Applied Physics Express 5 (2012) 032502
DOI: 10.1143/APEX.5.032502

Dependence of Brillouin Frequency Shift on Temperature and Strainin Poly(methyl methacrylate)-Based Polymer Optical Fibers
Estimated by Acoustic Velocity Measurement
Neisei Hayashi, Yosuke Mizuno, Daisuke Koyama, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Received February 7, 2012; accepted February 22, 2012; published online March 6, 2012
We estimated the dependences of Brillouin frequency shift (BFS) on temperature and strain in poly(methyl methacrylate)-based polymer opticalfibers using ultrasonic pulse–echo technique at 10 MHz. The estimated BFS dependence on temperature was linear with a coefficient ofapproximately 17 MHz/K at 650 nm pump, 34 times larger than that of silica fibers at 650 nm pump. In contrast, its strain dependence wasfound to be nonlinear, probably originating from the elastic-to-plastic transition. # 2012 The Japan Society of Applied Physics

ptical ﬁber sensors have a number of attractive
features compared with other sensor elements,
such as light weight, compactness, low cost, andtolerance to electromagnetic interference. Among them, due
to the capability of determining temperature and/or strain
distribution along sensing ﬁbers, optical ﬁber sensors basedon Brillouin scattering have been studied as a promisingtechnology for monitoring diverse structures and materials.
Up to now, glass optical ﬁbers (GOFs), in particular, silicabased single-mode ﬁbers (SMFs), have been mainly used todevelop Brillouin ﬁber sensors,1–5) which cannot, however,measure a large strain of >10%. One method to overcome
this problem is to implement such Brillouin sensors using
polymer optical ﬁbers (POFs), which oﬀer high ﬂexibility,
easy connection, low cost, and high safety.6) A so-called‘‘memory eﬀect’’ of POF-based distributed strain sensors has
also been demonstrated.7)
Commercially available POFs are classiﬁed into two
types: poly(methyl methacrylate) (PMMA)-based POFs andperﬂuorinated graded-index (PFGI)-POFs. We have so far
succeeded in observing Brillouin scattering in PFGI-POFs
with 120 and 62.5 m core diameters at 1.55 m wavelength.8–10) We have also investigated the dependences ofBrillouin frequency shift (BFS) on temperature and strain in
the PFGI-POFs, and found that their temperature and strain
coeﬃcients are 4:09 MHz/K and 121:8 MHz/% (within
the strain range of 0–1%), respectively.11) PMMA-POFs are,in contrast, much more cost-eﬀective and more widely usedin communication applications than PFGI-POFs, and so
the observation of Brillouin scattering in PMMA-POFs isimportant for predicting the performance as sensors but
diﬃcult for the following two reasons: (1) the Brillouinsignal is extremely small due to their large core diameter(typically 980 m), and (2) it is not easy to prepare all theoptical devices operating at 650 nm, where the propagation
loss of PMMA-POFs becomes lowest. Therefore, we haverecently developed a new method of estimating the BFS inPOFs from the sound speed measured through ultrasonicpulse–echo technique at much lower frequencies than BFS,
and calculated the BFS in PMMA-POFs at 650 nm to be
13 GHz.12) In order to evaluate the applicability of the POF
samples to distributed temperature and strain sensors basedon Brillouin scattering, the dependences of the BFS ontemperature and strain in PMMA-POFs need to be clariﬁed.
In this paper, the temperature and strain dependences ofthe BFS in PMMA-POFs are estimated using the ultrasonicpulse–echo technique. We ﬁnd that the BFS varies linearlyOdepending on temperature with a coeﬃcient of approximately 17 MHz/K at 650 nm pump. Since this value is34 times larger than that of silica ﬁbers at 650 nm (0.495MHz/K), and is even 10 times larger than that of PFGIPOFs at 650 nm (1:72 MHz/K), we think that PMMAPOFs are potentially applicable to high-precision temperature sensing. We also ﬁnd that the BFS varies nonlinearly
depending on strain, which seems to be caused by theelastic-to-plastic transition of PMMA.
Brillouin scattering is one of the most important nonlinear
phenomena in optical ﬁbers. When pump light is injected
into optical ﬁbers, part of the light is reﬂected due toBrillouin scattering, i.e., the interaction between phonons
and acoustic phonons.13) The frequency of the Brillouinscattered light is down-shifted by several GHz, and theamount of this frequency shift is called the BFS. In opticalﬁbers, the BFS B is given as13)
B ¼

2nvA;
p

ð1Þ

where n is the refractive index, vA is the acoustic velocity,and  p is the wavelength of the incident pump light.
Consequently, the BFS in optical ﬁbers can be estimatedby using a measured value of vA . Moreover, it is clear that,
if the dependences of vA on temperature and strain are
obtained, the BFS dependences on temperature and strain
can also be estimated, if we neglect the temperature andstrain dependences of n. Although measuring vA in SMFs
using the ultrasonic pulse–echo technique is extremely
diﬃcult due to their small core diameter (8 m), we
showed that it is feasible for PMMA-POFs with a large core
diameter (980 m).12)
The experimental setup for acoustic velocity measurement
is schematically shown in Fig. 1. An ultrasonic pulse
generated with a transducer (Panametrics M316) connected
to a pulser-receiver (Panametrics 5900PR) was directed toa POF sample ﬁxed in degassed water, and the reﬂected
waves were detected with the same transducer. The BFS wasestimated by substituting the measured acoustic velocity intoeq. (1) under the assumption that the acoustic velocity isindependent of the frequency. We employed PMMA-POFswith numerical aperture (NA) of 0.5, core diameter of 980
m, cladding diameter of 1000 m, core refractive index of1:49, propagation loss of 150 dB/km at 650 nm wavelength, and tolerable temperature range from 55 to 70  C.
The center frequency of the ultrasonic wave was approximately 10 MHz. The POF samples used to measure the strain

032502-1# 2012 The Japan Society of Applied Physics

Appl. Phys. Express 5 (2012) 032502

Fig. 1.

N. Hayashi et al.

Schematic setup for measuring the acoustic velocity in POF

samples.

Fig. 3.

Estimated BFS dependence on temperature in the PMMA-POF at

Stress–strain curve in the PMMA-POF.

650 nm.

Fig. 4. Stress–strain curve for the fabrication of each POF sample. The
inset shows a magniﬁed view.

dependence were fabricated using the following procedure:(1) measure the stress–strain curve of the POFs and obtain
their fracture strain "f , (2) keep strains of 2–40% (< "f )applied to the POFs for 15 min so that they do not relax tothe initial length,7) and (3) cut the elongated POFs into
samples of several mm length.
The estimated BFS dependence on temperature in
the PMMA-POF at 650 nm pump is shown in Fig. 2. The
temperature was increased from 26 to 60  C. We did not take
into account the refractive-index dependence on temperature, because its coeﬃcient in bulk PMMA is reported to beas small as 1:2  104 K1 .14) The BFS was estimated tovary linearly depending on temperature with a coeﬃcientof 17 MHz/K within this temperature range. This value
agrees well with that of bulk PMMA,12) which is 34 times
larger than that of silica ﬁbers at 650 nm (0.495 MHz/K)15)
and is even 10 times larger than that of PFGI-POFs at650 nm (1:72 MHz/K).11) Therefore, compared with silicaﬁbers and PFGI-POFs, PMMA-POFs can be potentiallyapplied to high-precision temperature sensing.
Figure 3 shows the stress–strain curve of one of thePMMA-POFs. Upper and lower yield points were observed
at 4.5 and 22%, respectively, and the fracture strain was55%. This stress–strain curve indicates that the elasticplastic transition of the PMMA-POF is induced at several %strain. Such stress–strain curves were also measured while
each POF sample was being fabricated, as shown in Fig. 4.
It is clear that, for each POF sample, residual strain exists

even after it is released. Since the residual strain is slightly
lower than the target strain, we deﬁne, for clarity, theresidual strain as the ‘‘applied strain’’ in the next experiment.
Figure 5 shows the estimated BFS dependence on applied
strain in the PMMA-POFs at 650 nm pump. The refractive
index n was assumed to be constant (1.49), and the temperature was kept at 19  C. The BFS dependence on applied
strain showed a nonlinear behavior; its coeﬃcient waspositive within the strain ranges of 0 to 10 and 20 to40%, but was negative within the range of 10 to 20%.
This feature is similar to that of the stress–strain curve
shown in Fig. 3, probably originating from the transition of
PMMA from the elastic to the plastic regime. Further study
is, however, needed to clarify this point. While the sign ofthe strain coeﬃcient of the PMMA-POFs around 0% applied
strain was positive, that of PFGI-POFs is reported to benegative.11) This diﬀerence indicates that the strain coeﬃcient of POFs for small strain can be controlled, including
its sign, by ﬂuorine doping; thus, we can expect thathigh-precision temperature sensing with zero strain sensitivity can be achieved by optimizing the ﬂuorine doping
concentration.
In conclusion, the BFS dependences on temperature andstrain in PMMA-POFs were estimated using ultrasonicpulse–echo technique. We found that the BFS varies linearly
depending on temperature with a coeﬃcient of approximately 17 MHz/K at 650 nm pump. Since this value is34 times larger than that of silica ﬁbers at 650 nm, and isFig. 2.

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Appl. Phys. Express 5 (2012) 032502

N. Hayashi et al.
Acknowledgments We are indebted to Professor Hosoda and Ms. Naruseof Tokyo Institute of Technology, Japan, for instructing us in the use of thetension tester. We are also grateful to the staﬀ of the Technical Department,
Tokyo Institute of Technology, Japan, for providing the ﬁxtures used in
the experiment. The work of Y. Mizuno was supported by the Research
Fellowships for Young Scientists from the Japan Society for the Promotion ofScience (JSPS).

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even 10 times larger than that of PFGI-POFs at 650 nm,PMMA-POFs appear to be a good candidate for Brillouinbased temperature sensing with high precision. We also
found that, in contrast, the BFS varied nonlinearly depending on applied strain, which seems to be related to theelastic-to-plastic transition of PMMA. More accurate
estimation will be feasible by taking the refractive-index
dependence on strain into consideration. We believe that
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# 2012 The Japan Society of Applied Physics