December 1, 2010 / Vol. 35, No. 23 / OPTICS LETTERS

3985

Potential of Brillouin scattering in polymer
optical fiber for strain-insensitive
high-accuracy temperature sensing
Yosuke Mizuno* and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku,
Yokohama 226-8503, Japan*Corresponding author: ymizuno@sonic.pi.titech.ac.jp
Received September 20, 2010; accepted October 23, 2010;
posted November 1, 2010 (Doc. ID 135374); published November 23, 2010
We investigated the dependences of Brillouin frequency shift (BFS) on strain and temperature in a perfluorinatedgraded-index polymer optical fiber (PFGI-POF) at 1:55 μm wavelength. They showed negative dependences withcoefficients of −121:8 MHz=% and −4:09 MHz=K, respectively, which are −0:2 and −3:5 times as large as those insilica fibers. These unique BFS dependences indicate that the Brillouin scattering in PFGI-POFs has a big potential
for strain-insensitive high-accuracy temperature sensing. © 2010 Optical Society of America
OCIS codes: 060.2370, 130.5460, 290.5830.

Brillouin scattering [1,2] is a fundamental nonlinear optical process in fiber-optic communication systems andhas been widely studied. So far, many useful applications
have been reported, such as microwave signal processing, slow-light generation, phase conjugation, tunable
delay, and strain/temperature sensing [3–5]. On the other
hand, polymer optical fibers (POFs) [6–8] are highly flexible and offer extremely easy and low-cost connection
compared to other standard glass fibers. In spite of theirhigher loss than that of silica fibers, POFs have been usedin medium-range communication applications, such ashome networks and automobiles, as well as in high-strain
monitoring applications [8]. Recently, we have reported
on the observation of Brillouin scattering in a perfluorinated graded-index polymer optical fiber (PFGI-POF) at
1:55 μm [9]. The Brillouin frequency shift (BFS) was
about 2:83 GHz, and the calculated Brillouin gain coefficient gB of 3:09 × 10−11 m=W was comparable to that ofsilica fibers. This indicated that, as Brillouin scattering insilica fibers has a wide field of application, Brillouin scattering in POFs can also be exploited for a variety of practical devices and systems with their low cost, ease of
installation, and high flexibility.
In this Letter, for sensing applications, we investigate
the dependences of the BFS on strain and temperature in
the PFGI-POF at 1:55 μm. It is found that the BFS in the
PFGI-POF moves toward lower frequency with increasing strain and temperature and that their coefficientsare −121:8 MHz=% and −4:09 MHz=K, respectively.
Compared to the coefficients of þ580 MHz=% andþ1:18 MHz=K in silica fibers, their absolute values are
0.2 and 3.5 times as large, respectively. These unique
BFS dependences seem to be caused by the unique dependences of the Young’s modulus on strain andtemperature in the PFGI-POF. We believe Brillouin scattering in PFGI-POFs can be potentially utilized to develop
strain-insensitive high-accuracy temperature sensors.
When a light beam is injected into an optical fiber, backscattered light (Stokes light) is generated through the interaction with acoustic phonons. This phenomenon iscalled the spontaneous Brillouin scattering. Since the phonons decay exponentially, the backscattered Brillouin0146-9592/10/233985-03$15.00/0

light spectrum, also known as the Brillouin gain spectrum(BGS), takes the shape of a Lorentzian function. The frequency at which the peak power is obtained in the spectrum is downshifted for several gigahertz from the incident
light frequency, and the amount of this frequency shift is
known as BFS. In optical fibers, the BFS νB is given as [2]2nνA 2n
¼
νB ¼
λp
λp

sﬃﬃﬃﬃ
E
;
ρ

ð1Þ

where n is the refractive index, νA is the acoustic velocity
in the fiber, λp is the wavelength of the incident pump light,
E is the Young’s modulus, and ρ is the density. If tensile
strain or temperature changes in a standard silica singlemode optical fiber (SMF), the BFS moves to higher frequency in proportion to the applied strain (þ580 MHz=%)[10] and the temperature change (þ1:18 MHz=K) [11]. In
some specialty fibers, such as tellurite glass fibers, it is
known that the BFS moves to lower frequency with increasing applied strain (−230 MHz=%) [12] and temperature (−1:14 MHz=K) [13]. In either case, by measuring the
BFS in the fiber, the strain amplitude or temperaturechange can be derived.
We employed a 5 m PFGI-POF [9,14] with an NA of
0.185, a core diameter of 120 μm, a core refractive indexof ∼1:35, and a propagation loss of ∼150 dB=km at
1:55 μm. The experimental setup for investigating the BFS
dependence on strain and temperature in the PFGI-POF isbasically the same as that previously reported in [9],where heterodyne detection was used to observe the
BGS with a high resolution, and one end of the PFGIPOF was connected to the silica SMF by so-called butt
coupling. The other end was kept open. Though the Stokes
light includes the Brillouin signal caused in the 1 m SMF
between the circulator and the PFGI-POF, it has no influence on the BGS measurement, because the BFS in the
SMF is about four times higher than that in the PFGIPOF [9]. Different strains were applied to the whole lengthof the PFGI-POF fixed on a translation stage using epoxy
glue, while the temperature along the whole length of the
PFGI-POF was adjusted with a heater.
© 2010 Optical Society of America

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OPTICS LETTERS / Vol. 35, No. 23 / December 1, 2010

Fig. 1.

(Color online) Measured dependences of (a) the BGS and (b) the BFS on strain in the PFGI-POF.

The strain dependence of the BGS in the PFGI-POF isshown in Fig. 1(a). The pump power was 19 dBm, andstrains of 0.2, 0.4, 0.6, 0.8, and 1.0% were applied. With
the increasing applied strain, the BGS shifted toward
lower frequency. Figure 1(b) shows the strain dependence of the BFS. The slope was almost linear, and its
coefficient was calculated to be −121:8 MHz=%. Whilethe negative sign is the same as in tellurite glass fibers[12], the absolute value was about one fifth of that ofa standard silica SMF (þ580 MHz=%) [10].
Then, the temperature dependence of the BGS in the
PFGI-POF is shown in Fig. 2(a). The pump power was
23 dBm, and the temperature was controlled from
30 °C up to 80 °C with a step of 10 °C. With increasing
temperature, the BGS also shifted toward lower frequency. The Stokes power at high temperature over
40 °C was lower than that at 30 °C by about 0:7 dB, probably due to the nonuniform temperature distribution on
the heater. Figure 2(b) shows the temperature dependence of the BFS, from which its coefficient was calculated to be −4:09 MHz=K. Though the negative sign isalso the same as in tellurite glass fibers [13], the absolutevalue was about 3.5 times as large as that of an SMF(þ1:18 MHz=K) [11].

Fig. 2.

The smaller strain coefficient indicates that PFGI-POFbased Brillouin sensors are less susceptible to the applied strain. On the other hand, the larger temperature
coefficient leads to accuracy enhancement of the temperature measurement. Thus, the Brillouin scatteringin the PFGI-POF can be potentially utilized in straininsensitive high-accuracy temperature sensors.
Next, the origins of the unique BFS dependences on
strain and temperature in the PFGI-POF are discussed.
The strain coefficient of the normalized BFS is expressed,by differentiating Eq. (1) with respect to strain, as
1 ∂νB 1 ∂n
1 ∂E
1 ∂ρ
¼
þ
þ −
:
νB ∂ε
n ∂ε 2E ∂ε
2ρ ∂ε

ð2Þ

Here it is known that the following equations hold true
[10]:
1 ∂n
p − κðp11 þ p12 Þ¼ −n2 12
;
n ∂ε
2

ð3Þ

1 ∂ρ 1 − 2κ
¼
;
ρ ∂ε
2

ð4Þ

−

where p11 and p12 are the elasto-optic coefficients and κ
is the Poisson’s ratio. Since their values in PFGI-POF(Color online) Measured dependences of (a) the BGS and (b) the BFS on temperature in the PFGI-POF.

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3987

coefficients of −121:8 MHz=% and −4:09 MHz=K, respectively, which are −0:2 and −3:5 times as large as those insilica fibers. With these unique BFS dependences, probably caused by the unique dependences of the Young’s
modulus on strain and temperature, we believe theBrillouin scattering in PFGI-POFs has a big potential
for strain-insensitive high-accuracy temperature sensing
systems. The next step needed to implement such systems is to enhance the Stokes power, for example, by reducing the core diameter of the PFGI-POFs.
Fig. 3. (Color online) Temperature dependences of (a) the
Young’s modulus and (b) the density of bulk PMMA, plottedusing the data reported in [19].

are unknown, we used the values for bulk polymethyl
methacrylate (PMMA): p11 ¼ 0:3 [15], p12 ¼ 0:297 [15],and κ ¼ 0:34 [16]. Then, the first and the third terms in
Eq. (2) were calculated to be −0:0857 and þ0:16, respectively. Though the second term is reported to vary drastically depending on the method to apply strain as well as on
the fabrication quality of the fiber, we used −5:75 as thesecond term, which is the value reported in [17] for a standard PMMA-based POF. Its absolute value is much larger
than the first and the third terms. Then, the theoreticalstrain coefficient was calculated to be −160:6 MHz=%.
Considering that each term in Eq. (2) was estimated using
the values of PMMA, this value is in moderate agreementwith the experimental value of −121:8 MHz=%. Thus, theunique strain dependence of the BFS seems to originate
from the unique dependence of the Young’s modulus on
strain in the PFGI-POF.
Finally, we discuss the BFS dependence on temperature in the same way. The temperature coefficient of
the normalized BFS is given as
1 ∂νB 1 ∂n
1 ∂E
1 ∂ρ
¼
þ
þ −
:
ð5Þ
νB ∂T
n ∂T 2E ∂T
2ρ ∂T
The first term can be calculated to be −0:0000889 using
the value reported for a standard PMMA-based POF [18].
To estimate the second and the third terms, we plotted
the Young’s modulus and the density of bulk PMMA atvarious temperatures that have been reported in [19],as shown in Figs. 3(a) and 3(b). Using their slopes(−0:0295 GPa=K and −0:409 kg=m3 =K), along with E ∼6 GPa and ρ ¼ 1187:5 kg=m3 , the second and the thirdterms were calculated to be −0:00246 and þ0:000172, respectively. Then, the theoretical temperature coefficient
was calculated to be −6:72 MHz=K, which roughly agrees
with the experimental value of −4:09 MHz=K. Thus, theunique temperature dependence of the BFS also seems
to be caused by the large negative dependence of theYoung’s modulus on temperature in the PFGI-POF.
In conclusion, the BFS dependences on strain and temperature in a 5 m PFGI-POF were investigated at 1:55 μm
wavelength. They showed negative dependences withWe are indebted to Prof. Nishiyama and Prof. Uenoharaof Tokyo Institute of Technology, Japan, for lending us
their high-power erbium-doped fiber amplifiers. Y. Mizuno
is grateful to the Research Fellowships for Young Scientists from the Japan Society for the Promotion of Science(JSPS).
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