHz at
1550 nm in PFGI-POFs),8 referred to as the BFS, isexpressed by21–23
sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2nva 2n
1r
E
BFS ¼
¼
;
(1)
kp
kp ð1  2rÞð1 þ rÞ q
where n is the refractive index, va is the acoustic velocity,
kp is the pump wavelength, r is Poisson’s ratio, E isYoung’s modulus, and q is the density; all of the parameters are those in the fiber core. Because n, r, E, and q are
dependent on temperature,24–27 BFS also shows temperature dependence (among the four parameters, the temperature dependence of E has the most significant influence onthat of the BFS in poly(methyl methacrylate)—based(PMMA-) POFs).8,28,29 The temperature dependence of

J. Appl. Phys. 117, 144505 (2015)

BFS is the fundamental principle of Brillouin-based temperature sensing.1–6
As presented above, the Brillouin scattering in POFs has
only been experimentally observed in PFGI-POFs. To estimate the Brillouin properties of POFs based on other polymer materials such as PMMA, which have low-loss windows
in the visible region, an ultrasonic pulse-echo technique has
been developed.30–32 In this scheme, ultrasonic pulses are
first launched to a polymer sample. Note that because of therelatively large core diameter of a POF, it makes almost no
difference whether the sample used here is fiber or bulk.30,32
Then, the waves reflected from the top and bottom surfaces
are detected (Fig. 1). Using the time delay Dt of their detection along with the sample length l, the acoustic velocity va
in the sample can be calculated as
va ¼

2l
:
Dt

(2)

Finally, using Eq. (1), the BFS in the sample can beobtained. By repeatedly performing this measurement on thesame sample in degassed water at various temperatures, theBFS dependence on temperature can also be obtained.
III. EXPERIMENTS
A. Preparation of polymer samples

We synthesized five PTFEMA samples with different
amounts of dopant by free-radical polymerization in bulk.
Monomer mixtures (SynQuest Laboratories) containing theinitiator (benzoyl peroxide (BPO); Sigma Aldrich) and the
dopant (benzyl benzoate (BB); Sigma Aldrich) were transferred into glass ampoules and subjected to repeated freezepump-thaw cycles. In this step, the amount of BB in eachmonomer mixture was adjusted to range the Tg values of thesamples from 35 to 75  C (samples #1–5). The ampoules
were then flame-sealed in vacuo, and the polymerization was
performed in an oil bath. The monomers were distilled usinga spinning band column; the BPO was recrystallized from asolution of chloroform and methanol, and the BPO wascompletely dried in vacuo at room temperature. The BB wasused as received.

FIG. 1. Schematic of experimental setup for estimating BFS in PTFEMA
sample.

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
131.112.174.59 On: Thu, 16 Apr 2015 09:11:03

144505-3

Minakawa et al.

B. Differential scanning calorimetry curve

The Tg values of each sample were measured by DSC(DSC-60, Shimadzu). Before the DSC measurements, inorder to prevent enthalpy relaxation,18 we placed the polymer samples at temperatures 30  C higher than their roughly

J. Appl. Phys. 117, 144505 (2015)

estimated Tg values for 10 min and then rapidly cooled thesamples to room temperature. The temperature of the sample
chamber was constantly monitored using a thermocouple
with a maximal error of 60.1  C. The obtained DSC curves
for samples #1–5 are presented as solid lines in Figs.
2(a)–2(e), respectively. The vertical axes were normalized soFIG. 2. (a)–(e) Temperature dependence of BFS at 1550 nm (circles) and DSC curves (solid curves) in PTFEMA samples #1–5, respectively.

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
131.112.174.59 On: Thu, 16 Apr 2015 09:11:03

144505-4

Minakawa et al.

J. Appl. Phys. 117, 144505 (2015)that the maximal and minimal values in the measured temperature range are 1 and 0, respectively. In all samples, thecurves showed an abrupt drop, corresponding to the phasetransition. The calculated Tg values of samples #1, #2, #3,#4, and #5 were 72.5, 66.8, 51.8, 44.5, and 38.2  C,
respectively.
C. Brillouin critical temperature

To investigate the BFS dependence on temperature in
the PTFEMA samples, the temperature dependence of theacoustic velocity va and the refractive index n of each sample
must be obtained (See Eq. (1)).
First, the temperature dependence of va was investigatedusing the ultrasonic pulse-echo technique. Each bulk sample
was cut into a cylindrical shape with a thickness of 1.50 mm;
the top and bottom surfaces were carefully polished with
3-lm alumina powders. To ensure a similar thermal history
as that for the DSC-curve measurement, the samples were
held at temperature 30  C higher than Tg for 10 min andthen rapidly cooled to room temperature. The samples werethen placed in degassed water (see Fig. 1) and were irradiated by ultrasonic pulses with a central frequency of 20
MHz, which were generated by a focus-type transducer connected to a pulser/receiver. The va values obtained at room
temperature for each sample are presented in Table I. Theirtemperature dependence was then obtained by changing thetemperature of the degassed water from 10 to 80  C. The
temperature was constantly monitored using a platinum resistance temperature detector with a maximal error of
60.4  C.
Next, we measured the refractive indices of each sample
using a prism coupler (Model 2010/M, Metricon) with an accuracy of 60.0005. The probe wavelengths were 532, 632.8,
839, and 1544 nm. The coupling profiles were analyzed asfunctions of the incident angle. The measured values werefitted to the three-term Cauchy’s equation,33 and the refractive indices at 1550 nm (where the Brillouin properties of
PFGI-POFs10 have been studied) were obtained, as presented
in Table I. The refractive indices solely depend on the BB
concentration. As reported for PMMAs,24 the temperaturedependence of the refractive indices was assumed to be
negligible.
By substituting the measured values of va, n, and kp(¼1550 nm) into Eq. (1), we then calculated the BFS in
PTFEMA samples #1–5 at each temperature, which is plotted using circles in Figs. 2(a)–2(e), respectively. The

FIG. 3. The Tc (circles) and the Tg (squares) values plotted as functions of
the dopant concentration. The error bars of Tc are 63  C.

temperature-dependent coefficients suddenly decreased at
the Tc of 66.6, 55.6, 41.4, 34.0, and 26.2  C in samples#1–5, respectively. These values, calculated using the intersection of two straight lines fitted to the BFS curve in its linear regions at sufficiently low and high temperatures, containmaximal errors of 63  C. Water absorption was negligibly
small because each temperature dependence of the BFS was
almost identical to that measured when temperature wasdecreasing from 80  C. Figure 3 shows Tc and Tg plotted asfunctions of the dopant concentration. With increasing concentration, both Tc and Tg monotonically decreased, and Tc
was always lower than Tg by 10  C, irrespective of the concentration. As far as we know, this is the first observationthat Tc exactly follows Tg in a single polymer material when
the dopant concentration varies. In Fig. 4, the temperaturedependence coefficients of the BFS at 20  C and 75  C are

TABLE I. The dopant (BB) concentration, acoustic velocity at room temperature, and refractive indices of PTFEMA bulk samples.

Sample
#1
#2
#3
#4
#5

BB (mol%)

Acoustic
velocity va (m/s) atroom temperature

Refractive index
n at 1550 nm

0
1.99
4.04
6.02
7.98

2.01  103
2.03  103
2.01  103
2.04  103
1.99  103

1.408
1.415
1.419
1.424
1.426

FIG. 4. Temperature-dependence coefficients of the BFS plotted as functions of the dopant concentration; measured at 20  C (blue holy circles) and75  C (orange solid circles).

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
131.112.174.59 On: Thu, 16 Apr 2015 09:11:03

144505-5

Minakawa et al.

presented as functions of the dopant concentration.
Regardless of whether the temperature is below or above Tc,
the coefficients decreased as the dopant concentration
increased. For example, at room temperature (20  C), theBFS coefficient varies from 5.0 to 9.4 MHz/K when the
dopant concentration varies approximately from 0 to
8 mol%. This corresponds to 90-% improvement in the temperature sensitivity (the absolute value of the coefficient).
While the mechanism is not clear, we believe that the temperature sensitivity of the Young’s modulus E in Eq. (1)might increase by the plasticization effect.
IV. CONCLUSION

We prepared five doped PTFEMA samples and studied
the influence of the dopant on the temperature dependence of
the BFS. The Tc value was experimentally proved to follow
the Tg value that was artificially controlled by the dopant
concentration. We also found that the absolute values of thetemperature-dependence coefficients increase as the dopant
concentration increase, probably because the temperaturesensitivity of the Young’s modulus is increased. These
results lead to the conclusion that the doping method is aneasy and efficient way to design POF-based Brillouin temperature sensors with extremely high sensitivities in specificdesired temperature regions.
ACKNOWLEDGMENTS

This work was partially supported by the Funding
Program for World-Leading Innovative R&D on Scienceand Technology (FIRST), Grants-in-Aid for Young
Scientists (A) (No. 25709032) and for Challenging
Exploratory Research (No. 26630180) from the Japan
Society for the Promotion of Science (JSPS), and byresearch grants from the General Sekiyu Foundation, theIwatani Naoji Foundation, and the SCAT Foundation. N.
Hayashi acknowledges a Grant-in-Aid for JSPS Fellows (No.
25007652).
1

T. Kurashima, T. Horiguchi, and M. Tateda, Appl. Opt. 29, 2219 (1990).
T. Horiguchi and M. Tateda, J. Lightwave Technol. 7, 1170 (1989).
3
K. Hotate and T. Hasegawa, IEICE Trans. Electron. E83-C, 405 (2000).
2

J. Appl. Phys. 117, 144505 (2015)4

Y. Mizuno, W. Zou, Z. He, and K. Hotate, Opt. Express 16, 12148 (2008).
T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada,
IEICE Trans. Commun. E76-B, 382 (1993).
6
D. Garus, K. Krebber, F. Schliep, and T. Gogolla, Opt. Lett. 21, 1402
(1996).
7
Y. Mizuno and K. Nakamura, Appl. Phys. Lett. 97, 021103 (2010).
8
Y. Mizuno and K. Nakamura, Opt. Lett. 35, 3985 (2010).
9K. Minakawa, K. Koike, N. Hayashi, Y. Koike, Y. Mizuno, and K.
Nakamura, IEICE Electron. Express 11, 20140285 (2014).
10
K. Minakawa, N. Hayashi, Y. Shinohara, M. Tahara, H. Hosoda, Y.
Mizuno, and K. Nakamura, Jpn. J. Appl. Phys., Part I 53, 042502 (2014).
11
Y. Koike and K. Koike, J. Polym. Sci. Part A: Polym. Phys. 49, 2 (2011).
12
E. A. Friedman, A. J. Ritger, and R. D. Andrews, J. Appl. Phys. 40, 4243
(1969).
13
E. Kato, J. Chem. Phys. 73, 1020 (1980).
14
L. N. Durvasula and R. W. Gammon, J. Appl. Phys. 50, 4339 (1979).
15
Y. Y. Huang and C. H. Wang, J. Chem. Phys. 61, 1868 (1974).
16
H. Yoshida, R. Nakao, Y. Masabe, K. Koike, and Y. Koike, Polym. J. 46,
823 (2014).
17
K. Koike and Y. Koike, J. Lightwave Technol. 27, 41 (2009).
18
S. D. Clas, C. R. Dalton, and B. C. Hancock, Pharm. Sci. Technol. Today
2, 311 (1999).
19
G. W. H. Hohne, W. Hemminger, and H. J. Flammersheim, Differential
Scanning Calorimetry: An Introduction for Practitioners (SpringerVerlag, Berlin, 1996).
20
D. T. Haynie, Biological Thermodynamics (Cambridge University Press,
Cambridge, 2008).
21
G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego,
1995).
22
K. F. Graff, Wave Motion in Elastic Solids (Dover Publications, New
York, 1975), p. 276.
23
T. Horiguchi, T. Kurashima, and M. Tateda, IEEE Photon. Technol. Lett.
1, 107 (1989).
24
J. M. Cariou, J. Dugas, L. Martin, and P. Michel, Appl. Opt. 25, 334(1986).
25
R. Kono, J. Phys. Soc. Jpn. 15, 718 (1960).
26
M. Fukuhara and A. Sampei, J. Polym. Sci. Part B: Polym. Phys. 33, 1847
(1995).
27
J. J. Curro and R. J. Roe, Polymer 25, 1424 (1984).
28
M. Silva-Lopez, A. Fender, W. N. MacPherson, J. S. Barton, J. D. C.
Jones, D. Zhao, H. Dobb, D. J. Webb, L. Zhang, and I. Bennion, Opt. Lett.
30, 3129 (2005).
29
J. Saneyoshi, Y. Kikuchi, and O. Nomoto, Handbook of UltrasonicTechnology (Nikkan Kogyo, Tokyo, 1978), Chap. 5.
30
N. Hayashi, Y. Mizuno, D. Koyama, and K. Nakamura, Appl Phys.
Express 4, 102501 (2011).
31
K. Minakawa, N. Hayashi, Y. Mizuno, and K. Nakamura, Appl. Phys.
Express 6, 052501 (2013).
32
N. Hayashi, Y. Mizuno, D. Koyama, and K. Nakamura, Appl. Phys.
Express 5, 032502 (2012).
33
A. L. Cauchy, Memoire sur la Dispersion de la Lumière (J. G. Calve,
Praque, 1836).
5[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:
131.112.174.59 On: Thu, 16 Apr 2015 09:11:03