Applied Physics Express 8, 072502 (2015)
http://dx.doi.org/10.7567/APEX.8.072502

Drastic sensitivity enhancement of temperature sensing
based on multimodal interference in polymer optical ﬁbers
Goki Numata, Neisei Hayashi, Marie Tabaru, Yosuke Mizuno, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Received April 2, 2015; accepted June 6, 2015; published online June 24, 2015
It has been reported that temperature sensors based on modal interference in perﬂuorinated graded-index polymer optical ﬁbers show extremely
high temperature sensitivity at room temperature. In this work, we conﬁrm that the temperature sensitivity (absolute value) is signiﬁcantly enhanced
when the temperature increases toward >70 °C, which is close to the glass-transition temperature of the core polymer. When the core diameter is62.5 µm, the sensitivity at 72 °C at 1300 nm is 202 nm/°C/m, which is approximately 26 times the value obtained at room temperature and >7000
times the highest value previously reported using a silica multimode ﬁber. © 2015 The Japan Society of Applied Physics

iber-optic temperature sensors have been thus far
successfully developed by utilizing various physicalstructures and phenomena, such as ﬁber Bragg
gratings,1,2) long-period gratings,3,4) Raman scattering,5,6)
Brillouin scattering,7–11) and optical interference.12,13) Among
various conﬁgurations of interference-based temperature
sensors, those based on the interference of multiple guided
modes in multimode ﬁbers (MMFs)14) have been attracting
much attention owing to their system simplicity, costeﬃciency, and high sensitivity. Since the ﬁrst demonstration
by Mehta et al.,15) a number of conﬁgurations have been
implemented (see Table I in Ref. 16). The most commonlyused conﬁguration is the so-called “single-mode–multimode–
single-mode” (SMS) structure17–21) — an MMF sandwiched
between two single-mode ﬁbers (SMFs).
To date, many researchers have evaluated the performanceof SMS-based temperature sensors. Using a 1.8-m-long silica
graded-index (GI) MMF, Liu et al.17) observed a temperaturesensitivity of +32.5 pm=°C=m at 1550 nm (corresponding to+27.3 pm=°C=m at 1300 nm, under the simple assumptionthat the sensitivity is proportional to the optical wavelength).
Tripathi et al.18) experimentally proved that the absolutevalues, as well as the signs of the temperature sensitivities,
are determined by the “critical wavelengths”, which dependon the core diameter and=or the dopant of silica MMFs. As
SMS-based temperature sensors can also measure strain, theimplementation of polymer optical ﬁbers (POFs) as MMFs is
a promising method for increasing the maximal measurable
strain. Huang et al.21) developed a large-strain sensor using a
0.16-m-long standard poly(methyl methacrylate) (PMMA)
based step-index POF and reported a temperature sensitivityof +581.9 pm=°C=m at 1570 nm (corresponding to +481.8
pm=°C=m at 1300 nm). Nevertheless, PMMA-based POFs
suﬀer from extremely high propagation loss over a wide
wavelength range, resulting in an operable POF length
inherently limited to <1 m. To overcome this problem, we
have recently implemented SMS-based temperature sensors
using 1-m-long perﬂuorinated (PF) GI-POFs,22) which are theonly POFs with relatively low losses of ∼250 dB=km evenat 1550 nm (or ∼50 dB=km at 1300 nm). When the core
diameter was 62.5 µm, the obtained temperature sensitivity
at room temperature at 1300 nm was as high as +49.8
nm=°C=m.23) This corresponds to the highest yet reported
absolute value, over 1800 times and 100 times higher thanthose measured in a silica GI-MMF17) and a PMMA-based
POF,21) respectively. However, the sensing performanceof these sensors was evaluated only at room temperature,Fand no reports have been provided at high temperature, close
to the glass-transition temperature.
In this work, we investigate the performance of temperature sensors composed of 1-m-long PFGI-POFs with three
diﬀerent core diameters (50, 62.5, and 120 µm) in a wide
temperature range from room temperature to high temperatures near the glass-transition temperature. When the core
diameter was 62.5 µm, the temperature sensitivity (absolutevalue) increased with increasing temperature, reaching +202
nm=°C=m at ∼72 °C, which is ∼7400 times higher than thatmeasured at room temperature. This behavior is unique to
POFs with relatively low glass-transition temperature, which
was conﬁrmed by showing that the temperature sensitivity ofa silica MMF-based sensor does not change with increasing
temperature to 130 °C. In general, the glass-transition temperature of polymers can be arbitrarily adjusted; thus, we
expect that in the future, by exploiting this unique property of
POF sensors, ultra-high temperature sensing will be feasible
not only at ∼70 °C, but at arbitrary temperatures.
The SMS structure generally comprises an MMF sandwiched by identical SMFs. At the ﬁrst SMF-to-MMF interface, light is guided from the lead-in SMF into the MMF. The
spot-size diﬀerence between the fundamental (or 0-th) modesin the SMF and the MMF excites a few lower modes in the
MMF, which propagate along the MMF with their respective
propagation constants. Then, at the second MMF-to-SMF
interface, the net ﬁeld coupled to the lead-out SMF is determined by the relative phase diﬀerences between the multiple
modes guided in the MMF. Supposing that the MMF and
SMFs are axially aligned, only the axially symmetric modes
are excited in the MMF. A detailed calculation20) gives anexpression of the optical power in the lead-out SMF as
Pout ¼ ja20 þ a21 exp ið0  1 ÞLþ a22 exp ið0  2 ÞL þ    j2 ;

ð1Þwhere ai is the ﬁeld amplitude of the i-th mode at the ﬁrst
SMF-to-MMF interface, βi is the propagation constant of thei-th mode, and L is the MMF length. This equation showsthat the optical power in the lead-out SMF is aﬀected byphysical changes caused by strain and temperature, as they
have non-negligible inﬂuence on the propagation constants
and the MMF length. These changes can be quantitatively
evaluated by measuring the shift of spectral dips (or peaks).
The temperature sensitivity is often expressed using unitsof “pm=°C=cm”, where the value expressed with “cm” is thelength of the heated section. When the whole length of the
MMF is heated, it corresponds to the MMF length itself. This

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Appl. Phys. Express 8, 072502 (2015)

G. Numata et al.

Fig. 1. Schematic of the experimental setup. OSA: optical spectrum
analyzer; PFGI-POF: perﬂuorinated graded-index polymer optical ﬁber;
SMF: single-mode ﬁber; UWS: ultra-wideband source.

can be explained as follows: for simplicity, suppose theinterference of the lights only of the fundamental and ﬁrstorder higher modes propagating along the MMF. If the MMF
length is the same, a longer heated section leads to theirlonger optical-path diﬀerence (due to thermal expansion),resulting in a larger temperature-dependence coeﬃcient of
the dip wavelength. Similarly, even when the MMF length isreduced, if the length of the heated section remains the same,the induced optical-path diﬀerence (and thus the temperaturedependence coeﬃcient) is unchanged. Therefore, when thefull length of the MMF is heated, the use of the unit “pm=°C=
cm” (or “nm=°C=m”, in the case of PFGI-POFs) is valid.
The MMFs used in the experiment were PFGI-POFs withthree diﬀerent core diameters (50, 62.5, and 120 µm), andtheir core and cladding layers were composed of doped andundoped poly(perﬂuorobutenylvinyl ether), respectively. The
lengths of the three PFGI-POFs were all set to 1 m, similarly
to those used in Ref. 23, for an easy comparison of their
sensing characteristics. The refractive indices at the center ofthe core and in the cladding layer were approximately 1.35
and 1.34, respectively, regardless of the optical wavelength.24)
Outside the cladding layer, an overcladding layer (diameter:
500 µm) composed of polycarbonate was coated to suppress
microbending loss and to improve the load-bearing capability.
Figure 1 depicts an experimental setup for characterizing
the PFGI-POF-based temperature sensors in a wide temperature range. Both ends of the PFGI-POF were butt-coupled tosilica SMFs via “SC=PC-FC=PC” adaptors,25) and the whole
length of the PFGI-POF was placed in a thermostatic chamber
to control the ambient temperature (the heated adaptors wereconﬁrmed to have no quantiﬁable inﬂuence on the experimental results). Because spectral measurements with thewidest possible span were preferable for this experiment, we
employed an ultra-wideband source (Santec UWS-1000) thatemits super-continuum light with an output spectrum from1100 to 1760 nm (pumped at 1550 nm), instead of the
wavelength-tunable laser used in previous reports.23,26) The
spectral power density of the source was higher than −30
dBm=nm over the full range; this value is much larger thanthat of a standard white-light source, which cannot be used inthis case because of the high propagation loss of the PFGIPOF. The ultra-wideband source output was injected into the
PFGI-POF, and the transmission spectrum was measured
using an optical spectrum analyzer (OSA). The room temperature was 20 °C.
The measured optical spectra of the PFGI-POF with 50 µm
core diameter before and after transmission at room temperature are shown in Fig. 2. Before transmission, a relatively
ﬂat spectrum ranging from 1100 to 1760 nm was observed.
The peak at 1550 nm corresponds to the pump frequency ofthe super-continuum generation. After transmission, botha relatively uniform ∼10–20 dB loss and a wavelength-

Fig. 2. Measured optical spectra before and after transmission through the
PFGI-POF.

dependent loss were observed in the spectrum, resulting inseveral characteristic dips and peaks. These dips and peaks
originate from modal interference and their wavelengths are
dependent on the ambient temperature of the POF.
We then investigated the wide-range temperature dependence of the wavelengths of some relatively clear spectral
dips in the spectrum of the PFGI-POF with 50 µm core
diameter [Fig. 3(a)]. The measured data are discontinuously
plotted because of two reasons: (1) a measurement at one
ﬁxed temperature required ∼10 min because of the timeneeded for the temperature to stabilize. Therefore, themeasurements were performed separately in each 10 °C
interval (i.e., 20–30 °C, 30–40 °C), and the corresponding
data were merged later (some peaks appeared or disappearedwith time owing to polarization ﬂuctuations;17) this instability
could be mitigated by employing polarization diversity orpolarization scrambling). (2) When the dips shifted close to
the 1550 nm pump peak, they were buried in the spectral
ﬂoor (this problem could be resolved by the use of a properly
designed optical ﬁlter at 1550 nm). As shown in Fig. 3(a),with increasing temperature, the wavelengths of all the dips
decreased. The dependence coeﬃcient at room temperature at
1300 nm was approximately −5.3 nm=°C=m (calculated byinterpolation=extrapolation), which moderately agrees withthe previously reported value (−4.7 nm=°C=m).23) In thiswavelength range, the absolute values of the coeﬃcients atshorter wavelengths were slightly smaller than those at longer
wavelengths, which indicates that the critical wavelength18) islonger than ∼1700 nm. In the temperature range from 20 to∼50 °C, the dependence coeﬃcient of all dips remained
almost constant; however, over ∼50 °C, their absolute values
gradually increased. The coeﬃcient at 67 °C at 1300 nm
reached −85 nm=°C=m, which was ∼16 times the value atroom temperature. Over ∼67 °C, the spectral change was so
drastic that correct measurements were no longer possible.
Subsequently, we conﬁrmed that this peculiar behavior is aunique characteristic of POFs by performing the same measurement using a silica GI-MMF with the same core diameter(50 µm). Figure 3(b) shows the dip wavelengths measured asfunctions of temperature in the range from 20 to 130 °C. The
dependence coeﬃcient at room temperature at 1300 nm (−2.2nm=°C=m) was similar to that at ∼130 °C (−2.3 nm=°C=m),which indicates that the gradual temperature-dependentchange in the coeﬃcients (in this temperature range) is
unique to POFs. This behavior, similar to the nonlinear tem-

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Appl. Phys. Express 8, 072502 (2015)

G. Numata et al.

(b)

(a)

(c)
Fig. 3. Temperature dependence of the dip wavelength in a wide
temperature range for (a) the PFGI-POF and (b) the silica GI-MMF with
50 µm core diameter. The diﬀerent colors represent diﬀerent dips.
(c) Temperature sensitivity (absolute value of the temperature-dependence
coeﬃcients) at 1300 nm in the PFGI-POF and the silica GI-MMF plotted asfunctions of temperature.

perature dependence of the Brillouin frequency shift in
POFs,27) seems to result from the partial phase transition of thepolymer material. The temperature of ∼67 °C, at which thelargest coeﬃcient (absolute value) was obtained for the PFGIPOF, probably corresponds to the glass-transition temperatureof poly(perﬂuorobutenylvinyl ether) (∼108 °C; note that thephase transition, which has some inﬂuence on the thermal
expansion coeﬃcient and each modal index, generally occurs
at a temperature of approximately 50 °C in polymers28)
and that the starting temperature of the phase transition islower than the glass-transition temperature by several tensof degrees). Figure 3(c) shows the temperature sensitivities,i.e., the absolute values of the temperature-dependence
coeﬃcients of the dip wavelengths, at 1300 nm for the
PFGI-POF and the silica GI-MMF, plotted as functions oftemperature. It is clear that the temperature sensitivity of the
PFGI-POF increases abruptly at 67 °C, while that of the silica
GI-MMF remains almost constant. Measurements using
the silica GI-MMF up to its glass-transition temperature(∼1000 °C) would provide even more reliable information.
We also performed the same measurements using the
PFGI-POFs with 62.5 and 120 µm core diameters [Figs. 4(a)–4(d)]. In both cases, the dip wavelengths increased withincreasing temperature. The diﬀerence in the absolute value
and the sign has been previously reported23) and explained by
the structural inﬂuence on the critical wavelengths18) (which
are shorter than 1100 nm for the 62.5-µm-core PFGI-POF
and longer than 1700 nm for the 120-µm-core PFGI-POF).
The coeﬃcients at room temperature at 1300 nm were
+7.7 nm=°C=m for the 62.5-µm-core PFGI-POF and+1.1 nm=°C=m for the 120-µm-core PFGI-POF. The diﬀerence between these values and those previously reported23) is

(a)

(b)

(c)

(d)

Fig. 4. Temperature dependence of (a) the dip wavelengths and (b) thecoeﬃcient of the PFGI-POF with 62.5 µm core diameter and of (c) the dip
wavelength and (d) the coeﬃcient of the PFGI-POFs with 120 µm core
diameter.

probably caused by the manually prepared end-surfaces andlot-to-lot non-uniformity, leading to the diﬀerent excitedmodes. The maximal values obtained at high temperature at
1300 nm were +202 nm=°C=m for the 62.5-µm-core PFGIPOF and +85.6 nm=°C=m for the 120-µm-core PFGI-POF,
which are ∼26 and ∼78 times larger, respectively, than thosemeasured at room temperature. The temperature sensitivity of+202 nm=°C=m at 1300 nm, obtained at ∼72 °C using the62.5-µm-core PFGI-POF, is well over 7000 times larger thanthe highest value previously reported for a silica GI-MMF;17)
to the best of our knowledge, this is the highest value everreported in modal-interference-based temperature sensors.
The temperatures at which the largest temperature sensitivities (absolute values of the temperature-dependence coeﬃcients) were experimentally obtained were ∼69, ∼72, and∼82 °C for the PFGI-POFs with 50, 62.5, and 120 µm core
diameters, respectively, suggesting a positive correlation
between the highest operable temperature and the core
diameter of the POF. It would be worthwhile to clarify thispoint, although PFGI-POFs with other core diameters are notcommercially available at present.
In conclusion, we investigated the performance of SMSbased temperature sensors comprising 1-m-long PFGI-POFs
with 50, 62.5, and 120 µm core diameters in a wide temperature range. When the core diameter was 62.5 µm, thetemperature sensitivity, i.e., the temperature-dependence coeﬃcients of the spectral dips, increased with increasing
temperature, reaching +202 nm=°C=m at ∼72 °C at 1300 nm;
this value is over 7000 times higher than that obtained atroom temperature. Over ∼72 °C, a correct measurement wasdiﬃcult owing to spectral instability. We veriﬁed that thisbehavior is unique to POFs with relatively low glasstransition temperature by demonstrating that the temperature

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Appl. Phys. Express 8, 072502 (2015)

G. Numata et al.

sensitivity of a silica-MMF-based sensor exhibits almost nochange with increasing temperature up to 130 °C. We also
showed that the highest operable temperature might becorrelated to the core diameter of the PFGI-POFs. Furthermore, considering that the phase-transition temperature ofpolymers can be controlled by adding plasticizers and by
copolymerizing=blending diﬀerent materials,29) we expectthat such ultra-high temperature sensitivity will be achievable
not only near 70–80 °C but also at arbitrary temperatures,
opening the way for more useful and practical applications.
Acknowledgments We are indebted to Professors Fumio Koyama and
Hiroyuki Uenohara (Precision and Intelligence Laboratory, Tokyo Institute ofTechnology) for permitting us to use their ultra-wideband light source. This
work was partially supported by Grants-in-Aid for Young Scientists (A) (No.
25709032) and for Challenging Exploratory Research (No. 26630180) from theJapan Society for the Promotion of Science (JSPS) and by research grants fromthe Iwatani Naoji Foundation, the SCAT Foundation, and the Konica Minolta
Science and Technology Foundation. N.H. acknowledges a Grant-in-Aid for JSPS
Fellows (No. 25007652).

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