of 4
SupplementaryInformation:Chemicallyetchedultra-high-Qresonatoronasilicon
chip
HansuekLee
,TongChen
,JiangLi
,KiYoulYang,SeokminJeon,OskarPainter,andKerryJ.Vahala
T.J.WatsonLaboratoryofAppliedPhysics,CaliforniaInstituteofTechnology,Pasadena,California91125,USA
Theseauthorscontributedequallytothiswork.
correspondingauthor;email:vahala@caltech.edu
(Dated:May1,2012)
1
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DOI: 10.1038/NPHOTON.2012.109
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I.EFFECTOFWEDGEANGLEONOPTICALQ
Asnotedinthemaintext,thephysicalprincipleatworkinthepresentstructuresisdistinctfromtheprevious
workinreference15.Inparticular,becausetheedgeroughnesshasbeeneliminatedthewedgestructurenolonger
playstheroleofisolatingtheopticalmode.Thisbehaviorcanbeobservedinthedataoffigure2inthemaintext
andisfurtherconfirmedinthemodeloffigure1ofthissupplementalsection.Here,theopticalQfactoriscalculated
versusresonatordiameterwithafixedoxidethicknessof10micronsandforthreedifferentangles.Ascanbeseenin
thedata,theQfactorsteadilyimprovesasthewedgeangleisincreased.
0
2
4
6
8
10
2
10
3
Resonator diameter (mm)
Q (million)
wedge angle: 11 degree
wedge angle: 27 degree
wedge angle: 63 degree
FIG.1:OpticalQversusdiameterforthreedistinctwedgeanglesshowingthesystematicimprovementofQvalue
withincreasingwedgeangle.Themodelusedisthesameasthatinfigure2ofthemaintext.
II.FREQUENCYNOISEOFBRILLOUINLASER
TocharacterizethestimulatedBrillouinlaser(SBL)frequencynoise,aMach-Zehnderinterferometer(MZI)havinga
freespectralrangeof6
.
72MHzisusedasadiscriminatorandthetransmittedopticalpowerisdetectedandmeasured
usinganelectricalspectrumanalyzer(ESA).Tosuppresstheintensitynoise,thecomplementaryoutputsofthe
interferometerweredetectedusingabalancedreceiver.ThisESAspectrumisrelatedtothefrequency-fluctuation
spectraldensity,
S
ν
(
f
),throughthefollowingrelation:
W
ESA
(
f
)=
V
2
pp
2
π
2
τ
2
d
sinc
2
(
τ
d
f
)
S
ν
(
f
)
R
L
(1)
where
τ
d
istheMach-Zehnderdelayand
V
pp
isthepeak-to-peakvoltageofthedetectedMZIoutputoveronefringe.
Usingthisformula,thefrequency-fluctuationspectraldensityisplottedinFigure2a.Thesingularityintheplotsat
6
.
72MHzisanartifactofthedataconversionnearthezeroofthesinc
2
function.Thefrequencyfluctuationspectra
havearelativelyflat(whitenoise)regionforcarrieroffsetfrequenciesabove2MHzandthena1
/f
-likeregionat
frequenciesbelow2MHz.ThevalueofthewhitenoiseregionisplottedbothasafunctionofSBLpowerandexternal
cavityQfactorinFigures2band2c,respectively.Alsoplottedarefitstoinversepowerandinverse
Q
2
curves.These
2
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0
5
10
10
−2
10
0
10
2
10
4
Offset freqency (MHz)
S
ν
(f) (Hz
2
/Hz)
0.1
0.2
0.3
0.4
0
0.2
0.4
0.6
SBS power (mW)
S
ν
(Hz
2
/Hz)
50
100
150
200
250
0
0.2
0.4
0.6
0.8
1
Q
ex
(million)
S
ν
(Hz
2
/Hz)
a
b
c
d
100
1k
10k
100k
1M
Offset frequency (Hz)
S
ν
(f) (Hz
2
/Hz)
SBL
Pump laser
10
−2
10
0
10
2
10
4
10
6
10
8
FIG.2:MeasurementsoftheSBLfrequencynoisecharacteristics.
a,
Laserfrequencynoisespectrumatdifferen-
toutputpowerlevelsfrom0
.
047mWto0
.
375mW(indicatedbycolor).
b,
STnoiseplottedversusoutputpow-
er.Thedashedlineisaninversepowerfittothedata.
c,
STnoiseplottedversustheexternalcavityqualityfactor
Q
ex
.Thedashedlineisafitusingthefunction
Q
0
+
Q
ex
Q
2
ex
.
d,
AtypicalSBLfrequencynoisespectrumandthepump
laser(externalcavitydiodelaser)frequencynoisespectrumatoffsetfrequenciesfrom100Hzto1MHz.Theshaded
regionisthefrequencynoiseperformanceofcommercial,narrowlinewidthfiberlasers.
dependencesaswellascalculationconfirmthatthemeasuredfrequencynoisecomponentistheSchawlow-Townes
(ST)quantumnoiseofthelaser.Theminimumvalueof0
.
06Hz
2
/
HzistoourknowledgethesmallestrecordedST
noiseforanychip-basedlaser.Itisalsointerestingtonotethat,totheauthorsknowledge,theSTnoisedependence
onloadinghasnotpreviouslybeenrecorded.This,normallydifficultmeasurement,waspossiblehereonaccountof
theabilitytovarythetaperloadingoftheresonator
1
.
The1
/f
noisethatappearsatlowercarrieroffsetfrequenciesisgiveninFigure2dandapproximatelytracksa
similar-shapednoisespectruminthelaserpumpoverthisfrequencyrange.However,theabsolutelevelof1
/f
noise
oftheSBLatagivenoffsetfrequencyisreducedbyabout30dBrelativetothe1
/f
noiseinthepump.Indeed,the
leveloftechnicalnoiseinthisbandiscomparabletoseveralcommercialfiberlasersthatwerecharacterizedaspart
ofthisstudy.Assuch,theperformanceoftheSBL,bothinthequantumlimitedSTregimeandthetechnical-noise
limited1
/f
regime,isexcellent.
3
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0
0.1
0.2
0.3
0.4
0.5
0.6
−0.05
0
0.05
0.1
0.15
Relative wavelength (nm)
Transmission (a.u.)
FSR
0.178nm
FIG.3:Broadspectralscanover3freespectralranges(FSR)ofa3mmdiameterresonator.
III.BROADSPECTRALSCANOFTHERESONATOR
Figure3providesawidespectralscanofaresonatorwithadiameterof3mmandacorrespondingfreespectral
range(FSR)ofapproximately0
.
178nm.Thescanincludes3completeFSRs.
1
Spillane,S.,Kippenberg,T.,Painter,O.&Vahala,K.J.Idealityinafiber-taper-coupledmicroresonatorsystemforappli-
cationtocavityquantumelectrodynamics.
Phys.Rev.Lett.
91
,043902(2003).
4
4
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DOI: 10.1038/NPHOTON.2012.109
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