High-performance vector bending and orientation distinguishing curvature sensor based on asymmetric coupled multi-core fibre

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High‑pe o mance ec o bending
and o ien a ion dis inguishing
cu a u e senso based
on asymme ic coupled mul i‑co e
ib e
oska A izabalaga1*, Qi Sun2, Ma ynas Be esna2, imo hy Lee2,
Joseba Zubia1, Ja ie Velasco pascual3, idu e Sáez de ocá iz3, Axel Schülzgen4,
Jose en ique An onio‑Lopez4, Rod igo Amezcua‑co ea4, Joel Villa o o1,5 &
Gilbe o B ambilla2
ib e op ic echnology is apidly e ol ing, d i en mainly by elecommunica ion and sensing
applica ions. excellen eliabili y o he manu ac u ing p ocesses and low cos ha e d awn e e
inc easing a en ion o ib e-based senso s, e.g. o s udying mechanical esponse/limi a ions o
ae ospace composi e s uc u es. He e, a ec o bending and o ien a ion dis inguishing cu a u e
senso , based on asymme ic coupled mul i-co e ib e, is p oposed and expe imen ally demons a ed.
By op imising he mode coupling e ec o a se en co e mul i-co e ib e, we ha e achie ed a sensi i i y
o − 1.4 nm/° as a ec o bending senso and − 17.5 nm/m−1 as a cu a u e senso . hese a e he highes
sensi i i ies epo ed so a , o he bes o ou knowledge. In addi ion, ou senso o e s se e al
ad an ages such as epea abili y o ab ica ion, wide ope a ing ange and small size and weigh which
bene i i s sensing applica ions.
Mechanical s uc u es a e becoming mo e and mo e complex wi h he in oduc ion o in ica e geome ies and
composi e ma e ials1. Fib e ein o ced polyme s a e composi es used in almos e e y ype o ad anced enginee -
ing s uc u es, wi h hei usage anging om ai c a , helicop e s and spacec a h ough o boa s, ships and ci il
in as uc u e such as b idges and buildings. They a e made wi h ein o cemen ib es among he se e al ypes
o composi es2,3 ha a e embedded in a polyme esin (mos ly epoxy).
Composi e ma e ials ep esen a g owing piece o he ae ospace ma e ial pie. They educe weigh and inc ease
uel e iciency while being easy o ope a e, design, shape, and epai . Thus, he s udy o he mechanical beha iou
o hese s uc u es has eno mous signi icance. In o de o ob ain he equi ed le el o pe o mance o ligh
s uc u es, de ailed knowledge o ma e ial limi a ions, s uc u al s abili y and s eng h aspec s is equi ed. Key
sou ces o in o ma ion on he mechanical pe o mance a e senso s based on elec onic echnology4–6. Some o
he bene i s o his ype o senso include accu acy, a wide a ie y o sizes and shapes, and a simple ope a ing
p inciple. Howe e , hey also ha e se e al c i ical sho ages. Thei pe o mance is a ec ed by humidi y, empe a-
u e and hys e esis, epea abili y and accu acy all wi h p olonged use, and also hey can be damaged by s a ics
o cu en o e loads. Ano he cons ain is ha hey canno wo k in he p esence o elec omagne ic ields.
O e he las ew yea s, op ical ib e senso s (OFSs) ha e eme ged as an al e na i e o hei elec onic equi a-
len s in he p ocess o es ing ma e ial limi a ions o enginee ing s uc u es7,8. Fib e-based senso s can be used o
measu e s ain, empe a u e, p essu e, bending and o he quan i ies9,10. Such senso s a e no mally in e oga ed
by coupling he ligh om a lase (o en a single- equency ib e lase ) o om a supe luminescen sou ce. The
open
1Depa men o Communica ions Enginee ing, Uni e si y o he Basque Coun y (UPV/EHU), Ingenie o
To es Que edo s/n, 48013 Bilbao, Spain. 2Op oelec onics Resea ch Cen e, Uni e si y o Sou hamp on,
Sou hamp on SO17 1BJ, UK. 3Fundación Cen o de Tecnologías Ae onáu icas (CTA), Miñano, Spain. 4CREOL, The
College o Op ics and Pho onics, Uni e si y o Cen al Flo ida, O lando, USA. 5IKERBASQUE-Basque Founda ion
o Science, 48011 Bilbao, Spain. *email: oska [email p o ec ed]
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ligh p opaga ing in he ib e changes i s pa ame e s such as spec al composi ion, in ensi y, pola iza ion, which
can be easily analysed and quan i ied by means o an op ical spec um analyse (OSA) o powe me e .
OFSs in gene al o e some big ad an ages o e hei elec ical equi alen s such as hei immuni y o elec o-
magne ic in e e ence and high ol age, low haza d po en ial, immuni y o ligh ning s ikes, capabili y o emo e
sensing and small size, jus o men ion a ew. All desc ibed ea u es make hem e y a ac i e, e.g. in he s udy
o ma e ial limi s in ae onau ical s uc u es11.
Many ib e-based echnologies a e being de eloped bu comme cial solu ions mainly boil down in o wo
ca ego ies: poin sensing whe e he ac i e pa is a sho segmen o ib e12 and dis ibu ed sensing whe e he
en i e ib e ope a es as he senso 13.
Fib e B agg g a ing14 (FBG) senso s a e by he a he mos widely ib e-based echnology used as a poin
senso . They a e se ling hea ily in he indus ial ma ke and hei ange o applica ions con inues o g ow. How-
e e , he mal and ans e sal s ain sensi i i ies, high-cos o building and main aining, limi ed supplies and
he di icul y in demodula ing wa eleng h shi a e hei main d awbacks o his app oach15,16.
In o de o enhance he sensi i i y in he las ew yea s, di e en ib e-based senso s schemes ha e been
p oposed. An FBG in a wa eguide-a ay mic os uc u ed op ical ib e17, a long-pe iod ib e g a ing in an index-
guiding pho onic c ys al ib e18 o Fab y–Pe o in e e ome e s19,20 (FPIs) a e some examples. O hese, he
la e o e he highe sensi i i y21. Ne e heless, due o he ai -ca i ies o FPI s uc u es, he de ices ha e a low
mechanical s eng h. The e o e, he p e iously epo ed echniques ha e he incon enience o a low sensi i i y
o weak mechanical s eng h.
An al e na i e app oach is o use special op ical ib es ha con ain mul iple co es, which may e.g. be a anged
on a ing a ound he ib e axis o on six co es on he edges o a hexagon and a cen al co e in addi ion. Such
ib es a e called mul i-co e ib es (MCF)22. In p inciple, each o he ib e co es in such a ib e can ac as a sepa a e
wa eguide, so ligh can independen ly p opaga e h ough hose co es. Howe e , i he dis ance be ween he co es
is small, mode coupling be ween he co es akes place because he co esponding mode ields ha e a signi ican
spa ial o e lap23. Tha is o say, he ligh which is ini ially coupled in o one co e can e en ually be coupled o e
o o he co es. The exchange o ligh be ween he co es is ex emely sensi i e o ex e nal in luences such as s ain
o empe a u e changes. In ac , se e al au ho s ha e al eady p oposed a ious ypes o schemes o de elop
senso s wi h MCF in o de o achie e senso s wi h unc ionali ies supe io o hose based on con en ional
ib es24,25. Ne e heless, al hough MCF-based senso s ha e been al eady demons a ed26–29, we belie e ha he
coupling mode e ec in s ongly coupled MCFs has no ye been ully exploi ed. Fo ins ance, he MCF used in
he p e iously epo ed wo ks was ab ica ed wi h an iden ical index o all co es and wi h symme ic geome y.
This ac es ic s e icien exploi a ion o he mode coupling be ween co es because he e ec is no sensi i e o
complemen a y ac ions e.g. dis inguishing cu a u e o ien a ion.
In his wo k, we epo on he MCF-based senso capable o dis inguishing cu a u e o ien a ion. We b eak
he symme y o a MCF by using em osecond lase w i ing o modi y he index o one o he six su ounding
co es o a se en co e ib e, which a e symme ically a anged a ound a cen al co e. The absence o he sym-
me y enabled us o implemen a sensing de ice capable o de ec ing he o ien a ion as well as magni ude o he
cu a u e wi h high sensi i i y. Taken in o accoun he ib e op ics ad an ages men ioned abo e, we belie e ha
ou p oposed de ice is sui able o be used in he s udy o mechanical beha iou o e.g. ae onau ical s uc u es.
In ac , ou senso was e alua ed in a s a ic es o an ae onau ical componen , made o ca bon ib e. In such es ,
i beha ed in he same way ha a s ain senso wi h which i was compa ed.
Resul s
Ou p oposed senso is based on a s ongly-coupled mul i co e ib e (MCF) ab ica ed a he Uni e si y o Cen-
al Flo ida (O lando, USA) by he well-es ablished s ack and d aw me hod. The MCF consis s o a symme ical
s uc u e o med wi h a cen al co e su ounded by ano he six co es made o silica doped wi h ge manium
and embedded in pu e silica cladding (see Fig.1a). The nume ical ape u e (NA) o he co es a λ = 1.55μm is
0.14, ma ching wi h a s anda d SMF. The adius o each co e ( ) is 4.5μm wi h a co e- o-co e pi ch (d) o 11μm.
The sensing mechanism is based on b eaking he e ac i e index symme y a ound he cen al co e. One
o he ex e nal co es is modi ied by means o em osecond lase di ec w i ing o inc ease he e ac i e index
o a selec ed olume ic egion wi hin he ib e. The lase pulses pe manen ly change he e ac i e index o he
i adia ed zone, hus de uning coupling condi ions wi h he neighbou ing co es. The dimensions o he insc ibed
s uc u e we e 10μm × 10μm in c oss sec ion and 4cm in leng h.
To analyse he p opaga ion o ligh guided in he MMCF, he in e -co e coupling beha iou can also be in e -
p e ed as he bea ing o supe modes. F om a ull ec o ini e-elemen mode sol e (Pho on Design, Ox o d, UK)
i has been ound ha ou modi ied mul i co e ib e (MMCF), in he ange om ~ 1,250 o ~ 1,650nm, suppo s
se en supe -modes each o which has wo o hogonal linea pola iza ions (x and y pola iza ions). They can be
di ided in o h ee ca ego ies: undamen al modes, highe o de modes wi h a cen al peak and highe o de
modes wi hou cen al peak (see Fig.1). We ha e labelled hem as SM1, SM2 and SM3, espec i ely.
The s uc u e o ou p oposed sensing de ice consis s o wo single mode ib es (SMF), spliced axially aligned,
a bo h he ends o a sho segmen o MMCF o leng h L as can be seen in he Fig.2a. The eby, when he unda-
men al mode o he SMF (HE11) is injec ed om he inpu -SMF o he cen al co e o he MMCF, he SM1 and
SM2 will be exci ed due o la ge nonze o modal o e lap wi h he inpu mode. The SM3 modes a e no p esen , o
hei powe is so low ha hey can be neglec ed. The SM1 and SM2 will bea wi h each o he as hey a el h ough
MMCF, leading o a pe iodic coupling spec um which can be obse ed ia he ou pu SMF.
To s udy he powe in only he cen al co e, no e ha he mode coupling be ween all he co es o a MMCF is
gi en by a se o coupled mode equa ions30–32. Then, when he undamen al mode o he SMF is launched in o
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cen al co e o MMCF, he heo e ical solu ion o he ield ampli ude in he cen al co e a dis ance L is gi en
by33,34:
The C pa ame e deno es he coupling coe icien be ween adjacen co es and i can be app oxima ed om
hei modal ield spa ial o e lap o gi e:
whe e
U=

k
0
n2
co −
β2
1/2
,W
=

β2
−
k
0
n2
cl 1/2
and V
=
k
0
n2
co −
n2
cl 1/2
; K0 and K1 a e modi ied Bes-
sel unc ions a o de m (m = 0, 1); nco and ncl a e he e ec i e e ac i e indices o he co e and he cladding,
(1)
A
(L)
=
Cos
√
7CL
+j
√7
Sin
√
7CL

e−
jCL
(2)
C
=

2πn
co
U2
2V2
K0

Wd

K
2
1
(
W
)
Figu e1. (a) Mic og aph o he c oss sec ion o he MMCF. (b,c) Simula ed undamen al mode ield p o ile,
and highe o de mode wi h a cen al peak, espec i ely. (d) One o he i e y-pola ised highe o de modes
wi hou cen al peak. In he simula ions, he MMCF was exci ed a 1,550nm and he colou s ep esen he
ampli ude o he ield.
Figu e2. (a) Illus a ion o he s uc u e o he MMCF senso de ice. (b) Expe imen al se up. SCLS supe
con inium ligh sou ce.
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espec i ely; k0 = 2π/λ ep esen he wa eleng h wa e numbe and β deno es he p opaga ion cons an o each
co e wi hou mode coupling.
The no malised powe o he mode is de ined as PA =|A|2, which is pe iodic in L. In he Fig.3a and a he
op o he Fig.3b i can be seen he heo e ical simula ion (in Pho on Design) o he powe dis ibu ion along a
leng h (L) o MMCF when i s cen e ed co e is exci ed a 1,550nm. This powe a a leng h (L) can be exp essed
ma hema ically as:
Acco ding o Eq.(3), he ansmission powe o he cen al co e eaches a maximum when he phase condi-
ion sa is ies (71/2)CL = mπ (m is a posi i e in ege ). The e o e, he co esponding wa eleng h wi h maximum
powe (λm) will be loca ed a :
A he bo om o he Fig.3b, we show he heo e ical simula ion o he powe a a leng h L = 4cm o a wa e-
leng h ange be ween 1,500 and 1,600nm.
In he case o he ben MMCF, he ib e elonga es/comp esses a he ci cula bend and he local index changes
because o s ess-op ic e ec upon bending. The index ans o ma ion is gi en as ollows22,34:
wi h n(x,y) being he e ac i e index o he undis u bed MCF, P11 and P12 a e componen s o he elas o-op ical
enso , υ is Poisson’s a io, R is he adius o cu a u e and x is dis ance om cen e o ib e. This ans o ma ion
allows a ci cula ly cu ed MCF segmen o be modelled as an equi alen s aigh one.
Bending causes a di e en pe cen age o each supe mode o be exci ed and some o he SM3 may also become
p esen in he cen al co e. Ano he consequence induced by he bending is ha some highe o de supe modes
won’ be suppo ed o will ha e high bending losses. As he change in mode p o ile also al e s hei e ec i e
index, he powe dis ibu ion along o he cen al co e o he MMCF will be also a ec ed. Consequen ly, he
spec al peak wa eleng hs desc ibed by Eq.(4) will shi (as well as change in powe ), p o iding a measu able
quan i y o e alua ing he bend.
Ou de ice was es ed in wo di e en con igu a ions; as a ec o bending o a cu a u e di ec ion senso .
Fi s , i was e alua ed as a ec o bending senso . The senso was p epa ed using a 4cm segmen o MMCF. Then,
he w i en co e was placed in such a way ha he index o he su ounding co es was asymme ical wi h espec
o he bending plane (y,z) (Fig.4a). This con igu a ion o he ib e leads o he di e en exci a ion and bea ing o
supe modes o bending in he + y-di ec ion (see Fig.4b) compa ed o he –y-di ec ion (see Fig.4c). The e o e,
acco ding o he Eq.(4), λm will shi o sho e o la ge wa eleng h depending on he bending di ec ion.
To place he w i en co e in such posi ion, i s , he inpu SMF was connec ed o he expe imen al se up (see
Fig.2b) and he collec ed spec um was analysed wi h an OSA (Yokogawa AQ6370D). A e wa ds, he inpu -SMF
was secu ed o a p ecision ib e o a o lea ing he segmen composed o MMCF-ou SMF in ee space (Fig.5a).
The whole assembly was ixed o a lexu e p ecision s age wi h a s eppe mo o ac ua o (Fig.5b). The nex s ep
was o place he ib e wi h he w i en co e in a symme ical posi ion wi h espec o he bending plane as i is
shown in he Fig.4a. To do his, he ou pu SMF was ixed and ansla ed in he ± x-axis wi h he lexu e p ecision
s age. Simul aneously, he ib e was o a ed o ind he posi ion, whe e he spec um shi is he same ega dless
o whe he he displacemen is on he + x-axis o on he –x-axis (Figs.6a, 7a). Then, by o a ing he MMCF ± 90º
om he e e ence posi ion (see Fig.5b), he w i en co e is placed in such a way ha i lies in he bend plane, so
(3)
P
A(L)
=
1
7+
6
7
Cos2
√
7CL

(4)

m=
2mπ
√7∂C()
∂
L
Wi h m =1, 2, 3,
...
(5)
n
′(x,y)
=
n(x,y)

1
−
n(x,y)
2
x
2R
(P12
−
ν(P11
+
P12))

exp

x
R
Figu e3. (a) 1cm MMCF ield p o ile simula ed by ini e-elemen mode sol e so wa e. The cen ed co e was
exci ed a 1550nm. (b) A he op: heo e ically ob ained no malised powe densi y along 7mm o he cen ed
co e o a MMCF exci ed a 1,550nm. A he bo om: spec um o he cen ed co e a a leng h L = 4cm.
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he ib e index p o iles o le and igh bends a e no longe iden ical. Thus, acco ding o he Eq.(4), posi i e o
nega i e bending on he ib e will cause he la ges spec al shi s o sho e o la ge wa eleng hs (see Figs.6b,
7b–d) enabling o de ec he magni ude and di ec ion o he bending.
A e loca ing he desi ed posi ion o he ib e, we expe imen ally e alua ed i s pe o mance. The MMFC was
displaced by means o he s eppe mo o om he s aigh posi ion in he di ec ion o he + x-axis in s eps o
0.5mm un il eaching 5mm. Nex , i was e u ned o he s aigh posi ion in he same s eps. The la e ope a ion
was epea ed on he −x-axis di ec ion (Fig.7b,c). In hese g aphics we ha e con e ed he displacemen dis ance
Figu e4. (a) Illus a ion o he dis ibu ion o he co es o he MMCF when he index p o ile is simme ical
espec o he bending plane. (b,c) Illus a ions when he MMCF is o a ed 90° wi h espec o he e e ence.
The index p o ile is asymme ical wi h espec o he bending plane and i a ies depending i he w i en co e
expe iences ension o comp ession.
Figu e5. (a) Illus a ion o he p ecision ib e o a o used o o a e he MMCF. (b) Se up used o ind he
co ec posi ion o he co es.
Figu e6. (a) Theo e ical spec um o he MMCF de ice when i s index p o ile is symme ical wi h espec o
he bending plane. (b) The same bu wi h he index p o ile asymme ical wi h espec o he bending plane.

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o deg ees and i can be seen how when he bending causes expansion in he w i en co e (as i is illus a ed in
Fig.4b he spec um ed-shi and on he con a y, when he bending causes con ac ion, he spec um blue-shi .
In Fig.7d we ha e plo ed he wa eleng h shi e sus he bend angle. F om his calib a ion, we ound ha he
sensi i i y o ou senso o posi i e and nega i e bending is −1.4nm/° and 1nm/°, espec i ely. The e o ba s
ep esen he ange in which a e ound he e u n om he maximum ben angle o s aigh posi ion. F om he
wid h o he e o ba s i can be seen ha ou p oposed ec o -bend senso does no exhibi hys e esis.
The abili y o dis inguish he bend di ec ion can also be unde s ood by analogy. Conside a symme ic MCF
unde bending, in which one side is unde comp ession and he o he ension. I he MCF is ini ially s aigh ,
due o geome ic symme y, he spec al peak wa eleng h shi is iden ical whe he he MCF is ben o he le
o igh , so o ien a ion is un esol able. Howe e , i he MCF began om an ini ially cu ed posi ion, i would
be able o esol e whe he he bend has become igh e o weake due o di e en peak shi di ec ion. By modi-
ying he index o an ou e co e o he MCF, we e ec i ely ’bias’ ou MCF senso in o his egime o ope a ion:
he pe manen lase -induced index inc ease he e simula es he comp ession expe ienced on he inne bend and
has a simila e ec on he supe mode p o iles. In his way, he asymme ic MMCF can esol e bend di ec ion
om a s aigh ini ial posi ion.
Ou p oposed senso was also e alua ed as a di ec ional cu a u e senso . To ca y ou he expe imen al
es , i s we placed he co e dis ibu ion o a leng h o ~ 4cm o MMCF symme ically wi h espec o he y-axis
using he same echnique as desc ibed abo e. A e wa ds, a shee o PVC was placed unde nea h he MMCF
and bonded oge he (Fig.8a). In o de o ansmi he cu a u e om he PVC shee o he MMCF segmen ,
he MMCF was co e ed along he whole leng h wi h a cyanoac yla e adhesi e (Fig.8b) and le o cu e o 24 h.
Once he de ice was bonded o he PVC, i was e ically placed and ixed by wo poin s wi h a ixing leng h
o 10cm (see Fig.8b). Nex , by means o he mo o ised lexu e s age, i was subjec ed o displacemen s o 5mm
in s eps o 0.5mm in on he ± x-axis di ec ion, applying a o ce a he cu a u e o ce poin as desc ibed in he
Fig.8b. I causes ension on he w i en co e when he displacemen is on he + x di ec ion and comp ession
when he – x-di ec ion. Taken in o accoun he ixing leng h we ha e con e ed displacemen s o cu a u e
(m−1) (Fig.8).
F om he da a (Fig.9), i can be seen ha he wa eleng h peak is ed-shi ed when he lase modi ied co e
unde goes ension (posi i e cu a u e) and blue-shi ed when he co e comp esses (nega i e cu a u e). The
e o ba s ep esen he shi ange in which a e ound when he cu a u e e u n om i s maximum o s aigh
posi ion. F om he calib a ion we ound ha ou de ice has a sensi i i y o 15.9 and −17.5nm/m−1 o posi i e
and nega i e cu a u e, espec i ely. Once again, i can be seen ha he de ice does no exhibi hys e esis.
Figu e7. (a) Expe imen al ec o bending spec um o he MMCF de ice wi h symme ic index p o ile wi h
espec o he bending plane. (b,c) The same bu wi h asymme ic index p o ile. (d) Peak wa eleng h e sus
angle o bo h di ec ions o ec o bending.
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Ou de ice also was assessed in a s a ic es o an ae onau ical componen made o ca bon ib e. This com-
ponen was de eloped by Ae nno a, a company specialising in he design and manu ac u ing o ae onau ical
s uc u es and componen s. The es consis ed o a S a ic Tes a oom empe a u e ca ied ou a he Ae onau ical
Technology Cen e (CTA) placed in Miñano, Spain. The es consis ed o applying a load o he specimen using
hyd aulic ac ua o s con olled by a wo ks a ion (MTS Sys ems Co po a ion). The applied load causes bending
de o ma ion o he specimen. In pa allel, he de o ma ion was measu ed by s ain gauges (HBM, Ge many)
placed a di e en poin s.
Ou de ice was bonded o a hickness gauge oil (TGF) o 0.05mm (Vogel, Ge many) wi h he co es in he
same way as shown in Fig.8a. The ip o he ou -SMF was coa ed wi h a 100nm hick gold laye by means o a
spu e coa e (see Fig.10a). The gold coa ing ac s as a mi o and p o ec s om he en i onmen al di .
In o de o compa e ou p oposed de ice wi h comme cial s ain senso s, he s uc u e o med wi h he TGF
and ou de ice was glued wi h cyanoac yla e o he specimen in he icini y o he s ain gauges ins alled by he
CTA echnicians (see Fig.10b). The se up o ca ying ou such es is as shown in Fig.3b. A supe luminescen
diode (SLD) was used as a b oadband ligh sou ce cen ed a 1,550nm. The spec um was collec ed in eal- ime
by means o a minia u e in e oga ion moni o (Ibsen Pho onics, Denma k) (Fig.10c). To measu e he de o ma-
ion o he specimen a he poin whe e we placed ou de ice, he local peak o he spec um (λm) was acked.
The eal- ime e olu ion o he es , while he specimen was subjec ed om 0 o 3,300 mic o-s ain (με), can
be seen in Fig.10d. The o ce was applied o he specimen con inuously wi h wo s ops made a 1,000 and 1,500
με (labelled in he Fig.10d as “ i s s op” and “second s op”). F om he a o emen ioned igu e i can be seen ha
ou de ice can de ec he e olu ion o he de o ma ion o he specimen acco ding o he applied o ce jus like he
comme cial s ain gauge wi h which i has been compa ed. F om a ound 2000 με, he spec al peak shi occu s
in a mo e ab up ashion. F om he eco ded ideos o he es , we ha e iden i ied ha hese ab up shi s a e
Figu e8. (a) Illus a ion o he dis ibu ion o he co es o measu e cu a u e. (b) Se up used o measu e he
cu a u e expe imen ally. (c,d) Illus a ion o he expansion and comp ession, espec i ely, o he w i en co e
depending on he di ec ion o he cu a u e.
Figu e9. (a,b) Expe imen al spec a ob ained om he MMCF de ice when i was subjec ed o di e en
di ec ion o cu a u e. (c) Plo o peak wa eleng h shi Δλm agains cu a u e o bo h di ec ions.
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caused by he delamina ion o he laye s o he specimen a his a ea. I is impo an o no e ha he a ea chosen
o placing ou senso was p edic ed o ail by he heo e ical simula ions when he load eaches ~5,000 με. No e
ha ou de ice co e s a wide a ea compa ed o he a ea co e ed by he s ain gauge.
Discussion
We ha e p oposed and expe imen ally demons a ed a ec o bending and dis inguishing cu a u e o ien a ion
senso based on coupling be ween he 7 co es o a mul i-co e ib e. By b eaking he e ac i e index symme y
o he co es, bend di ec ion can be dis inguished. The measu ed sensi i i ies o −17.5nm/m−1 and −1.4nm/°
as a cu a u e and a ec o bending senso , espec i ely, a e highe han any o he epo ed so a . The senso
has he ad an ages o high epea abili y, low-cos , s aigh o wa d and ep oducible ab ica ion, and does no
ha e hys e esis. When ou senso was e alua ed in a s a ic es o an ae onau ical componen , made o ca bon,
i s beha iou success ully ma ched ha o a comme cial senso .
Me hods
Ou em osecond lase sys em Pha os (Ligh Con e sion L d., Li huania) ope a es a 1030nm wa eleng h, wi h
a pulse du a ion o 200 s and a epe i ion a e o 200kHz. Fo enhancing w i ing esolu ion, lase w i ing was
ca ied ou using he second ha monic a 515nm. The lase beam was ocused by a 0.4NA objec i e in o he
bulk o he MCF, which was ixed on o a compu e con olled ansla ion s age. An i is wi h 65% ansmission
was placed be o e he objec i e o imp o e he beam homogenei y. Du ing he w i ing, he lase w i ing powe
was se o 6 mW a e he objec i e, which co esponds o a single lase pulse ene gy o 30 nJ. The modi ica ion
was w i en by he mul iscan lase scanning me hod35 whe e he lase scanlines we e insc ibed consecu i ely one
nex o he o he , sepa a ed la e ally by 200nm, and he pulse densi y was 3 × 105 pulses/mm along each scanline.
Recei ed: 27 May 2020; Accep ed: 7 Augus 2020
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Acknowledgemen s
This wo k has been unded in pa by he Fondo Eu opeo de Desa ollo Regional (FEDER), in pa by he Min-
is e io de Ciencia, Inno ación y Uni e sidades unde p ojec s RTI2018-094669-B-C31 and GC2018-101997-
B-I00, in pa by he Gobie noVasco/Eusko Jau la i za IT933-16, ELKARTEK KK-2019/00101 (μ4Indus ) and
ELKARTEK KK-2019/00051 (SMARTRESNAK) and in pa by NE/S012877/1 and EP/S013776/1. We also a e
g a e ul o Ae nno a o allowing us o es ou senso in a eal en i onmen .
Au ho con ibu ions
O.A., Q.S. and M.B. pe o med he expe imen s and w o e he manusc ip ; M.B. and G.B. helped supe ise he
p ojec ; T.L. concei ed he idea o modi ying he MCF; Q.S. modi ied he MCF; O.A. analysed and in e p e ed he
da a; A.S, J.E.A.L. and R.A.C. ab ica ed and p o ided he MCF. J.Z. e ised he da a and ob ained he unding;
G.B and J.V. p oposed he use o em osecond lase o modi y MCF; I.S.O. and J.V.P. ha e pe o med he es s
ca ied ou in eal en i onmen . All au ho s e iewed he manusc ip .
compe ing in e es s
The au ho s decla e no compe ing in e es s.
Addi ional in o ma ion
Co espondence and eques s o ma e ials should be add essed o O.A.
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