optic coupler

7/30/2019 optic coupler

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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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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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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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[ ]

[ ]

=

=

=

+=

+

+

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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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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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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4.3.2CO2Laser

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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(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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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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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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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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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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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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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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4.3.6Couplercrosssection

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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drawbacksforeachwasdiscussed.Finallytheinfluenceofthefibrecouplerstapered

transitionregiononthepowerevolutionalongthecouplerlengthwasdescribed.It

willbeshown(inchapter8)thatinordertooptimiseanadd-dropmultiplexer; the

influenceofthetransitionregionhastobetakenintoaccount.

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