optic coupler
TRANSCRIPT
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4
IntroductiontoFibre-
Couplers
Theaimofthischapteristoprovideanoverviewoffibrecouplertechnology.The
principles of how fibre couplers exchange power between the two ports are
presented and different methods of fabrication are compared. The information
providedinthischapterintroducestheworkonthecharacterisationoffibrecouplers
(Chapter 9) and is relevant to the optimisation of all-fibre add-dropmultiplexers
basedontheinscriptionofgratingsinthecouplerwaist(Chapter8).
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4-IntroductiontoFibre-Couplers 33
4.1 CouplerTechnology
Fibre- and integrated-optic couplers are extremely important components in a
number of photonics applications. They are generally four-port devices and their
operationreliesonthedistributedcouplingbetweentwoindividualwaveguidesin
closeproximity,whichresultsinagradualpowertransferbetweenmodessupported
bythetwowaveguides.Thispowertransferandcross-couplingatthecoupleroutput
ports can be viewed also, as a result of the beating between eigenmodes of the
compositetwo-waveguidestructurealongthelengthofthecompositecouplerwaist
[56].Themost commonuse of fibre- and integrated-optic couplers isasapower
splitter,thisis,thefibre-opticequivalentofafreespaceopticbeam-splitter.They
canbeusedtosplittheopticalpowerofanopticalchannel(ofcertainwavelength)
betweentheoutputports[57].Anotherapplicationistocombineorsplitthepower
ofdifferentchannels,correspondingtodifferentwavelengths(wavelength-division-
multiplexing (WDM) splitters/combiners) [58]. Lately fibre- and integrated-optic
couplers,havebeencombinedwithreflectiveBragggratingswrittenin theirwaist,
toprovideselectiveaddinganddroppingofdifferentchannelsinWDMsystems[41,
42].
4.2 TheoreticalCouplerDescription
Afibrecouplerisafour-portdeviceconsistingoftwofibresthathavebeenfused
together, etched, or polished over a small interaction region. The mechanism
through which light is exchanged between the two fibres is dependent upon the
fabricationmethod.Whenthefibresareetchedorpolishedandpositionedinclose
proximity, the otherwise insensitive and well confined core modes interact by
exchangingpowerbetweeneachfibrecoreduetotheoverlapofthemodesinthe
commoncladding.Thestrengthofthecouplingbetweenthetwomodesisdescribed
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4-IntroductiontoFibre-Couplers 34
by anoverlap integralof the fields associatedwith each ofthe individual guides.
Fusedcouplersareobtainedbyfusingtogetherandstretchingtwoparalleluncoated
fibres.As the fibres are stretched the core sizesdecrease until themodes (at the
wavelength of interest) are no longer guided by the core but by the composite
cladding-airstructure.Ifthetaperisadiabaticonlythetwolowest-ordereigenmodes
of this structure will be excited and the power exchange is due to the beating
betweenthesetwoeigenmodes.Intheworkpresentedhereonlyfusedfibrecouplers
arediscussed.
Figure 4.1 - Four-port coupler schematic showing the coupling region (LC), which is
comprisedoftwotaperregions(LT1,LT2)andthecouplerwaist(LW).
Consider the 2x2 coupler shown schematically inFigure 4.1. When light islaunchedintoport1,thenormalisedfieldamplitudesoftheeven(Ae)andodd(Ao)
eigenmodesatthecouplerinput(z=0)canbeapproximatedby[56]:
2
)0()0()0(;
2
)0()0()0( 2121
AAA
AAA oe
=
+= (4.1)
whereA1(0)andA2(0)arethenormalisedamplitudesofthefieldslaunchedintothe
twoinputports1and2,respectively.Forsingleportexcitation,A1(0)=1andA2(0)=0
and,throughEquation(4.1),Ae(0)=Ao(0)=1/ 2 .Therefore,lightlaunchedintoone
oftheinputportsofa2x2couplerexcitesequallythetwolowest-order(evenand
odd) eigenmodes along the coupling region. The two eigenmodes propagate
adiabaticallyalong theentirecouplingregionwithpropagationconstantse(z)and
o(z)respectively.Thebeatingbetweenthesetwomodesthenprovidesthecoupling
ofpoweralongthecoupler.
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4-IntroductiontoFibre-Couplers 35
Even
+ + +
Odd
eo
0 3/2 2
P1
P1
P2
P2
/2
Figure4.2-Schematicofevenandoddeigenmodebeatingandtotalpowerevolutionalong
a2x2full-cycle(eo=2)coupler.
Thepropagatingtotalelectricfieldatanypointalongthecouplerisdescribedby:
+
=+=
z
o
z
e di
o
di
eoet ezAezAzEzEzE00
)()(
)()()()()(
(4.2)
During adiabatic propagation, the even and odd eigenmodes retain their
amplitude(Ae(z)=Ae(0)andAo(z)=Ao(0))andchangeonlytheirrelativephase.This
resultsinspatialbeatingalongthecouplerwaistandpowerredistributionbetween
the two individual waveguides comprising the optical coupler. The peak field
amplitudes for each individual waveguide, along the coupling region, can be
approximatedby[56]:
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4-IntroductiontoFibre-Couplers 36
[ ]
[ ]
=
=
=
+=
+
+
z
oe
z
oe
di
oe
di
oe
ezizEzE
zE
ezzEzE
zE
0
0
)()(2
1
2
)()(2
1
1
)(2
1sin
2
)()()(
)(2
1cos
2
)()()(
(4.3)
where [ ] ===z
oe
z
eoeo ddzz00
)()()()()( is the relative
accumulatedphasedifferencebetweentheevenandoddeigenmodes. eandoare
the propagation constants of the even and odd eigenmodes, respectively. The
correspondingnormalisedpeakpowercarriedbytheindividualwaveguidesisgiven
byP1(2)=|E1(2)|2,namely
=
=
)(2
1sin)(
)(2
1cos)(
2
2
2
1
zzP
zzP
(4.4)
Atthepointsalongthecoupler,whereiszerooramultipleof2,thetotal
powerisconcentratedpredominantlyaroundwaveguide#1(P1=1andP2=0).Atthe
pointsalongthecoupler,whereismultipleof,ontheotherhand,thetotalpower
isconcentratedpredominantlyaroundwaveguide#2(P1=0andP2=1).Finally,atthe
pointswhereismultipleof/2, thetotalpowerisequallysplit betweenthe two
waveguides (P1=P2).The even/odd eigenmode beating and totalpower evolution
alongafull-cyclecoupler(=2)isshownschematicallyinFigure4.2.Thecoupling
coefficient k(z) describing thestrength of theinteraction betweentheeigenmodes
andisgivenby:
2
)()()(
zzzk oe
= (4.5)
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4-IntroductiontoFibre-Couplers 37
The coupler beat length LB isdefinedastheminimum interaction length the two
eigenmodes,initiallyinphase,musttravelinordertointerfereconstructivelyi.e.,to
beagaininphase:
oe
BL
=
2 (4.6)
4.3 FabricationofFusedFibreCouplers
4.3.1 Flame-BrushTechnique
The flame-brush technique for the fabrication of fibre couplers is based on the
scanningofapoint-likeflamewhilepullingthefibres[59].Twofibresareclamped
parallel to each other and the flame is scanned over a given interaction region.
Figure4.3showstheexperimentalconfigurationofsucharigforfabricatingfibre
tapersorcouplers.
Figure4.3Flamebrushtechniqueexperimentalsetup
The couplers and tapers fabricated during this work where made using a
configurationsimilartothatofFigure4.3.Thefibresarepulledbytwocomputer
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4-IntroductiontoFibre-Couplers 38
controlledAerotechstages.TheflameisscannedusingathirdAerotechstage.The
flame gas consists of a mixture of isobutene and oxygen. Both cleaning and
alignmentofthefibresiscrucialforfabricatinguniformtapersorcouplerswithlow
insertion losses. Air draughts or gas pressure variations can severely affect the
quality of the devices, due tovariations in the flame temperature and consequent
localnon-uniformitiesalongthetapers/couplers.Duringthepullingofthefibresthe
outputpowerismonitoredandtheprocesshaltedatthedesiredfibreradius(inthe
case of taper fabrication) or extinction ratio (in the case of coupler fabrication).
Figure4.4showsthepoweratboththeoutputports(Port3andPort4)duringthe
pulling process for a half-cycle coupler fabricated using this technique. Couplerelongation of46mm represents the point atwhich coupling of light between the
waveguides starts to occur, corresponding to the monomode regime [60]. As
illustrated,thepoweratport3dropsto0Vwhilethepower inport4 increases to
around 7V. The pulling process was halted when Port 3 reached its minimum,
producingthiswayahalf-cyclecoupler.
0
2
4
6
8
46 51 56 61 66 71CouplerElongation(mm)
Coupledpower(a.u.)
Port4
Port3
50%
splitter
100%coupler
Figure4.4Powerevolution ofa coupler fabricatedusing the flame-brushtechnique at
=1.55mduringpullingprocess.
The spectral characteristics of the fabricated couplers are determined by
launchingawhitelightsourceintooneoftheportsofthecouplerwhilstmeasuring
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4-IntroductiontoFibre-Couplers 40
4.3.2CO2Laser
RecentlyDimmicket.al.[61]reportedthedevelopmentofafused-fibrecouplerand
fibre taper rig that uses a scanning, focused,CO2 laser beam as the heat source,
insteadofthegasburner.Thesetupissimilartothatoftheflame-brushtechnique,
withtwopullingstagesthatstretchthefibreatadesiredspeedwhilsttheCO 2laser
radiationisscannedacrossthefibresbyarotatingmirror.Thebeamisfocusedusing
aZnSelenswitha30mmfocallengthgivingaspotsizeof820m.Anexperimental
setupusedtofabricatefibre-couplersusingaCO 2laserisillustratedinFigure4.6.
Figure 4.6 Experimental setup of the fabrication of fibre tapers/couplers using the
radiationofafocusedCO2laser.
Thissetupprovidesabettercontroloftheshapeofthetaper/couplertaperedregion
duetothesmallerhotspotproducedbythefocusedCO2laserwhencomparedtothe
flame-brush technique. It also allows greater control in producing non-uniform
tapersorcouplersduetothepossibilityofrapidpositioningofthelaserspotandfast
switchingofthelaserbeampowerwithashutter.
However,themaindisadvantageofthistechniqueisthatthetemperatureofthe
heatsourcevariesduringthepullingofthefibre.Heatingofopticalfibresusinga
lasersourcedependsonmanyparameterssuchas;theabsorptioncoefficient(which
varies with temperature and wavelength), the laser power, the fibre-cooling rate
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4-IntroductiontoFibre-Couplers 41
(which dependson the fibre radius and temperature), and the laser spot size.To
overcome this problem the laserpowerhas to be adjusted constantly in order to
maintainaconstanttemperatureduringthefibrepulling.Incontrast,whenheating
withaflameburner,thepresenceornotofthefibrehaslittleornoeffectonthe
temperatureoftheheatsourceduetothemechanismofheatgeneration.
4.3.3HeatingOven
Anothertechniqueusedinindustryforfabricatingfibrecouplersandtapersrelieson
heatingthewholeuniformsectionusinganovenorresistiveelectricalheaterwhilepullingthefibres.Duetothelongheatzonethistechniquehasnocontroloverthe
shape of the tapered region although the sensitivity to environmental factors is
reduced. The quality of the tapers/couplers is essentially dependent on the oven
design,andthetemperatureuniformityalongthelengthofwaistregion.
4.3.4 ShapeoftheTaperedRegion
Accuratecontrolofthetaperedregionshapeofbothfibrecouplersandfibretapers
canbecrucialfortheperformanceofdevicesusingthesecomponents.Forexample,
inchapter5anAOtunablefilterisdiscussed,whichreliesontheaccuratecontrolof
thefibre-tapershapeandlength.Birkset al.[62],usingtheflame-brushtechnique,
producedalonguniformtaperwaist(90mm)withshorttransitionregions(35mm)
and very small waist diameters (~2m), for generating a supercontinuum light
spectrum. Also in fibre couplers, the accurate control of the tapered region is
extremelyimportantforthefabricationofnon-uniformcouplersthatcanbeusedas
an add-dropmultiplexer when a grating is inscribed in thewaist (chapter 8). In
general, the transition region for both fibre couplers and tapers should obey the
adiabaticcriterion[63],inordertominimiseinsertionlosses.
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4-IntroductiontoFibre-Couplers 42
The shape of fibre tapers/couplers produced by using scanning point-like
heatingsourceshasbeenextensivelystudiedbyBirkselal.[64].Assumingthatthe
localisedheatingofthefibremakestheglasssoftenoughtobestretchedwhilstnot
being so soft that it falls under its own weight, the shape of the tapers can be
calculated without having to recur to fluid mechanics beyond the principle of
conservation of mass. A tapered fibre, at any given time (or elongation) of the
pullingprocess,canbecharacterisedby theparametersshowninfigure4.7a).rois
theinitialfibreradiuscorrespondingtoatransitionlength,z0,andr(z)theradiusof
thetapertransitionatagivenpositionz.Thelengthoftheuniformtaperwaistl w(t)
isequaltothelengthofthehot-zoneL(t)atthattime.Thesizeofthehot-zoneL(t)mayvarywithtimebutissubjecttotheconstraintsL0anddL/dx1.Thissecond
constraint ensures that the hot-zonedoes not overtake the pulled transitions. The
time change is proportional to the extension or elongation of the taper i.e., the
pullingspeed isconstant.Figure4.7b)showstheequivalentuntaperedfibrewhere
theinitialhotspotlength(att=0)isL0andxisthetotalpullingextensionatagiven
time.Comparingthetaperedwiththeuntaperedfibreitmaybeobservedthatpoints
AandB areelongatedbyx. In theparticularcasewherethehot-zone isconstant
duringthepulling,thewaistlengthisconstantlw(x)=L0andthetapertransitionis
equaltohalfoftheextensionz=x/2.
Figure4.7-Schematic representationof afibretaperstructure.a)Ata timet during the
pulling.b)Initialfibrebeforepulling.
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4-IntroductiontoFibre-Couplers 43
From the conservation ofmass principle, the following expression can easily be
derived:
L
r
dx
dr ww
2= (4.7)
Secondly, the extension x can be related to the taper transition length z by
comparingtheinitiallengthABatt=0,withthetotaltaperlengthABatanygiven
time:
02 LxLz +=+ (4.8)
The particular case where the hot-zone remains constant during the fibre
extensionhasbeenanalysedby[64-66].InthiscaseL(z)=L0andz=x/2.Integrating
(4.7)givesthewaistshapeforatotalfibreextensionx.
( )00 20
)'(
'2/1
0)(LxxL
dx
wererxr
x
=
= (4.9)
Thetaperprofileis calculatedbysubstituting x=2z in(4.9), resultinginthewell-
knownexponentialdecayprofile.Allthetaperandcouplerdevicesdiscussedinthis
thesiswerefabricatedusingaconstanthot-zone,thusexpression(4.9)issufficientto
describe the profiles of the tapered regions. Further examples of interest are
discussedin[64]whereequation(4.7)isdemonstratedaswell.
Inordertominimizelossesbetweenthefundamentalandthenearestcladding
modes,thetaperangle|dr/dz|hastoobeytheadiabaticcriterion[63].
( ) ( )( )
2
21 zzr
dz
dr (4.10)
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4-IntroductiontoFibre-Couplers 44
Where 1(z) and 2(z) are respectively the local propagation constants of the
fundamentalmode and the closest claddingmodes, and r is the localcore radius.
Experimentally it was observed that intrinsic loss of the fabricated couplers and
tapers using the flame-brush technique were very low and justify the use of the
aboveparametersdescribingsmoothadiabatictransitions.
4.3.5 Effect of the tapered transition on the coupler power
evolution
Thelong transitionregionsincouplersfabricatedusing theflame-brush technique
withconstanthotzone,playaroleinthewaythepowerevolvesalongthecoupler.
For a full-cycle coupler with a constant hot zone of L0=30mm fabricated with
standardtelecommunicationssinglemodefibre, the evolutionof the powerat the
outputportsis illustratedinFigure4.8.Light fromaDFB-LDatawavelengthof
1.55mislaunchedinport1andmonitoredatport3andport4duringthepulling
process.Thepowerevolutionisonlyplottedfromanextensionofx=47mm(from
x=0tox=47therewasnocoupling)inordertoemphasisethecouplingprocess.
0
1
2
3
4
5
47 52 57 62 67 72 77
CouplerElongation(mm)
Measuredoutput(V)
Port4
Port3
50%
splitter
coupler2coupler
x1
x
x3x2x0 xm xN
........
........ ........
Figure4.8Measuredpowerevolutionofa30mmlongfull-cyclecouplerata=1.55m
duringthepullingprocess.
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4-IntroductiontoFibre-Couplers 45
Light starts tobecoupled between the two fibres for a coupler extension around
x=51mm,thehalf-cyclepointisreachedataroundx=73.5mmwhenallthelightisin
Port4andthepullingprocesswashaltedafteronefull-cycle,i.e.,whenalllightwas
coupledbacktoPort3.UsingtheinformationplottedinFigure4.8andthefactthat
dL/dx=0 (constant hot-zone pulling), an iterative method to extract the coupling
strengthprofileduetothetaperedtransitionregioncanbedeveloped.Afteragiven
extension,x,wherecouplingstarts tooccur,all the interactionisdueto thewaist
section with length L0. The coupling coefficient, k(x), can be evaluated for that
extension(orequivalentlyforthatwaistradius)assumingthatthehot-zonesectionisuniform and constant during the fabricationprocess,by solving equation(4.4) in
ordertodetermine(x)=(x)L0=2k(x)L0.Nowthephasedisplacementbetweenthe
evenandoddeigenmodescorrespondingtothecoupledpowerP1(x0)atextensionx0
isgivenby:
[ ] 0011
0 )(cos)( LxPx= (4.11)
andthevalueof(x1)atthenextextensionx1=x0+xcanbecalculatediteratively
using;
[ ] 010111
1 )()(cos)( LxxLxPx = , (4.12)
finallyatthemthsection,xm=x0+mx,ityields;
[ ]
=
=1
00
01
1 )()(cos)(m
n
nmm xL
xLxPx (4.13)
Thereaderisremindedthatz=x/2andtherefore,(z)=(x)/2.Usingthisgeneral
recursive expression and the couplerpower evolution Port 3 (blue line inFigure
4.8),thecouplingstrength(solidline)wascalculatedandplottedinFigure4.9thisis
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4-IntroductiontoFibre-Couplers 46
comparedtotheidealcoupler(dashedline)withoutataperedtransitionregion.The
originofthegraphinFigure4.9correspondstoacouplerextensionofx=47mmand
thereforeatransitionlengthofz=23.5mm.Atthispositionthenormalisedcoupler
radiuscanbecalculatedusing(4.9)yieldingr(z=23.5)/r0=exp(-z/L0)0.457.
Theidealcouplerhasahighercouplingstrengthalongtheuniformwaistthan
the fabricated coupler; although the total coupler phase displacement (L)
correspondingtotheintegrationof thecouplingstrengthalongthewholelength,is
thesameinbothcouplersat=1.55m.By comparing thepowercoupling inthe
transition regions with that in the uniform region of the fabricated coupler, it is
realisedthat22.1%ofthetotalphasedisplacementalongthecouplerisduetothe
tapered transition regions and 77.9% due to the uniform waist. Therefore, when
optimising add-drop multiplexers based on full-cycle couplers with gratings
inscribedinthewaist,byplacingthembetweentheexactpointsalongthecoupler
wherethepowerisequallysplitbetweenthefibres,thecouplertransitionregionhas
to be taken into account. However, the non-destructive coupler characterisation
methodpresentedinChapter9overcomesthisproblem.
0
0.5
1
1.5
0 7.5 15 22.5 30 37.5 45 52.5 60
CouplerPosition(mm)
k(z)(x104
m-1)
Idealcoupler
Realcoupler
Figure4.9Comparisonofthecouplingstrengthsofanideal(dashedline)andfabricated
(solidline)30mmlongfull-cyclecoupler.
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4-IntroductiontoFibre-Couplers 47
The effect of the tapered transition region on the powerevolution along the
couplerlength is illustrateddirectly inFigure 4.10.Boththe output couplerports
(Port3 andPort4)areshown.Thedashedlinerefers totheidealcouplerandthe
solidlinetothefabricatedcoupler.Itisobservedthatthefabricatedcouplerislonger
and the coupling smoother corresponding to the transition regions. The coupler
positionswherethe power isequallydistributed inboth thewaveguides (50-50%
points) are shifted towards the tapered regions. Identification of these coupler
positionsiscriticalfortheoptimisationofadd-dropmultiplexersbasedongratings
inscribedinthecouplerwaistandwillbediscussedinChapter8.
The accuracyof expression (4.13), in determining the coupling strength andhencethe50-50%pointsofthecoupler,dependsontheuniformityofthehot-zone
lengthandtheadiabaticevolutionofthetaperedtransitionregionduringthepulling
process.Inordertocharacterisethecoupleranddetermineits50-50%pointsanovel
non-destructivecharacterisationtechniqueforfibrecouplerswasdevelopedandis
discussedinChapter9.
0
0.5
1
0 7.5 15 22.5 30 37.5 45 52.5 60
CouplerPosition(mm)
NormalisedPower
P1(z)
P2(z)
Figure 4.10 Power evolution along the length of an ideal uniform (dashed line) and
fabricated(solidline)30mmlongfull-cyclecoupler.
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4-IntroductiontoFibre-Couplers 48
4.3.6Couplercrosssection
When fabricating couplers using the flame-brush technique, the degree of fusion
beforepullingthefibresdefinesthecrosssectionalshapeofthecoupler.Thehigher
the degree of fusion the closer the crosssection of the fabricated coupler is toa
cylinder.Inthecaseofveryweakfusion,thecouplerhasacharacteristicdumbbell
shapeandforintermediatedegreesoffusion,thecross-sectionhasapproximatelyan
elliptical shapewith varying eccentricity [67]. The theoretical description of the
couplerintermsofthecouplereigenmodes,alsoknownassupermodes,isrelatedto
thecouplercross-section,differentapproximationsforcalculatingthesemodeshave
beenaddressedintheliterature.InBureset.al.[68]thefibreswerenotfusedandthe
coreswereneglected;[69]approximatedthecouplercrosssectionusingdifferenta
rectangular cross section, and [70, 71] gives analytical expressions for the two
lowestordermodes,LP01andLP11,fordifferentcouplercross-sections(rectangular,
elliptical,circular)alsoneglectingthefibrecores.
Furtherwork,[67,72]usedaFieldCorrectionMethodtoaccuratelycalculate
the coupler eigenmodes,while [73-75] use the rigorous surface integral equation
methoddeterminethecouplercharacteristics.
4.4 Summary
FibrecouplersareimportantcomponentsusedinWDMsystemstorouteandsplit
signals,monitorthenetwork,orcombinesignalandpumpwavelengthsforfeeding
optical amplifiers. Recently add-drop multiplexer configurations relying on the
inscriptionofBragggratingsinthecouplerwaisthavebeeninvestigated[41,42].In
order to optimise these devices accurate control of the fabrication and suitable
methods of characterisation for the couplers are required. In chapter 9 a non-
destructivemethodforcharacterisingfibre-couplersisdescribed.
In conclusion this chapter gave an introduction to coupler technologies and
describedhow light is transferredbetween the twowaveguides along the coupler
length. A review of fibre-coupler fabrication technologies, their advantages and
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4-IntroductiontoFibre-Couplers 49
drawbacksforeachwasdiscussed.Finallytheinfluenceofthefibrecouplerstapered
transitionregiononthepowerevolutionalongthecouplerlengthwasdescribed.It
willbeshown(inchapter8)thatinordertooptimiseanadd-dropmultiplexer; the
influenceofthetransitionregionhastobetakenintoaccount.