Silicon Ring Resonator Add-Drop Multiplexers

108 Pages·2011·8.31 MB·English

Silicon Ring Resonator Add-Drop Multiplexers
by
RobertBoeck
B.A.Sc.,TheUniversityofBritishColumbia,2009
A THESIS SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MasterofAppliedScience
in
THE FACULTY OF GRADUATE STUDIES
(ElectricalandComputerEngineering)
TheUniversityOfBritishColumbia
(Vancouver)
October2011
(cid:13)c RobertBoeck,2011
Abstract
Wavelength-divisionmultiplexing(WDM)usingsilicon-on-insulator(SOI)waveg-
uideshavebecomeanattractiveareaofresearchtodecreasethefootprintofoptical
interconnects as well as to ensure high speed data transmission. Specifically, re-
search into using SOI ring resonator add-drop filters for WDM applications have
been increasingly pursued. A ring resonator coupled on both sides by straight
waveguidesenablesonetoadd(multiplex)ordrop(demultiplex)wavelengths. Us-
ing series-coupled ring resonators, with each resonator having a different length,
enables better spectral performance than single ring resonators. In this thesis, we
haveanalyzedthepropertiesofSOIstripwaveguidesanddirectionalcouplers. We
have compared different spectral properties of single and series-coupled ring res-
onators and showed the advantages of using series-coupled ring resonators. SOI
strip waveguide series-coupled racetrack resonators exhibiting the Vernier effect
were designed by us and fabricated at a leading edge foundry. The free spectral
rangewas36nm,whichiscomparabletothespanoftheopticalC-band. Thedrop
port response showed interstitial peak suppression between 9 dB and 17 dB and
minimalresonancesplitting.
ii
Preface
I am the main author of the conference paper and Optics Express journal paper
titled, “Experimental Demonstration of the Vernier Effect using Series-Coupled
Racetrack Resonators”[6] and “Series-Coupled Silicon Racetrack Resonators and
the Vernier Effect: Theory and Measurement,”[7] respectively. Over a span of
eight months, I proposed the design of the Vernier effect device, modelled and
simulated the device using analytical and numerical methods, and optimized its
performance. IthencreatedadesignlayoutthatwasfabricatedatIMEC.Icharac-
terizedthedeviceusinganexperimentalset-upcreatedbyDr. NicolasRouger. My
supervisors, Drs. Nicolas Jaeger and Lukas Chrostowski, guided my research by
providingimportantinsightsintothedesignofthedeviceaswellaseditingdrafts
oftheconferencepaper,poster,andjournalpaper.
Thecompletelistofpublicationsare:
1. R. Boeck, N. A. F. Jaeger, and L. Chrostowski, “Experimental Demon-
strationoftheVernierEffectusingSeries-CoupledRacetrackResonators,in2010
International Conference on Optical MEMS & Nanophotonics, Sapporo, Japan,
Aug. 9-12,2010.
2. R.Boeck,N.A.Jaeger,N.Rouger,andL.Chrostowski,“Series-coupledsil-
iconracetrackresonatorsandtheVerniereffect: theoryandmeasurement,”Optics
Express,18(24): 2515125157,Nov. 2010.
iii
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
TableofContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 CurrentStateofOpticalInterconnects . . . . . . . . . . . . . . . 1
1.2 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 ThesisOrganization . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Silicon-On-InsulatorRingResonators . . . . . . . . . . . . . . . . . 12
2.1 Silicon-On-InsulatorStripWaveguides . . . . . . . . . . . . . . . 13
2.1.1 EffectiveIndexandGroupIndex . . . . . . . . . . . . . . 18
2.1.2 DirectionalWaveguideCouplers . . . . . . . . . . . . . . 20
2.2 SignalFlowGraphsandMason’sRule . . . . . . . . . . . . . . . 27
2.3 SingleRingResonatorAdd-DropFilters . . . . . . . . . . . . . . 30
2.3.1 SingleRingResonatorAdd-DropFilterTransferFunctions 30
iv
2.3.2 SpectralCharacteristicsoftheSingleRingResonatorAdd-
DropFilters . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Series-CoupledRingResonatorAdd-DropFilters . . . . . . . . . 45
2.4.1 Series-Coupled Ring Resonator Add-Drop Filter Transfer
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.2 SpectralCharacteristicsofSeries-CoupledRingResonator
Add-DropFilters . . . . . . . . . . . . . . . . . . . . . . 48
3 Series-Coupled Silicon Racetrack Resonators and the Vernier Ef-
fect: TheoryandMeasurement . . . . . . . . . . . . . . . . . . . . . 65
3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Curve-Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 ConclusionandSuggestionsforFutureWork . . . . . . . . . . . . . 78
4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 SuggestionsforFutureWork . . . . . . . . . . . . . . . . . . . . 79
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A DerivationoftheFreeSpectralRange . . . . . . . . . . . . . . . . . 89
B Derivation of the Full-Width-at-Half-Maximum and the Quality
Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
C DerivationoftheResonanceSplittingWavelengths . . . . . . . . . 94
v
List of Tables
Table1.1 Performanceofcommercialsingle-channelDWDMfilters. . . 3
Table2.1 Propagationlossesversuswaveguidewidth[8]. . . . . . . . . 15
vi
List of Figures
Figure1.1 Exampleofathree-channelDWDMsystem. . . . . . . . . . 2
Figure1.2 (a)showshowaringresonatorcanbeusedasademultiplexer
and(b)showshowitcanbeusedasamultiplexer . . . . . . . 4
Figure1.3 (a)ImageofcascadedSOIdiscresonatorsexhibitingtheVernier
effectand(b)theexperimentaldropportresponse[32]. (cid:13)c Optical
SocietyofAmerica,2006,adaptedbypermission.. . . . . . . 9
Figure1.4 (a)SEMofseries-coupledSOIracetrackresonatorsexhibiting
the Vernier effect and (b) theexperimental drop port response
[57]. (cid:13)c ChineseOpticsLetters,2009,adaptedbypermission. 10
Figure2.1 GeneralstructureofanSOIstripwaveguide. . . . . . . . . . 14
Figure2.2 Refractiveindexof(a)siliconand(b)silicondioxideversusλ 16
Figure2.3 Refractiveindexof(a)siliconand(b)silicondioxideversusT 17
Figure2.4 (a) n versus λ and (b) n versus λ for various waveguide
eff g
widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure2.5 (a)n and(b)n versusT . . . . . . . . . . . . . . . . . . . 20
eff g
Figure2.6 Schematicofadirectionalcoupler. . . . . . . . . . . . . . . . 21
Figure2.7 Schematicshowingthecross-sectionofadirectionalcoupler. . 22
Figure2.8 Normalized electric field (Ex) of the (a) even and (b) odd su-
permodeforagapdistanceof200nm . . . . . . . . . . . . . 23
Figure2.9 Difference between the effective index of the even and of the
oddsupermodesversuswavelengthforvariouswaveguidewidths 24
Figure2.10 |κ|2 and|t|2 versusL foragapdistanceof200nm . . . . . . 26
c
Figure2.11 |κ|2 versusλ forvariouswaveguidewidths . . . . . . . . . . 26
vii
Figure2.12 Example of a signal flow graph with two forward paths and
onefeedbackloop(adaptedfrom[39]). . . . . . . . . . . . . 27
Figure2.13 Reductionmethodusedtodeterminethetransferfunctionx /x
4 1
where (a) shows feedback transformation, (b) shows cascade
transformation,and(c)showsthemultipathtransformation. . 28
Figure2.14 (a) Schematic of ring resonator add-drop filter and (b) shows
thefeedbackloopandforwardpaths. . . . . . . . . . . . . . 31
Figure2.15 n versus λ and curve-fit for a waveguide width and height
eff
of500nmand220nm,respectively . . . . . . . . . . . . . . 33
Figure2.16 (a) shows the through port and drop port spectral characteris-
tics of a single ring resonator add-drop filter and (b) shows a
zoominoftheresonancepeakofthedropportresponse. . . . 34
Figure2.17 IL versus |κ |2 =|κ |2 for (a) various propagation losses
drop 1 2
and(b)forvariousresonatorlengths . . . . . . . . . . . . . . 36
Figure2.18 OBRR versus |κ |2 =|κ |2 for (a) various propagation losses
1 2
and(b)forvariousresonatorlengths . . . . . . . . . . . . . . 38
Figure2.19 ER versus|κ |2=|κ |2for(a)variouspropagationlosses
through 1 2
and(b)forvariousresonatorlengths . . . . . . . . . . . . . . 40
Figure2.20 ∆λ versus|κ |2=|κ |2for(a)variouspropagationlosses
FWHM 1 2
and(b)forvariousresonatorlengths . . . . . . . . . . . . . . 42
Figure2.21 Q versus |κ |2 =|κ |2 for (a) various propagation losses and
1 2
(b)forvariousresonatorlengths . . . . . . . . . . . . . . . . 44
Figure2.22 (a) shows the schematic of series-coupled ring resonator add-
dropfilterand(b)showsthefeedbackloops. . . . . . . . . . 46
Figure2.23 (a), (b), (c), and (d) show the forward paths for the series-
coupledringresonatoradd-dropfilter. . . . . . . . . . . . . . 47
Figure2.24 Comparison between the drop port response of a single and
series-coupledringresonatoradd-dropfilter . . . . . . . . . . 49
Figure2.25 Dropportresponsesensitivitytovariousvaluesof|κ |2 witha
2
fixedvaluefor|κ|2 . . . . . . . . . . . . . . . . . . . . . . . 51
Figure2.26 |κdrop|2 versus |κ|2 for (a) various propagation losses and (b)
c
forvariousresonatorlengths . . . . . . . . . . . . . . . . . . 52
viii
Figure2.27 (a) shows the resonance splitting wavelengths versus |κ |2 for
2
a fixed |κ|2 = 0.001 and resonator lengths equal to 100 µm
using equations 2.47 and 2.48 and the closely matched values
determinedgraphicallyfromthedropportresponse. (b)shows
theresonancesplittingwavelengthsversus|κ|2forafixed|κ |2
2
=0.3. Theincreasingerrorinusingequations2.47and2.48is
clearly shown for large values of |κ|2 compared to the values
determinedfromthedropportresponse . . . . . . . . . . . . 54
Figure2.28 OBRR atκdropversus|κ|2for(a)variouspropagationlosses
2ring c
and(b)forvariousresonatorlengths . . . . . . . . . . . . . . 56
Figure2.29 Through port response sensitivity for various values of |κ |2
2
when|κ|2 isfixedat0.5 . . . . . . . . . . . . . . . . . . . . 57
Figure2.30 ThroughportinsertionlossatβL=2πmversus|κ |2 forvari-
2
ousvaluesof|κ|2 . . . . . . . . . . . . . . . . . . . . . . . . 59
Figure2.31 Comparisonbetween|κthru|2 and|κdrop|2 versus|κ|2. . . . . 60
c c
Figure2.32 Comparison of single and series-coupled ring resonator add-
drop filters based on (a) the through port ER and (b) the drop
portOBRR . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Figure2.33 Comparison of the drop port response of series-coupled ring
resonatoradd-dropfilterswithidenticalanddifferentringres-
onatorlengthsthathaveFSRsgreaterthanthespanoftheC-band. 64
Figure3.1 Theoretical drop port response of the un-optimized device il-
lustrating the twin peaks, extended FSR, and minimum inter-
stitialpeaksuppression,and(b)themainresonancepeaksplit-
ting[7]. (cid:13)c OpticalSocietyofAmerica,2010,bypermission . 68
Figure3.2 (a) Theoretical drop port response of the optimized device il-
lustrating large interstitial peak suppression and (b) no main
resonance splitting [7]. (cid:13)c Optical Society of America, 2010,
bypermission . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure3.3 SEMof(a)fabricatedseries-coupledracetrackresonators,and
(b) coupling region [7]. (cid:13)c Optical Society of America, 2010,
bypermission . . . . . . . . . . . . . . . . . . . . . . . . . . 71
ix
Figure3.4 (a) Experimental and curve-fit drop port response for series-
coupledracetrackresonators,(b)showstheminimalmainres-
onance splitting (zoom in of Figure 3.4(a)), and (c) shows the
straightwaveguidetransmissionresponseusedforcalibration.
(Although minor modifications were made to the above fig-
ures, permission was obtained to reproduce figures from [7]).
(cid:13)c OpticalSocietyofAmerica,2010,bypermission. . . . . . 73
Figure3.5 (a) Main resonance intensity, (b) minimum interstitial peak
suppression,and(c)mainresonancesplittingdepthversus|κ |2,
1
|κ |2, and |κ |2. Purple circles indicate values used for curve-
2 3
fitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Figure3.6 Experimentaldropportresponseforsingleracetrackresonators
with a radius of 6.545 µm and 4.225 µm. (Although minor
modifications were made to the above figure, permission was
obtained to reproduce the figure from [7]). (cid:13)c Optical Society
ofAmerica,2010,bypermission. . . . . . . . . . . . . . . . 77
Figure4.1 SchematicofaC-banddemultiplexerusingseries-coupledring
resonatorsandon-chipGePINdetectors. . . . . . . . . . . . 81
x