OPTICS AND OPTOELECTRONICS VOLUME: 12 |NUMBER: 2 |2014 |JUNE
The Response o Pola iza ion Main aining Fibe s
upon Tempe a u e Field Dis u bance
Filip DVORAK1, Jan MASCHKE2, Ces mi VLCEK2
1Depa men o ada echnology, Facul y o Mili a y Technology, Uni e si y o De ence, Kounico a 65,
B no, 602 00, Czech Republic
2Depa men o elec ical enginee ing, Facul y o Mili a y Technology, Uni e si y o De ence, Kounico a 65,
B no, 602 00, Czech Republic
ilip.d [email p o ec ed], jan.maschk[email p o ec ed], [email p o ec ed]
Abs ac . The pape deals wi h he esponse o po-
la iza ion main aining (PM) ibe s upon he a ia ion
o he empe a u e ield, on condi ion bo h pola iza-
ion axes a e exci ed. P ope use can be applied in
he a ea o op ical ibe he mal ield dis u bance sen-
so . Fo a desc ip ion o pola iza ion p ope ies he
cohe en Jones and Mulle ma ices we e used. The
Poinca e sphe e was applied o depic he de elopmen
o he ou pu o he pola iza ion s a e o PM ibe s o
wa eleng hs 633 nm, 1310 nm and 1550 nm we e a -
anged in a p oposed senso se up and we e s udied in
he labo a o y. A wide ile o esul s con aining depen-
dencies o phase shi a ia ions upon di e en con ig-
u a ions o measu ed PM ibe was ob ained. The he -
mal ield dis u bance o he PM ibe was applied by
an objec wi h de ined p opo ions and a de ined ange
o empe a u es. Dependencies o phase shi upon he
objec ’s empe a u e, i s dis ance om he ibe and ex-
posed leng h o PM ibe we e measu ed.
Keywo ds
Bea leng h, cohe ency ma ix, ibe esponse,
Poinca e sphe e, senso , s a e o pola iza ion.
1. In oduc ion
F om he beginning o ibe ealiza ion in he elecom-
munica ions a ea i go o he big de elopmen o he
heo y and p ac ical applica ions. Almos in he same
ime he e we e ideas on he applica ion o ibe s also
in senso s. Iso opic ibe s [1], pola iza ion main aining
ibe s (PMF) and a e ea h doped ibe s [2] ha e been
used in he numbe o senso applica ions. One exam-
ple o an applica ion is he in e e ome ic senso o
gy oscope [3], [4]. Pola iza ion main aining ibe s we e
es ablished o exci ing o op ical adia ion o one po-
la iza ion axis only and main enance pola iza ion s a e
along he whole leng h o he ibe . Acco ding o he
induced bi e ingence, ibe s we e applied in senso s,
e.g. o measu emen o mechanical p essu e [5].
The a i icial bi e ingence caused by he di e en
he mal expansibili y be ween s eng h elemen s and
he ibe cladding eaches high sensi i i y o he ambi-
en empe a u e o su ounding en i onmen [6]. Fo
uni o m exci a ion o bo h ibe axes he e is a pola iza-
ion s a e change o op ical adia ion in he ibe ou -
pu caused by he ambien he mal ield dis u bance.
The change o he pola iza ion s a e o ou pu op ical
adia ion immedia ely de ec s any he mal ield dis u -
bance caused by an ambien he mal sou ce. High ibe
sensi i i y o he ou e he mal ield ini ia ed he idea
o use he PMF applica ion as a senso o he mal ield
dis u bance.
In an o he esea ch wo k, ime de elopmen o ou -
pu pola iza ion luc ua ion in PANDA PMF and bow-
ie o equal exci a ion o bo h pola iza ion axes we e
s udied. Exp essi e luc ua ion led o he cons uc ion
o a ibe senso ealized and e alua ed o λ= 633 nm,
u ilizing good pola iza ion p ope ies o He-Ne lase .
The measu ed esul s alida ed high senso sensi i i y
upon he ex e nal he mal ield. The disad an age o
his senso is i s cons uc ion a angemen using gas
He-Ne lase as a sou ce o op ical adia ion. To elimi-
na e his disad an age and o compa e di e en p op-
e ies o he componen s used, he expe imen was ex-
ended o PANDA PM ibe s and semiconduc o lase s
wi h wa eleng hs o 1550 nm and 1310 nm wa eleng hs.
Resul s o heo e ical analysis and pa ial expe i-
men al es s o λ= 633 nm and 1550 nm we e pub-
lished in p e ious pape s [7], [8], [9], [10]. Two pa ial
expe imen s o λ= 1550 nm ha e been made he e.
The a e o ibe esponse depending upon he dis-
ance be ween ex e nal he mal sou ce and he ibe
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was s udied in he i s one. E ec s o PMF esponse
o i s exposed leng h we e s udied in he second one.
P esen ed wo k is an ex ension o p e ious expe imen s
o a wa eleng h o 1310 nm. This wo k ocuses mainly
on he de e mina ion o ibe esponse in bo h depen-
dences du ing an exci a ion by an ex e nal he mal ield
wi h a iable ini ial empe a u e. All he esul s ob-
ained o he h ee pa icula PM ibe s will be com-
pa ed.
2. P inciple o Senso Func ion
The pa o PMF can be, in p inciple, s udied as a
mul iple linea e a de con aining no pa ial pola iz-
e s and can be desc ibed by means o a uni a y Jones
ma ix. Ou pu op ical adia ion om he PMF can be
desc ibed by cohe ency ma ix C0, ha is de e mined
by he uni a y Jones ma ix o he gi en componen L
and also by a cohe ency ma ix o inpu op ical adia-
ion Cacco ding o: [11]
C0= (LE)⊗(LE)+= (LE)⊗(L+E+) =
=L(E)⊗(E+)L+=LCL+,(1)
whe e + is labelling o he He mi ian conjuga e ma-
ix. By decomposi ion o he cohe ency ma ix o he
ou pu op ical adia ion elemen s o S okes ec o can
be ound, enabling desc ip ion o he ibe senso ea-
u es o he mal ield dis u bance om he poin o
iew op ical in ensi y I.
To de e mine a cohe ency ma ix o ou pu op ical
adia ion a cohe ency ma ix o inpu op ical adia ion
and Jones uni a y ma ix o PMF we e needed. Fo
exci a ion o bo h pola iza ion axes a any angle o
he ibe a clockwise pola ized op ical adia ion was
in oduced, desc ibed by Jones ma ix JRC:
JRC =−i
1.(2)
The su ix RC exp esses igh ci cula pola iza ion.
The cohe ency ma ix o an inpu op ical adia ion p o-
ides as:
C=hE⊗E+i=Ex
Ey⊗E∗
xE∗
y=
=hExE∗
xiExE∗
y
hEyE∗
xiEyE∗
y=Cxx Cxy
Cyx Cyy,(3)
whe e Eis he Jones column ma ix (Jones ec o ) and
E+is i s He mi ian conjuga e ma ix . Equa ion (2)
is exp essed by ma ix Cij o de ine Eq. (10). A e
subs i u ion o Eq. (2) we ob ain he cohe ency ma ix
o ci cula op ical adia ion:
CRC =−i
1⊗i1=1−i
i1.(4)
The phase shi o he linea e a de φis pu in o
he Jones ma ix o a linea e a de wi h azimu h 0 ◦.
By his common ela ion o linea e a de is ob ained
as:
L=



eiφ
20
0e
−iφ
2




.(5)
He mi ian conjuga e ma ix o he ma ix Eq. (5)
can hen be exp essed as:
L+=



e
−iφ
20
0eiφ
2




.(6)
By he subs i u ion o ma ices Eq. (4), Eq. (5) and
Eq. (6) in o Eq. (1) we ob ain cohe ency ma ix o ou -
pu op ical adia ion:
C0
RC =LCRCL+=
=



eiφ
20
0e
−iφ
2



1−i
i1



e
−iφ
20
0eiφ
2




.(7)
By calcula ing he ma ix p oduc in Eq. (7), a e-
sul an ela ion o cohe ency ma ix o ou pu op ical
adia ion can be ob ained:
C0=1−ieiφ
ie−iφ 1.(8)
By decomposi ion o Eq. (8) in o he spin ma ices
using he ollowing equa ion,
C=Cxx +Cyy
21 0
0 1+Cxx −Cyy
21 0
0−1+
+Cxy +Cyx
20 1
1 0+(9)
+Cxy −Cyx
20−i
i0,
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we ob ain:
C0=1 0
0 1+ sinφ0 1
1 0+ cosφ0−i
i0.(10)
F om he ela ion Eq. (10) i is ob ious an assign-
men o componen s on he igh side o he equa ion o
he co esponding componen s o S okes ec o . Uni
ma ix co esponds o he componen S0, he compo-
nen wi h mul iple sinφco esponds o S2and he com-
ponen wi h mul iple cosφco esponds o S3. Dis i-
bu ion o op ical in ensi y Iin he e ical p e e ence
is ze o acco ding o he de ini ion S1=Cxx −Cyy.
Fo he leng h o he op ical ibe equaling o he
mul iple o i s bea leng h and o exci a ion o bo h
pola iza ion axes by means o ci cula pola ized op ical
adia ion wi h no dis u bance o ex e nal he mal ield,
he phase shi φwill be equal o ze o and he co e-
sponding S okes componen S2= 0. Fo op ical ibe
leng h di e en om a mul iple o i s bea leng h and
wi hou e ec o he ex e nal he mal ield dis u bance
he phase shi will be none ze o and will be de e min-
ing he pa icula s a e o pola iza ion. In he case o
ambien he mal ield dis u bance by means o an ex-
e nal he mal sou ce he phase shi will be exci ed
and i will esul as a change o he ou pu pola iza-
ion s a e. This a ia ion o he pola iza ion s a e is
di ec ly p opo ional o he change o φacco ding o
he ela ion Eq. (11). De e mina ion o his change
is ealized by means o pola ize - analyze placed in
he ou pu o ibe . Fo ob aining he maximum sen-
so sensi i i y he o ien a ion o he ou pu pola ize
– analyze is 45 ◦ owa ds pola iza ion axes. By his
a angemen we can measu e he whole ange o he
phase shi , exp essed by he minimum and he maxi-
mum alue o he measu ed op ical in ensi y I.
Due o he cha ac e o he measu ed quan i y, he
op ical in ensi y I, is p e e able o nex desc ip ion
o use a Muelle ma ix. Beha io o he inpu ci -
cula pola ized op ical adia ion p opaga ing h ough
he senso unde conside a ion, he linea e a de , is
exp essed by he Muelle ma ix as ollows:




S0
S1
S2
S3




=



1 0 0 0
0 1 0 0
0 0 cosφsinφ
0 0 −sinφcosφ








1
0
0
1




=
=



1
0
sinφ
cosφ




.(11)
The ou pu op ical adia ion Eq. (11) hi s he linea
pola ize – analyze in he equi ed o ien a ion owa ds
he pola iza ion axes. In he ou pu o pola ize we
ob ain he op ical adia ion exp essed by he S okes
ec o :




S0
0
S0
1
S0
2
S0
3




=1
2




1010
0000
1010
0000








1
0
sinφ
cosφ




=
=1
2




1 + sinφ
0
1 + sinφ
0




.(12)
F om his esul an equa ion i is clea ha he ou -
pu op ical adia ion o he pola ize – analyze will be
linea ly pola ized wi h an o ien a ion o 45 ◦and he
change o op ical in ensi y is di ec ly p opo ional o
he change o phase shi in ibe . F om Eq. (12) i is
e iden ha o gi en a angemen we measu ed by he
pho ode ec o di ec ly he alue o S okes elemen S2.
Since he a ia ions o phase shi in ibe and de el-
opmen o he pola iza ion s a e o p opaga ing op ical
adia ion h ough he ibe , hese a ia ions a e p o-
po ional o he S2and S3acco ding o Eq. (10). To
e alua e hese a ia ions we need know only one mea-
su ed S okes elemen S0
2o S0
3. I S0
2is known, S0
3can
be calcula ed. The measu ed S okes elemen S0
2is de-
e mined om Eq. (12) as:
S0
2=1
2(1 + sinφ) = sinφ
2+ cosφ
22
.(13)
As we measu e op ical in ensi y Io S okes elemen
S0
2and no a phase shi , we de e mine φ om Eq. (13)
as:
φ= a csin(2S0
2−1).(14)
Such analysis deals wi h he desc ip ion o senso
om he poin o iew o he ou e op ical in ensi y
I. In o de o desc ibe in e nal phenomenon in mo e
de ail heo e ical analysis ocusing on he change o he
bea leng h depending upon he empe a u e a ia ion
exci ed by an ex e nal subjec was conduc ed.
3. Phase Shi Va ia ion
Depending on Tempe a u e
When s udying PM ibe empe a u e dependency, i
can be p esumed ha he ou pu pola iza ion s a e
a ia ion is dependen on he e ac i e indices change
o as and slow pola iza ion axes, i.e. he e ac i e
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indices change in oked by a empe a u e change is p o-
po ional o he bea leng h LB a ia ion. This is he
leng h whe e 2πphase shi is in oduced be ween he
wo pola iza ion axes. The a ia ion o bea leng h
depending upon empe a u e can be desc ibed by he
ollowing me hod. The bea leng h can be exp essed
as: [11]
LB=λ
∆ne
,(15)
whe e λis he wa eleng h and ∆neis he di e en ial
index. The di e en ial index is de ined as:
∆ne= ∆ns−∆n ,(16)
whe e ∆nsand ∆n a e di e ences be ween e ac i e
indices o pa icula axes ns,n and he cladding e-
ac i e index nc:
∆ns=ns−nc,
∆n =n −nc.(17)
The dependency o bea leng h a ia ion LBon ∆ne
can be w i en as:
dLB
d∆ne
=−λ
∆n2
e
=−LB
1
∆ne
.(18)
Unde he condi ion ha phase shi a ia ion δis
linea ly dependen on he bea leng h a ia ion LB, i
can be exp essed as:
−dδ
2π=dLB
LB
,(19)
whe e he sign – (minus) indica es he s a e o which
he bea leng h LBdec eases and he phase shi a i-
a ion δinc eases.
By in eg a ion o equa ion Eq. (19) he ollowing e-
la ion is ob ained:
δ=−2πZdLB
LB
=−2π(lnLB+C).(20)
Fo he ambien empe a u e he bea leng h is LB0
and he phase shi a ia ion δ= 0. Fo hese condi-
ions he ollowing o mula is alid:
C=−lnLB0.(21)
By subs i u ing he cons an CEq. (21) in o
Eq. (20), he phase shi a ia ion shall be:
δ=−2πln LB
LB0
.(22)
By subs i u ing Eq. (15) in o Eq. (22), he bea
leng h depending on a di e en ial index ∆ne, phase
shi a ia ion can be ob ained:
δ= 2πln ∆ne
∆ne0
,(23)
whe e ∆ne0is co esponding o LB0. Unde he con-
di ion ha ∆neis linea ly changing wi h empe a u e
ϑ, he ollowing o mula applies:
∆ne(ϑ−ϑ0) = K(ϑ−ϑ0)+∆ne0,(24)
whe e Kis a p opo ion cons an , ϑis he exci a ion
sou ce empe a u e and ϑ0is he ambien empe a u e.
The phase shi a ia ion dependence on empe a u e
is hen exp essed by subs i u ing Eq. (24) in o Eq. (23):
δ(ϑ−ϑ0)=2πln K(ϑ−ϑ0)
∆ne0
+ 1.(25)
The phase shi a ia ion dependence on empe a-
u e exp essed in Eq. (25) is alid on condi ion ha
he di e ence o e ac i e indices o as and slow axes
is p opo ional o he empe a u e. The esul an PM
ibe esponse is dependen on he numbe o exposed
bea leng hs he hea sou ce is a ec ing. The esponse
is di e en due o he cons an sou ce leng h and di -
e en bea leng hs o pa icula PM ibe s. The e o e
i is sui able o conside PM ibe esponses ela ed
only o one bea leng h. The o al phase shi a ia-
ion δdependence on he o al numbe o exposed bea
leng hs and he phase shi a ia ion δLB dependence
on one bea leng h is exp essed by he ollowing o -
mula, whe e Nis he numbe o exposed bea leng hs
LBe ec ed by he hea sou ce:
N=l
LB
,(26)
whe e lis he exposed leng h o PM ibe . As he
hea sou ce e ec a he ends is no de ined exac ly he
numbe Ncan be ounded o an in ege numbe . The
phase shi a ia ion o one bea leng h δLB is exp essed
as:
δLB =δ
N=δLB
l.(27)
Fo a di e en ial index he ollowing o mula is alid:
∆ne=λ
LB
.(28)
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Tab. 1: Fea u es o PM ibe s.
Type o OF Wa eleng h Bea leng h ∆neFac o LB/l
[nm] LB[mm] [×10−3] [×10−3]
PM630-HP 633 2 0.316 7.2
PM1300-HP 1310 4 0.327 14.5
PM1550-HP 1550 5 0.31 18
Tab. 2: Phase shi a ia ion pe one bea leng h o ibe PM630-HP.
Phase shi a ia ion pe one bea leng h
Tempe a u e sou ce dis ance om PMF
5 [cm] 8 [cm] 11 [cm]
Temp.
50 ◦C 13.00 12.00 8.90
π×10−3[ ad]
45 ◦C 10.90 8.20 7.10
40 ◦C 7.70 6.80 5.30
35 ◦C 5.70 4.70 2.90
Fac o s LB/l and di e en ial e ac i e index alues
∆neo pa icula PM ibe s a e p esen ed in Tab. 1. In
he case he e is m mumbe o exposed leng hs o PMF
he alue o he ac o shall be LB/ml. The di e en-
ial indices ∆neo s udied PM ibe s a e p ac ically
he same and ha he di e ence o e ac i e indices
be ween as and slow axes and mechanism o bi e in-
gence gene a ion is e y simila o all he selec ed PM
ibe s. This conclusion is suppo ed by he p oduc ion
echnology o iden ical p oduce du ing indus ial p o-
cess o PANDA s uc u es o pa icula PM ibe s. The
empe a u e esponse ela ed o he one bea leng h
should be li e ally he same.
A coe icien o de e mining sensi i i y pe bea
leng h o leng h l= 27.5cm is p esen ed in Tab. 1.
The leng h lis co esponding o he leng h o he ap-
plied hea sou ce.
4. Expe imen al Resul s
The aim o ou expe imen al es s is o de e mine PM
ibe PANDA ype esponse du ing i s he mal ield dis-
u bance when an ex e nal he mal sou ce wi h di e -
en ini ial empe a u es was applied. The empe a u e
was changed om 50 ◦C o 35 ◦C in 5 ◦C s eps. Mea-
su emen s we e aken o wo di e en exposed ibe
leng hs. The ibe esponse was in es iga ed o h ee
di e en dis ances (5 cm, 8 cm and 11 cm) be ween
he he mal sou ce and he op ical ibe . Dis u bance
o he he mal PM ibe ield was done using a plas-
ic basin wi h a cons an amoun o wa e hea ed o
he desi ed empe a u e. I was placed on a gap be-
ween 2 polys y ene boa ds Fig. 1 ha co e he unex-
posed pa o he PMF.
The abo e layou in he senso block enables he ex-
posi ion o he equi ed leng h o in es iga ed ibe and
Fig. 1: Tes se up o measu ing wo exposed leng hs [9].
also enables o a ange he equi ed dis ance o ambien
he mal ield om he ibe . In his expe imen , a ibe
esponse o 1 and 3 exposed leng hs we e es ed be-
ween co k cylinde s. One exposed leng h was 27.5 cm.
The sou ce o op ical adia ion used o λ= 633 nm
was He-Ne lase , o λ= 1310 nm and 1550 nm lase
diodes ML 725 B8F and ML 925 B45F, espec i ely,
we e used.
The bea leng h ca alogue alue o ibe PM630-HP
is LB≤2mm, o PM1300-HP is LB≤4mm and
o PM1550-HP is LB≤5mm. Op ical powe o
λ= 1310 nm and 1550 nm was measu ed in in e als
o 0.5 s using a GENTEC-EO P-LINK powe me e
wi h a PH78-Ge pho odiode. Fo λ= 633 nm, an
analog powe me e in combina ion wi h a HP 34401A
digi al mul ime e was used con olled by MATLAB.
The in e al o aking hese eadings was 0.64 s.
Figu e 2 shows an example o measu ed pola iza ion
s a e in he abo e desc ibed gi en con igu a ion.
Fo easie illus a ion and compu e modeling o
de elopmen o he ou pu pola iza ion s a e, he
Poinca e sphe e [12], [13] was c ea ed in he MAT-
LAB en i onmen . The pola iza ion s a e in Fig. 2
o 1550 nm is depic ed on Poinca é sphe e in Fig. 3.
The measu ed esul s we e p ocessed in wo g aphs
e sions o phase shi , as a dependency on empe a u e
o di e en dis ances be ween he he mal sou ce and
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Fig. 2: Example o ou pu op ical powe o λ= 1310 nm,
1310 nm and 1550 nm, 3 exposed leng hs o ibe , ini-
ial empe a u e 50 ◦C and 5 cm dis ance be ween he
ex e nal he mal sou ce and he PM ibe .
he ibe and as a dependency on he dis ance o he
selec ed empe a u es. The p esen ed app oxima ions
come om eadings a empe a u es o 50 ◦, 45 ◦, 40 ◦
and 35 ◦and a dis ances o 5 cm, 8 cm and 11 cm.
Examples o hese dis ances o one exposed leng h a e
shown in Fig. 4, Fig. 5, Fig. 8, Fig. 9, Fig. 12 and
Fig. 13, esul s o h ee exposed leng hs a e in Fig. 6,
Fig. 7, Fig. 10, Fig. 11, Fig. 14 and Fig. 15.
Fig. 4 and Fig. 6 show ha dependencies o phase
shi a ia ion on he empe a u e a e app oxima ely
linea . Simila ly wi h inc easing exposed leng h he
phase shi a ia ion inc eases oo, bu slowly. The e
was only one anomaly p esen ed a he dis ance o
5 cm, whe e a big alue o phase shi a ia ion was
caused by he he mal sou ce a ec ing also he neigh-
bo ing leng hs o he ibe ha we e no supposed o
be exposed.
Examples o he phase shi a ia ion dependence
on he dis ance o selec ed empe a u es a e shown in
Fig. 5 and Fig. 7. Nonlinea i y o he dependency o
one exposed leng h alida es he ac ha o sho e
dis ances and g ea e empe a u e emission o he mal
sou ce he e a e undesi ed in e e ences, e ec ing o he
Fig. 3: Pola iza ion s a e eadings o he ou pu op ical adia-
ion co esponding o he Fig. 2 a 1550 nm.
Fig. 4: Phase shi a ia ion dependency on empe a u e o
one exposed leng h o winding o PM630-HP.
Fig. 5: Phase shi a ia ion dependency on he dis ance o
he mal sou ce om PM ibe o one exposed leng h
o winding o PM630-HP.
han he equi ed exposed leng h. This hea e ec
is subs an ially smalle in he case o h ee exposed
leng hs, as he undesi ed co e age o e ec ed leng hs is
smalle . The p esen ed examples a e a pa o a la ge
se o measu emen s o sensi i i y es s depending on
he ibe con igu a ion and he ambien empe a u e.
One o he aims o his s udy is o compa e he mal
ield dis u bance o h ee PM ibe s wo king a n di e -
en wa eleng hs o 633 nm, 1310 nm and 1550 nm. As
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Fig. 6: Phase shi a ia ion dependence on empe a u e o
h ee exposed leng hs o winding o PM630-HP.
Fig. 7: Phase shi a ia ion dependence on dis ance be ween
he mal sou ce and PM ibe o h ee exposed leng hs
o winding o PM630-HP.
Fig. 8: Phase shi a ia ion dependence on empe a u e o one
exposed leng h o winding o PM1300-HP.
Fig. 9: Phase shi a ia ion dependence on dis ance be ween
he mal sou ce and PM ibe o one exposed leng h o
winding o PM1300-HP.
he phase shi a ia ion δis dependen on he numbe
o bea leng hs, he measu ed esponses we e ecalcu-
la ed acco ding o Eq. (27). Ob ained esul s o pa -
Fig. 10: Phase shi a ia ion dependence on empe a u e o
h ee exposed leng hs o winding o PM1300-HP.
Fig. 11: Phase shi a ia ion dependence on dis ance be ween
he mal sou ce and PM ibe o h ee exposed leng hs
o winding o PM1300-HP.
Fig. 12: Phase shi a ia ion dependence on empe a u e o
one exposed leng h o winding o PM1550-HP.
Fig. 13: Phase shi a ia ion dependence on dis ance be ween
he mal sou ce and PM ibe o one exposed leng h o
winding o PM1550-HP.
icula PM ibe s a e p esen ed in Tab. 2, Tab. 3 and
Tab. 4.
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Tab. 3: Phase shi a ia ion pe one bea leng h o ibe PM1330-HP.
Phase shi a ia ion pe one bea leng h
Tempe a u e sou ce dis ance om PMF
5 [cm] 8 [cm] 11 [cm]
Temp.
50 ◦C 4.70 3.85 3.18
π×10−3[ ad]
45 ◦C 3.71 2.72 2.05
40 ◦C 2.66 2.12 1.82
35 ◦C 1.89 1.56 1.44
Tab. 4: Phase shi a ia ion pe one bea leng h o ibe PM1550-HP.
Phase shi a ia ion pe one bea leng h
Tempe a u e sou ce dis ance om PMF
5 [cm] 8 [cm] 11 [cm]
Temp.
50 ◦C 2.85 1.14 0.80
π×10−3[ ad]
45 ◦C 2.00 0.95 0.67
40 ◦C 1.43 0.83 0.57
35 ◦C 0.58 0.48 0.27
Fig. 14: Phase shi a ia ion dependence on empe a u e o
h ee exposed leng hs o winding o PM1550-HP.
Fig. 15: Phase shi a ia ion dependence on dis ance be ween
he mal sou ce and PM ibe o h ee exposed leng hs
o winding o PM1550-HP.
All measu emen s show ela i ely high ins abili y
and sensi i i y o o he su ounding e ec s such as
andom empe a u e changes, mechanical ib a ions
e c. The e o e his applica ion is sui able as a sen-
so o he mal ield dis u bance, bu no as a p ecision
empe a u e senso . High sensi i i y o empe a u e
changes could be combined wi h sui able ibe con ig-
u a ion o ge he sensi i i y o mechanical ib a ions,
Such senso applica ions could be used o e i o y
moni o ing, o p e en undesi ed objec s app oaching,
e c.
5. Conclusion
The p esen ed esul s comple e he es s om a p e i-
ous s udy o λ= 633 nm. By compa ing hese esul s,
he expec ed conclusion can be s a ed, ha he e is a
highe sensi i i y o λ= 633 nm, mainly due o he
sho bea leng h and high cohe ency o he He-Ne lase
sou ce. To each compa able sensi i i y a 1550 nm a
longe segmen o he exposed ibe should be used. As
ad an age o LD o 1550 nm is he compac se up o
he sou ce- ibe -pola ize -de ec o .
The nex s udy should ocus on a de ailed analysis
o he e ec o sou ce cohe ency on he ibe beha io
in espec o a phase shi a ia ion du ing he mal
ield dis u bance. Gene ally, also analysis o phase shi
a ia ion in ime du ing all he ans o ma ions s ages
could be e y in e es ing, i s he ini ial abso p ion
o he he mal adia ion, hen successi e empe a u e
s abilizing and hen ansi ion in o a new s able s a e.
Based on his, a compac solu ions could be buil o be
u ilized in o he p ac ical applica ions.
Acknowledgmen
This wo k has been suppo ed by P ojec o he de el-
opmen o K217 Depa men , B no Uni e si y o De-
ense – Mode n elec ical elemen s and sys ems.
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Re e ences
[1] PERLICKI, K. Iden i ica ion o Pola iza ion con-
igu a ion based on o sion and Cu a u e Calcu-
la ion. WSEAS T ansac ions o Communica ions.
2006, ol. 5, iss. 4, pp. 631–633. ISSN 1109-2742.
[2] VLCEK, C. S udy o ex e nal e ec s on he po-
la iza ion p ope ies o selec ed ibe segmen s.
WSEAS T ansac ions on Communica ions. 2006,
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MIGNANI. Op ical senso s and mic osys ems,
new concep s, ma e ials, echnologies. New Yo k:
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0306463808.
[4] FRADEN, Jacob. Handbook o mode n senso s:
physics, designs, and applica ions. New Yo k:
Sp inge , 2010. ISBN 978-1-4419-6465-6.
[5] HOTATE, K. and S. O. S. LENG. T ans e sal
o ce senso using pola iza ion-main aining ibe
independen o di ec ion o applied o ce: p oposal
and expe imen . In: 15 h Op ical Fibe Senso s
Con e ence Technical Diges . OFS 2002. Po land:
IEEE, 2002, pp. 363–366. ISBN 0-7803-7289-1.
DOI: 10.1109/OFS.2002.1000586.
[6] ZHANG, F. and J. W. Y. LIT. Tempe a-
u e sensi i i y measu emen s o high-bi e ingen
pola iza ion-main aining ibe s. Applied Op ics.
1993, ol. 32, iss. 13, pp. 2213–2218. ISSN 1559-
128X.
[7] DVORAK, F., J. MASCHKE and C. VLCEK.
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4 h In e na ional Con e ence on Ci cui s, Sys ems
and Signal (CSS’10). Co u: Wo ld Scien i ic and
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[8] DVORAK, F., J. MASCHKE and C. VLCEK.
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empe a u e ield dis u bance. Radioenginee ing.
2009, ol. 18, no. 4, pp. 639–643. ISSN 1210-2512.
[9] DVORAK, F., J. MASCHKE and C. VLCEK.
Response analysis o he mal ield dis u bance
senso . In: Elec o-Op ical and In a ed Sys-
ems: Technology and Applica ions VIII. P ague:
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DOI: 10.1117/12.897707.
[10] DVORAK, F., J. MASCHKE and C. VLCEK.
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Abou Au ho s
Filip DVORAK was bo n in 1977. He ecei ed
his M.Sc. deg ee om he B no Mili a y Academy
in 2004 and Ph.D. deg ee in 2011. He is cu en ly
lec u e wi h he Depa men o Rada Technology,
B no Uni e si y o De ense. His wo k is ocused on he
modeling o ibe s and op ical componen s by means
o ma ix me hods in he MATLAB en i onmen and
analysis o ibe senso s.
Jan MASCHKE was bo n in 1942. He e-
cei ed his M.Sc. deg ee in 1965 and Ph.D. deg ee in
1978. He was a eache a he Technical school a
Lip o ský Mikulas and a he Mili a y Academy since
1968, and associa e p o esso o he Depa men o
elec ical enginee ing since 1985. He e i ed in 2005.
His esea ch wo k ocused on he p oblems o ibe
op ics and ibe senso s.
Ces mi VLCEK was bo n in 1946. He ecei ed his
M.Sc. deg ee in 1969 and Ph.D. deg ee in 1980. He
was a eache a he Mili a y Academy since 1969,
associa e p o esso since 1985, head o he Elec ical
Enginee ing and Elec onics Depa men since 1997
and p o esso since 2000. His esea ch wo k du ing
he las yea s was aimed a p oblems o op oelec onic
signals and sys ems, single mode ibe componen s
modeling, a mosphe ic op ical communica ion sys ems
and analysis o senso s o mili a y applica ions.
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