IEICE Electronics Express, Vol.16, No.8, 1–5

LETTER

Observation of multimodal interference in millimeter-long polymer
optical ﬁbers
Yosuke Mizuno1a), Sonoko Hagiwara1, Natsuki Matsutani1, Kohei Noda1, Heeyoung Lee1, and Kentaro Nakamura1

Abstract We observe multimodal interference in single-mode-multimodesingle-mode sensors comprising short polymer optical ﬁbers (POFs) withlengths from 100 mm down to 7 mm. Characteristic spectral peaks/dips
are observed not in the conventionally used telecom band but around1000 nm. We ﬁnd that the dip wavelength depends on temperature but thatthe sensitivity is much lower than those obtained in the longer wavelength
range when longer POFs are used. We discuss the possibility that, evenwith the reduced sensitivity, our success in observing multimodal interference in millimeter-long optical ﬁbers will be a basis toward the
combined use of frequency and intensity information in conventionalﬁber-optic single-point sensors for discriminative measurement of multiple
physical parameters.
Keywords: optical ﬁber sensors, multimodal interference
Classiﬁcation: Optical hardware

1. Introduction
Sensing technology of strain and temperature using opticalﬁbers has been an active area of research for many decades,
and a wide variety of conﬁgurations have been developed
thus far. They operate based on ﬁber Bragg gratings[1, 2, 3], long-period gratings [4, 5], Brillouin scattering[6, 7, 8, 9], Raman scattering [10, 11], optical interference[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], and manyothers. Among numerous types of interference-based sensors, those based on intermodal interference in multimodeﬁbers (MMFs) have recently attracted a considerable attention owing to their system simplicity and cost eﬃciency.
Of all the multimodal-interference-based sensors previously
developed, which are well summarized in Table 1 inRef. [12], the most widely used conﬁguration is what
is called a “single-mode-multimode-single-mode” (SMS)
structure [13, 14, 15, 16, 17, 18, 19, 20], in which two
single-mode ﬁbers (SMFs) sandwich an MMF.
To date, the strain and temperature sensitivities ofvarious SMS sensors have been extensively investigated.
When a 1.8-m-long silica graded-index (GI-) MMF wasused, a strain sensitivity of +18.6 pm/µε and a temperaturesensitivity of +58.5 pm/°C were obtained at 1550 nm [13].
Note that the sensitivities are known to be strongly dependent on optical wavelength; not only their absolute values
but also their signs depend on a so-called critical wave1
Institute of Innovative Research, Tokyo Institute ofTechnology, Yokohama 226–8503, Japana) ymizuno@sonic.pi.titech.ac.jp

DOI: 10.1587/elex.16.20190135
Received March 7, 2019
Accepted March 26, 2019
Publicized April 10, 2019
Copyedited April 25, 2019

length [14], which varies depending on the material andstructure of the SMS sensors. As silica glass ﬁbers are
relatively fragile and cannot withstand large strain, toextend the strain dynamic range, a 160-mm-long polymethyl methacrylate (PMMA)-based step-index polymer opticalﬁber (POF) was used as an MMF, leading to a strain
sensitivity of −1.72 pm/µε and a temperature sensitivityof −56.8 pm/°C at 1570 nm [15]. However, the propagation loss of PMMA-based POFs at telecom wavelength isextremely high (1  105 dB/km). To tackle this issue, wehave recently implemented SMS-based strain and temperature sensors using perﬂuorinated (PF) GI-POFs [16,17, 18, 19, 20, 21, 22], which are the only POFs with arelatively low propagation loss even at telecom wavelength(∼250 dB/km at 1550 nm; ∼50 dB/km at 1300 nm). Usinga PFGI-POF with a length of 1.0 m and a core diameter of
62.5 µm, we obtained a strain sensitivity of −111.8 pm/µε
and a temperature sensitivity of +49.8 nm/°C at 1300 nm[16]; these large absolute values suggest that PFGI-POFbased SMS sensors are extremely sensitive to strain andtemperature compared with other SMS sensors composedof silica MMFs or PMMA-POFs.
To enhance the usability of the PFGI-POF-based SMS
sensors, instead of a conventional two-end-access (or transmissive) conﬁguration, we have implemented a single-endaccess (or reﬂectometric) conﬁguration and proved its appropriate sensing operation [19]. We have also experimentally clariﬁed that the strain and temperature sensitivities do
not largely depend on the length of a POF, when the lengthis >300 mm [19]. If this trend holds true even when the POF
length is much shorter than 300 mm, we may be able todevelop a ﬁber-tip-type local-temperature sensor with ahigh sensitivity (note that, as it is diﬃcult to directly use
such a short POF attached at the ﬁber tip for strain sensing,hereafter we focus on temperature sensing). However, noprevious reports have veriﬁed whether multimodal interference can be observed in extremely short POFs (not in silica
MMFs, either); the inﬂuence of the POF length on thetemperature sensitivity also remains unclariﬁed.
In this work, we make an attempt to observe multimodal interference in SMS sensors using short PFGI-POFs
with lengths from 100 mm down to 7 mm. We show thatspectral peaks/dips induced by multimodal interference are
not observed in the conventionally used wavelength range(near the telecom band) but that they can be observed in the
shorter wavelength range around 1000 nm. In this range,
the dip wavelengths are clearly dependent on temperature,
but the sensitivities are much lower than those of longer
1

Copyright © 2019 The Institute of Electronics, Information and Communication Engineers

IEICE Electronics Express, Vol.16, No.8, 1–5

POFs measured in the longer wavelength range. Thus, itappears to be diﬃcult to fabricate ﬁber-tip-type temperature
sensors with high sensitivities by this method, but our
ﬁnding that multimodal interference can be observed evenin millimeter-long optical ﬁbers will add a new function—
frequency-based sensing function—to some of the conventional intensity-based single-point ﬁber sensors.
2. Principle
A conventional transmissive SMS structure is composed ofan MMF sandwiched by two SMFs. When the output ofa broadband light source is injected into one of the SMFs,
the transmitted light exhibits multiple characteristic dips(or peaks) in its spectrum, induced by multimodal interference. Refer to previous literatures [19, 23, 24] for its
detailed operating mechanism. The intervals of the neighboring dips are inconstant both in wavelength and frequency. When strain or temperature change is applied to
the MMF, these dips shift to longer or shorter wavelengths.
The dependence coeﬃcients including their signs are determined by a critical wavelength C [14]. Under theassumption that the MMF and the SMFs are axiallyaligned, the signs become opposite between the wavelength ranges shorter and longer than C , and the absolutevalues become larger when the dips are closer to C . Thus,though an exception based on spectral correlation has beenreported [19], we basically need to select one of the dips
suitable for our speciﬁc applications. If a higher sensitivity
is preferable, the dip nearest to C should be used; while if
a wider strain/temperature dynamic range is preferable, it
may not be the best dip to be selected. To date, when the
MMF is a PFGI-POF, a dip around 1350 nm has been often
used for its higher sensitivity [16, 19, 20].
An SMS structure can be implemented using an MMF
and a single SMF in a reﬂectometric manner, where theFresnel reﬂection at the open end of the MMF is exploited.
Using the same PFGI-POF, we compared the sensing
performances between the transmissive and reﬂectometricconﬁgurations at ∼1350 nm, and found that the strain andtemperature sensitivities are almost identical regardless ofthe conﬁgurations [19]. This fact indicates that the sensitivities do not change when the POF length is doubled. Wethen investigated the sensitivity dependence on the POF
length (>300 mm) using the transmissive conﬁguration,and clariﬁed that the sensitivities do not exhibit a clear
dependence on the POF length [19]. However, multimodal
interference has not been observed in POFs or silica MMFs
much shorter than 300 mm; the shortest MMF in which
multimodal interference has been observed is the aforementioned PMMA-POF with a length of 160 mm (actually,
limited by its high propagation loss) [15]. Considering thatthe visibility of the spectral dips/peaks tends to be reducedwith decreasing ﬁber length (refer to the discussion on a socalled refocus-length) [21], it is a challenge to observe
multimodal interference in a millimeter-long POF.
3. Experimental setup
The MMFs used in the experiment were PFGI-POFs [25]with a core diameter of 50 µm, a cladding diameter of
70 µm, and a overcladding diameter of 490 µm. The coreand cladding layers were doped and undoped polyperﬂuorobutenylvinyl ether, respectively. The refractive indices atthe center of the core and in the cladding layer wereapproximately 1.356 and 1.342, respectively, which do
not largely depend on optical wavelength. An overcladding
layer was composed of polycarbonate, which was coatedon the cladding to improve the load-bearing capability. The
lengths of the POFs were 100 mm, 40 mm, and 7 mm.
The experimental setup of the SMS-based temperature
sensor using the PFGI-POF is depicted in Fig. 1. The
output of a supercontinuum source (SCS) covering a wideband from 460 to 2000 nm (output power: 75 mW) was
injected into the POF via a 2.5-m-long SMF. The lighttransmitted through the POF was injected into another 3.0m-long SMF, and its spectrum was observed using an
optical spectrum analyzer (OSA; bandwidth: 600–1700
nm). The optical couplings between the POF and the SMFs
were performed using a butt-coupling technique [26]. As
the POF was short, its whole length was, along with thecouplings to SMFs, placed in a thermostatic chamber andheated from room temperature (∼20°C) up to ∼55°C. The
whole setup was ﬁxed during all the measurements, leading
to a negligible change in the polarization state.

Fig. 1. Experimental setup for investigating the temperature sensitivityof single-mode-multimode-single-mode sensors involving short polymer
optical ﬁbers (POFs) with diﬀerent lengths. OSA, optical spectrum
analyzer; SCS, supercontinuum source; SMF, single-mode ﬁber.

4. Experimental results
The measured spectra of the SCS output and the lighttransmitted through the 100-mm-long POF around 1350
nm are shown in Fig. 2(a). The result with a 1.0-m-long
POF is also included for comparison. When the POF length
was 1.0 m, clear dips caused by multimodal interference
were observed at the wavelengths where no dips wereobserved in the SCS output. However, when the POF
length was 100 mm, no clear dips were observed in thisrange; we conﬁrmed that, when the POF was heated,almost no spectral change was observed. This is naturalconsidering the aforementioned fact that the visibility ofthe peaks/dips tends to be reduced with decreasing lengthof the POF. Then, we scanned the wavelength range to bemonitored from 600 to 1700 nm, and found that a characteristic spectral pattern involving multiple dips can beobserved around 1000 nm even when the POF length was
100 mm. The locations of the dips were not identical tothose in the SCS output. In addition, the intervals between
the neighboring dips were not constant in the frequency
domain, which indicates that this pattern does not originate
from a ﬁber Fabry-Perot cavity [27, 28]. Thus, we conclude
that this pattern was caused by multimodal interference.
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IEICE Electronics Express, Vol.16, No.8, 1–5

(a)

(b)

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 2. Measured optical spectra of the supercontinuum source (SCS)
output and the light transmitted through the POFs. (a) When the POF
lengths were 1.0 m and 100 mm; around 1350 nm. (b) When the POF
length was 100 mm; around 1000 nm. The red circle indicates the dip used
for investigating the temperature dependence.

For all the POFs shorter than 100 mm, similar spectral
patterns were observed around 1000 nm.
Subsequently, we measured the temperature dependence of the one of the dips around 1000 nm (the one closest
to 1000 nm; indicated by a red circle in Fig. 2(b)) when the
POF length was 100 mm; see Appendix for the validity of
selecting this dip. The spectral dependence on temperature
is shown in Fig. 3(a). All the measured spectra werevertically shifted and normalized so that the dip power
became 0. With increasing temperature, the dip shifted tolonger wavelength. Then, we plotted the dip wavelength asa function of temperature (Fig. 3(b)). The dependence wasalmost linear in this range, and the dependence coeﬃcient
was 83.5 pm/°C. We also measured the temperature dependencies of the spectral dips and the dip wavelengths
when POFs with lengths of 40 mm and 7 mm were used
(Figs. 3(c)–(f )). Regardless of the POF lengths, similar
trends were obtained, and the dependence coeﬃcients were80.3 pm/°C and 93.8 pm/°C for the 40-mm-long and 7mm-long POFs, respectively. These values are approximately 100 times smaller than those measured around1350 nm using POFs longer than 300 mm [19], probably
because of the diﬀerent wavelength ranges where spectral
dips can be observed. Another ﬁnding is that, when a POF
is shorter than 100 mm, the temperature sensitivity did notlargely depend on the POF length, which is the same trend
as that of longer POFs. We can interpret that the sensitivity
does not largely depend on the POF length as long as the
wavelength range used for the measurement is identical.
5. Discussion
When the POF length was shorter than 100 mm, the obtained temperature sensitivity was much lower than thosewith longer POFs. As the most important advantage of
SMS-based temperature sensors using PFGI-POFs is theirhigh sensitivity, it is not beneﬁcial to fabricate a ﬁber-tiptype temperature sensor using such a short POF. However,
our success in observing multimodal interference in a
millimeter-long MMF, even with a low temperature sensitivity, has enormous signiﬁcance in terms of adding a new
function to intensity-based ﬁber-optic point sensors. One
example is what they call hetero-core sensors [29, 30],
which are composed of a short small-core SMF sandwiched between two larger-core SMFs. They are used toFig. 3. Measured temperature dependencies of the normalized spectra
and the dip wavelengths. (a) spectrum, 100-mm-long POF; (b) wavelength, 100-mm-long POF; (c) spectrum, 40-mm-long POF; (d) wavelength, 40-mm-long POF; (e) spectrum, 7-mm-long POF; (f ) wavelength,7-mm-long POF. The solid lines in (b), (d), and (f ) are linear ﬁts.

measure various physical parameters such as deformation,pressure [29], and acidity [30], based on optical loss (i.e.,
intensity information) induced at the hetero-core parts. As
multiple propagation modes including cladding modes exist in a small-core SMF, multimodal interference could also
be observed in this conﬁguration. If frequency-based sensing function is added to the conventional intensity-based
operating mechanism of hetero-core sensors, discriminative
sensing of multiple parameters will be feasible. Anotherexample is swelling-clad-based POF sensors [31, 32], inwhich claddings are partially removed and replaced withswelling polymer. Based on optical loss, some parameterssuch as ambient humidity [31] and alkane [32] can bemeasured. As the number of the propagation modes atthe cladding-removed part is diﬀerent from those of otherparts, multimodal interference could also be observed inthis kind of sensor. Thus, our ﬁnding will be a basis for the
combined use of intensity and frequency information inconventional single-point sensors.
6. Conclusion
Multimodal interference was observed, for the ﬁrst time tothe beset of our knowledge, in SMS sensors using short
PFGI-POFs with lengths of 100 mm, 40 mm, and 7 mm.
Spectral dips were observed not in the conventionally used3

IEICE Electronics Express, Vol.16, No.8, 1–5

telecom band but in the shorter wavelength range around1000 nm. The dip wavelengths showed a clear dependence
on temperature, but regardless of the POF length, thesensitivities were approximately 100 times lower than thevalues previously reported with longer POFs in the longer
wavelength range. This result indicates that it is not beneﬁcial to fabricate ﬁber-tip-type temperature sensors basedon multimodal interference in short POFs because of
the diﬃculty in obtaining high sensitivities. However, we
anticipate that the observation of multimodal interferencein millimeter-long optical ﬁbers will open up a new way toadding a frequency-based sensing function to some of theconventional intensity-based single-point sensors.
Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers 17H04930 and 17J07226 and by a research grant fromthe Fujikura Foundation.
Appendix
When a 100-mm-long POF was used, the spectrum of thetransmitted light had more than 10 dips around 1000 nm,
as shown in Fig. 2(b). We selected a particular dip andinvestigated its temperature dependence. However, as thetemperature sensitivity has been reported to depend on
optical wavelength [14], it may not be fair to evaluate thesensing performance using only a single dip. Here, wemeasure the diﬀerence in the temperature sensitivities ofthe diﬀerent dips. Fig. A·1(a) shows the temperature dependence of the spectrum of the transmitted light around1000 nm when the 100-mm-long POF was used. We selected two dips (located at ∼962 nm and ∼1045 nm whentemperature was 52.1°C; indicated by red circles) andmeasured their wavelength dependencies on temperature,

(a)

(b)

(c)

Fig. A·1. (a) Temperature dependence of the spectrum of thetransmitted light around 1000 nm when the POF length was 100 mm.
The red circles indicate the measured dips. (b, c) The temperaturedependencies of the two dip wavelengths. The solid lines are linear ﬁts.

as shown in Figs. A·1(b) and (c). The dependencies wereboth almost linear, and the coeﬃcients of the dips at shorterand longer wavelengths were 157 pm/°C and 69.4 pm/°C,
respectively. Although the former is approximately 2.3
times higher than the latter, this result suggests that the
selection of an arbitrary dip does not alter the conclusionthat the obtained sensitivity around 1000 nm is by far lower
than those in the telecom band.
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