4

IntroductiontoFibre-Couplers

Theaimofthischapteristoprovideanoverviewoffibrecouplertechnology.Theprinciples of how fibre couplers exchange power between the two ports arepresented and different methods of fabrication are compared. The informationprovidedinthischapterintroducestheworkonthecharacterisationoffibrecouplers(Chapter 9) and is relevant to the optimisation of all-fibre add-drop multiplexersbasedontheinscriptionofgratingsinthecouplerwaist(Chapter8).

4-IntroductiontoFibre-Couplers 33

4.1 CouplerTechnology

Fibre- and integrated-optic couplers are extremely important components in anumber of photonics applications. They are generally four-port devices and theiroperation relieson thedistributed couplingbetween two individualwaveguides incloseproximity,whichresultsinagradualpowertransferbetweenmodessupportedbythetwowaveguides.Thispowertransferandcross-couplingatthecoupleroutputports can be viewed also, as a result of the beating between eigenmodes of thecompositetwo-waveguidestructurealongthelengthofthecompositecouplerwaist[56]. The most common use of fibre- and integrated-optic couplers is as a powersplitter, this is, the fibre-optic equivalentof a free spaceopticbeam-splitter.Theycanbeusedtosplittheopticalpowerofanopticalchannel(ofcertainwavelength)betweentheoutputports[57].Anotherapplicationistocombineorsplitthepowerofdifferentchannels,correspondingtodifferentwavelengths(wavelength-division-multiplexing (WDM) splitters/combiners) [58]. Lately fibre- and integrated-opticcouplers,havebeencombinedwithreflectiveBragggratingswrittenintheirwaist,toprovideselectiveaddinganddroppingofdifferentchannelsinWDMsystems[41,42].

4.2 TheoreticalCouplerDescription

A fibrecoupler isa four-portdeviceconsistingof two fibres thathavebeen fusedtogether, etched, or polished over a small interaction region. The mechanismthrough which light is exchanged between the two fibres is dependent upon thefabricationmethod.Whenthefibresareetchedorpolishedandpositionedincloseproximity, the otherwise insensitive and well confined core modes interact byexchangingpowerbetweeneach fibre coredue to theoverlapof themodes in thecommoncladding.Thestrengthofthecouplingbetweenthetwomodesisdescribed

4-IntroductiontoFibre-Couplers 34

by an overlap integral of the fields associated with each of the individual guides.Fusedcouplersareobtainedbyfusingtogetherandstretchingtwoparalleluncoatedfibres. As the fibres are stretched the core sizes decrease until the modes (at thewavelength of interest) are no longer guided by the core but by the compositecladding-airstructure.Ifthetaperisadiabaticonlythetwolowest-ordereigenmodesof this structure will be excited and the power exchange is due to the beatingbetweenthesetwoeigenmodes.Intheworkpresentedhereonlyfusedfibrecouplersarediscussed.

Figure 4.1 - Four-port coupler schematic showing the coupling region (LC), which iscomprisedoftwotaperregions(LT1,LT2)andthecouplerwaist(LW).

Consider the 2x2 coupler shown schematically in Figure 4.1. When light islaunchedintoport1,thenormalisedfieldamplitudesoftheeven(Ae)andodd(Ao)eigenmodesatthecouplerinput(z=0)canbeapproximatedby[56]:

2)0()0()0(;

2)0()0()0( 2121 AAAAAA oe

=

+= (4.1)

whereA1(0)andA2(0)arethenormalisedamplitudesofthefieldslaunchedintothetwoinputports1and2,respectively.Forsingleportexcitation,A1(0)=1andA2(0)=0and,throughEquation(4.1),Ae(0)=Ao(0)=1/ 2 .Therefore,lightlaunchedintooneof the inputportsofa2x2couplerexcitesequally the two lowest-order (evenandodd) eigenmodes along the coupling region. The two eigenmodes propagateadiabaticallyalong theentirecouplingregionwithpropagationconstantse(z)ando(z)respectively.Thebeatingbetweenthesetwomodesthenprovidesthecouplingofpoweralongthecoupler.

4-IntroductiontoFibre-Couplers 35

Even

+ + +

Odd

eo 0 3pi/2 2pi

P1

P1

P2

P2

pipi/2

Figure4.2-Schematicofevenandoddeigenmodebeatingandtotalpowerevolutionalong

a2x2full-cycle(eo=2pi)coupler.

Thepropagatingtotalelectricfieldatanypointalongthecouplerisdescribedby:

+

=+=

z

o

z

e di

o

di

eoet ezAezAzEzEzE 00)()(

)()()()()(

(4.2)

During adiabatic propagation, the even and odd eigenmodes retain theiramplitude(Ae(z)=Ae(0)andAo(z)=Ao(0))andchangeonlytheirrelativephase.Thisresults inspatialbeatingalong thecouplerwaistandpowerredistributionbetweenthe two individual waveguides comprising the optical coupler. The peak fieldamplitudes for each individual waveguide, along the coupling region, can beapproximatedby[56]:

4-IntroductiontoFibre-Couplers 36

[ ]

[ ]

=

=

=

+=

+

+

z

oe

z

oe

dioe

dioe

ezizEzEzE

ezzEzE

zE

0

0

)()(21

2

)()(21

1

)(21

sin2

)()()(

)(21

cos2

)()()(

(4.3)

where [ ] ===z

oe

z

eoeo ddzz00

)()()()()( is the relative

accumulatedphasedifferencebetweentheevenandoddeigenmodes.eandoarethe propagation constants of the even and odd eigenmodes, respectively. Thecorrespondingnormalisedpeakpowercarriedbytheindividualwaveguidesisgiven

byP1(2)=|E1(2)|2,namely

=

=

)(21

sin)(

)(21

cos)(

22

21

zzP

zzP

(4.4)

At thepointsalong thecoupler,where iszerooramultipleof2pi, the totalpowerisconcentratedpredominantlyaroundwaveguide#1(P1=1andP2=0).Atthepointsalongthecoupler,whereismultipleofpi,ontheotherhand,thetotalpowerisconcentratedpredominantlyaroundwaveguide#2(P1=0andP2=1).Finally,atthepointswhere ismultipleofpi/2, the totalpower isequallysplitbetween the twowaveguides (P1=P2). The even/odd eigenmode beating and total power evolutionalongafull-cyclecoupler(=2pi)isshownschematicallyinFigure4.2.Thecouplingcoefficient k(z) describing the strength of the interaction between the eigenmodesandisgivenby:

2)()()( zzzk oe = (4.5)

4-IntroductiontoFibre-Couplers 37

The coupler beat length LB is defined as the minimum interaction length the twoeigenmodes,initiallyinphase,musttravelinordertointerfereconstructivelyi.e.,tobeagaininphase:

oe

BL pi

=2

(4.6)

4.3 FabricationofFusedFibreCouplers

4.3.1 Flame-BrushTechnique

The flame-brush technique for the fabrication of fibre couplers is based on thescanningofapoint-likeflamewhilepullingthefibres[59].Twofibresareclampedparallel to each other and the flame is scanned over a given interaction region.Figure4.3shows theexperimentalconfigurationofsucha rig for fabricatingfibretapersorcouplers.

Figure4.3Flamebrushtechniqueexperimentalsetup

The couplers and tapers fabricated during this work where made using aconfiguration similar to thatofFigure4.3.The fibres arepulledby two computer

4-IntroductiontoFibre-Couplers 38

controlledAerotechstages.TheflameisscannedusingathirdAerotechstage.Theflame gas consists of a mixture of isobutene and oxygen. Both cleaning andalignmentofthefibresiscrucialforfabricatinguniformtapersorcouplerswithlowinsertion losses. Air draughts or gas pressure variations can severely affect thequality of the devices, due to variations in the flame temperature and consequentlocalnon-uniformitiesalongthetapers/couplers.Duringthepullingofthefibrestheoutputpowerismonitoredandtheprocesshaltedatthedesiredfibreradius(inthecase of taper fabrication) or extinction ratio (in the case of coupler fabrication).Figure4.4showsthepoweratboththeoutputports(Port3andPort4)duringthepulling process for a half-cycle coupler fabricated using this technique. Couplerelongation of 46mm represents the point at which coupling of light between thewaveguides starts to occur, corresponding to the monomode regime [60]. Asillustrated, thepoweratport3drops to0Vwhile thepower inport4 increases toaround 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)

Cou

ple

dpo

we

r(a.

u.)

Port4

Port3

50%splitter

100%coupler

Figure 4.4 Power evolution of a coupler fabricated using the flame-brush technique at

=1.55mduringpullingprocess.

The spectral characteristics of the fabricated couplers are determined bylaunchingawhitelightsourceintooneoftheportsofthecouplerwhilstmeasuring

4-IntroductiontoFibre-Couplers 39

theoutputportswithanOpticalSpectrumAnalyser(OSA).Figure4.5illustratesthespectral characteristics of a 20mm long full-cycle coupler fabricated using thistechnique. It is observed that the extinction ratio was better than 30dB and themeausurement was noise-limited due to insufficient input power. The pulling

process was halted so that the full-cycle resonance peak was at =1.55m. Theresonanceat=1.175mis thehalf-cycleresonancecorrespondingtoa totalphasedisplacementof(L)=pi.

Disadvantagesofthisfabricationmethodare;thepossiblecontaminationofthetapers/couplers by the combustion by-products, the variations of the burnertemperature,andtheflamesize,thatmaynotbeapproximatedtoapointlikesource.Notwithstanding, throughout thisworkverygoodquality tapersandcouplerswereobtained.Infact,thequalityofthecouplersproducedwiththerig,asillustratedinFigure4.5,providedconfidence in theuniformityof the tapersandstabilityof theflame during the fabrication process. For example, using a standardtelecommunications single mode fibre, typical insertion losses of the fabricatedtaperswereonly0.1dB.

-90

-80

-70

-60

-50

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7Wavelength(m)

Pow

er

(dBm

)

Port3

Port4

Figure4.5Spectralresponseofa20mmlongfull-cyclecouplerfabricatedusingtheflamebrushtechnique.

4-IntroductiontoFibre-Couplers 40

4.3.2 CO2Laser

RecentlyDimmicket.al.[61]reportedthedevelopmentofafused-fibrecouplerandfibre taper rig that uses a scanning, focused, CO2 laser beam as the heat source,insteadofthegasburner.Thesetupissimilartothatoftheflame-brushtechnique,withtwopullingstagesthatstretchthefibreatadesiredspeedwhilsttheCO2laserradiationisscannedacrossthefibresbyarotatingmirror.Thebeamisfocusedusing

aZnSelenswitha30mmfocallengthgivingaspotsizeof820m.Anexperimentalsetupusedtofabricatefibre-couplersusingaCO2laserisillustratedinFigure4.6.

Figure 4.6 Experimental setup of the fabrication of fibre tapers/couplers using theradiationofafocusedCO2laser.

Thissetupprovidesabettercontroloftheshapeofthetaper/couplertaperedregionduetothesmallerhotspotproducedbythefocusedCO2laserwhencomparedtotheflame-brush technique. It also allows greater control in producing non-uniformtapersorcouplersduetothepossibilityofrapidpositioningofthelaserspotandfastswitchingofthelaserbeampowerwithashutter. However,themaindisadvantageofthistechniqueisthatthetemperatureoftheheatsourcevariesduring thepullingof thefibre.Heatingofoptical fibresusingalasersourcedependsonmanyparameterssuchas;theabsorptioncoefficient(whichvaries with temperature and wavelength), the laser power, the fibre-cooling rate

4-IntroductiontoFibre-Couplers 41

(which depends on the fibre radius and temperature), and the laser spot size. Toovercome this problem the laser power has to be adjusted constantly in order tomaintainaconstant temperatureduring thefibrepulling. Incontrast,whenheatingwith a flame burner, the presence or not of the fibre has little or no effect on thetemperatureoftheheatsourceduetothemechanismofheatgeneration.

4.3.3 HeatingOven

Anothertechniqueusedinindustryforfabricatingfibrecouplersandtapersreliesonheatingthewholeuniformsectionusinganovenorresistiveelectricalheaterwhile

pullingthefibres.Duetothelongheatzonethistechniquehasnocontrolovertheshape of the tapered region although the sensitivity to environmental factors isreduced. The quality of the tapers/couplers is essentially dependent on the ovendesign,andthetemperatureuniformityalongthelengthofwaistregion.

4.3.4 ShapeoftheTaperedRegion

Accuratecontrolofthetaperedregionshapeofbothfibrecouplersandfibretaperscanbecrucialfortheperformanceofdevicesusingthesecomponents.Forexample,inchapter5anAOtunablefilterisdiscussed,whichreliesontheaccuratecontrolofthefibre-tapershapeandlength.Birksetal.[62],usingtheflame-brushtechnique,produceda longuniformtaperwaist (90mm)withshort transitionregions(35mm)and very small waist diameters (~2m), for generating a supercontinuum lightspectrum. Also in fibre couplers, the accurate control of the tapered region isextremelyimportantforthefabricationofnon-uniformcouplersthatcanbeusedasan add-drop multiplexer when a grating is inscribed in the waist (chapter 8). Ingeneral, the transition region for both fibre couplers and tapers should obey theadiabaticcriterion[63],inordertominimiseinsertionlosses.

4-IntroductiontoFibre-Couplers 42

The shape of fibre tapers/couplers produced by using scanning point-likeheatingsourceshasbeenextensivelystudiedbyBirkselal.[64].Assumingthatthelocalisedheatingofthefibremakestheglasssoftenoughtobestretchedwhilstnotbeing so soft that it falls under its own weight, the shape of the tapers can becalculated without having to recur to fluid mechanics beyond the principle ofconservation of mass. A tapered fibre, at any given time (or elongation) of thepullingprocess,canbecharacterisedbytheparametersshowninfigure4.7a).ro istheinitialfibreradiuscorrespondingtoatransitionlength,z0,andr(z)theradiusofthetapertransitionatagivenpositionz.Thelengthoftheuniformtaperwaistlw(t)isequaltothelengthofthehot-zoneL(t)atthattime.Thesizeofthehot-zoneL(t)mayvarywithtimebutissubjecttotheconstraintsL0anddL/dx1.Thissecondconstraint ensures that the hot-zone does not overtake the pulled transitions. Thetime change is proportional to the extension or elongation of the taper i.e., the

pullingspeed isconstant.Figure4.7b)shows theequivalentuntaperedfibrewheretheinitialhotspotlength(att=0)isL0andxisthetotalpullingextensionatagiventime.ComparingthetaperedwiththeuntaperedfibreitmaybeobservedthatpointsAandB are elongated byx. In theparticular casewhere thehot-zone is constantduring thepulling, thewaist length isconstant lw(x)=L0 and the taper transition isequaltohalfoftheextensionz=x/2.

Figure4.7 -Schematic representationofa fibre taper structure.a)Ata time tduring thepulling.b)Initialfibrebeforepulling.

4-IntroductiontoFibre-Couplers 43

From the conservation of mass principle, the following expression can easily bederived:

Lr

dxdr ww

2= (4.7)

Secondly, the extension x can be related to the taper transition length z bycomparingtheinitiallengthABatt=0,withthetotaltaperlengthABatanygiven

time:

02 LxLz +=+ (4.8)

The particular case where the hot-zone remains constant during the fibreextensionhasbeenanalysedby[64-66].InthiscaseL(z)=L0andz=x/2.Integrating(4.7)givesthewaistshapeforatotalfibreextensionx.

( )00 20

)'('2/1

0)( LxxL

dx

w ererxr

x

=

= (4.9)

The taper profile is calculated by substituting x=2z in (4.9), resulting in the well-knownexponentialdecayprofile.Allthetaperandcouplerdevicesdiscussedinthisthesiswerefabricatedusingaconstanthot-zone,thusexpression(4.9)issufficienttodescribe the profiles of the tapered regions. Further examples of interest arediscussedin[64]whereequation(4.7)isdemonstratedaswell.

Inorder tominimizelossesbetweenthefundamentalandthenearestcladdingmodes,thetaperangle|dr/dz|hastoobeytheadiabaticcriterion[63].

( ) ( )( )pi

2

21 zzr

dzdr (4.10)

4-IntroductiontoFibre-Couplers 44

Where 1(z) and 2(z) are respectively the local propagation constants of thefundamental mode and the closest cladding modes, and r is the local core radius.Experimentally it was observed that intrinsic loss of the fabricated couplers andtapers using the flame-brush technique were very low and justify the use of theaboveparametersdescribingsmoothadiabatictransitions.

4.3.5 Effect of the tapered transition on the coupler powerevolution

The long transition regions in couplers fabricatedusing the flame-brush techniquewithconstanthotzone,playaroleinthewaythepowerevolvesalongthecoupler.

For a full-cycle coupler with a constant hot zone of L0=30mm fabricated withstandard telecommunications single mode fibre, the evolution of the power at theoutputports is illustrated inFigure4.8. Light fromaDFB-LD at awavelengthof

1.55mislaunchedinport1andmonitoredatport3andport4duringthepullingprocess.Thepowerevolution isonlyplotted fromanextensionofx=47mm(fromx=0tox=47therewasnocoupling)inordertoemphasisethecouplingprocess.

0

1

2

3

4

5

47 52 57 62 67 72 77CouplerElongation(mm)

Mea

su

red

ou

tpu

t(V)

Port4

Port3

50%splitter

picoupler2pi coupler

x1

xx3x2x0 xm xN

........

........ ........

Figure4.8Measuredpowerevolutionofa30mmlongfull-cyclecouplerata=1.55mduringthepullingprocess.

4-IntroductiontoFibre-Couplers 45

Light starts to be coupled between the two fibres for a coupler extension aroundx=51mm,thehalf-cyclepointisreachedataroundx=73.5mmwhenallthelightisinPort4andthepullingprocesswashaltedafteronefull-cycle,i.e.,whenalllightwascoupledbacktoPort3.UsingtheinformationplottedinFigure4.8andthefactthatdL/dx=0 (constant hot-zone pulling), an iterative method to extract the couplingstrengthprofileduetothetaperedtransitionregioncanbedeveloped.Afteragivenextension,x,where coupling starts tooccur, all the interaction isdue to thewaistsection with length L0. The coupling coefficient, k(x), can be evaluated for thatextension(orequivalentlyforthatwaistradius)assumingthatthehot-zonesectionisuniform and constant during the fabrication process, by solving equation (4.4) inordertodetermine(x)=(x)L0=2k(x)L0.NowthephasedisplacementbetweentheevenandoddeigenmodescorrespondingtothecoupledpowerP1(x0)atextensionx0isgivenby:

[ ] 00110 )(cos)( LxPx = (4.11)

andthevalueof(x1)atthenextextensionx1=x0+xcanbecalculatediterativelyusing;

[ ] 0101111 )()(cos)( LxxLxPx = , (4.12)

finallyatthemthsection,xm=x0+mx,ityields;

[ ]

=

=1

0001

1 )()(cos)(m

n

nmm xLxLxPx (4.13)

Thereaderisremindedthatz=x/2andtherefore,(z)=(x)/2.Usingthisgeneralrecursive expression and the coupler power evolution Port 3 (blue line in Figure4.8),thecouplingstrength(solidline)wascalculatedandplottedinFigure4.9thisis

4-IntroductiontoFibre-Couplers 46

comparedtotheidealcoupler(dashedline)withoutataperedtransitionregion.TheoriginofthegraphinFigure4.9correspondstoacouplerextensionofx=47mmandthereforea transition lengthofz=23.5mm.At thisposition thenormalisedcoupler

radiuscanbecalculatedusing(4.9)yieldingr(z=23.5)/r0=exp(-z/L0)0.457.Theidealcouplerhasahighercouplingstrengthalongtheuniformwaist than

the fabricated coupler; although the total coupler phase displacement (L)correspondingtotheintegrationofthecouplingstrengthalongthewholelength,is

the same in both couplers at =1.55m. By comparing the power coupling in thetransition regions with that in the uniform region of the fabricated coupler, it isrealised that22.1%of the totalphasedisplacementalong thecoupler isdue to thetapered transition regions and 77.9% due to the uniform waist. Therefore, whenoptimising add-drop multiplexers based on full-cycle couplers with gratingsinscribed in thewaist,byplacing thembetween theexactpointsalong thecouplerwherethepowerisequallysplitbetweenthefibres,thecouplertransitionregionhasto be taken into account. However, the non-destructive coupler characterisationmethodpresentedinChapter9overcomesthisproblem.

0

0.5

1

1.5

0 7.5 15 22.5 30 37.5 45 52.5 60CouplerPosition(mm)

k(z)(

x10

4 m

-1 )

Idealcoupler

Realcoupler

Figure4.9Comparisonofthecouplingstrengthsofanideal(dashedline)andfabricated(solidline)30mmlongfull-cyclecoupler.

4-IntroductiontoFibre-Couplers 47

The effect of the tapered transition region on the power evolution along thecoupler length is illustrated directly in Figure 4.10. Both the output coupler ports(Port3andPort4)are shown.Thedashed line refers to the idealcouplerand thesolidlinetothefabricatedcoupler.Itisobservedthatthefabricatedcouplerislongerand the coupling smoother corresponding to the transition regions. The couplerpositions where the power is equally distributed in both the waveguides (50-50%points) are shifted towards the tapered regions. Identification of these couplerpositionsiscriticalfortheoptimisationofadd-dropmultiplexersbasedongratingsinscribedinthecouplerwaistandwillbediscussedinChapter8.

The accuracy of expression (4.13), in determining the coupling strength andhencethe50-50%pointsofthecoupler,dependsontheuniformityofthehot-zonelengthandtheadiabaticevolutionofthetaperedtransitionregionduringthepullingprocess.Inordertocharacterisethecoupleranddetermineits50-50%pointsanovelnon-destructive characterisation technique for fibre couplerswasdevelopedand isdiscussedinChapter9.

0

0.5

1

0 7.5 15 22.5 30 37.5 45 52.5 60CouplerPosition(mm)

Norm

alis

edPo

wer

P1(z)

P2(z)

Figure 4.10 Power evolution along the length of an ideal uniform (dashed line) andfabricated(solidline)30mmlongfull-cyclecoupler.

4-IntroductiontoFibre-Couplers 48

4.3.6 Couplercrosssection

When fabricating couplers using the flame-brush technique, the degree of fusionbeforepullingthefibresdefinesthecrosssectionalshapeofthecoupler.Thehigherthe degree of fusion the closer the cross section of the fabricated coupler is to acylinder.Inthecaseofveryweakfusion,thecouplerhasacharacteristicdumbbellshapeandforintermediatedegreesoffusion,thecross-sectionhasapproximatelyanelliptical shape with varying eccentricity [67]. The theoretical description of thecouplerintermsofthecouplereigenmodes,alsoknownassupermodes,isrelatedtothecouplercross-section,differentapproximationsforcalculatingthesemodeshavebeenaddressedintheliterature.InBureset.al.[68]thefibreswerenotfusedandthecoreswereneglected;[69]approximatedthecouplercrosssectionusingdifferentarectangular cross section, and [70, 71] gives analytical expressions for the twolowestordermodes,LP01andLP11,fordifferentcouplercross-sections(rectangular,elliptical,circular)alsoneglectingthefibrecores.

Furtherwork, [67,72]usedaFieldCorrectionMethod toaccuratelycalculatethe coupler eigenmodes, while [73-75] use the rigorous surface integral equationmethoddeterminethecouplercharacteristics.

4.4 SummaryFibrecouplersare importantcomponentsused inWDMsystems to routeandsplitsignals,monitorthenetwork,orcombinesignalandpumpwavelengthsforfeedingoptical amplifiers. Recently add-drop multiplexer configurations relying on theinscriptionofBragggratingsinthecouplerwaisthavebeeninvestigated[41,42].Inorder to optimise these devices accurate control of the fabrication and suitablemethods of characterisation for the couplers are required. In chapter 9 a non-destructivemethodforcharacterisingfibre-couplersisdescribed.

In conclusion this chapter gave an introduction to coupler technologies anddescribed how light is transferred between the two waveguides along the couplerlength. A review of fibre-coupler fabrication technologies, their advantages and

4-IntroductiontoFibre-Couplers 49

drawbacksforeachwasdiscussed.Finallytheinfluenceofthefibrecouplerstaperedtransitionregiononthepowerevolutionalongthecouplerlengthwasdescribed. Itwillbeshown(inchapter8) that inorder tooptimiseanadd-dropmultiplexer; theinfluenceofthetransitionregionhastobetakenintoaccount.