Dispersive wave emission and supercontinuum generation in a silicon wire waveguide pumped around the 1550 nm telecommunication wavelength

0.39 MB·

by  François Leo

Dispersive wave emission and supercontinuum generation in a silicon wire
waveguide pumped around the 1550 nm telecommunication wavelength
Franc¸oisLeo,1,2,∗Simon-PierreGorza,3JassemSafioui,3PascalKockaert,3Ste´phaneCoen,4UtsavDave,1,2Bart
Kuyken,1,2andGuntherRoelkens1,2
1PhotonicsResearchGroup,DepartmentofInformationTechnology,GhentUniversity-IMEC,GhentB-9000,Belgium
2Centerfornano-andbiophotonics(NB-photonics),GhentUniversity,Belgium
3OPERA-Photonique,Universite´LibredeBruxelles(ULB),50Av.F.D.Roosevelt,CP194/5,B-1050Bruxelles,Belgium
4PhysicsDepartment,TheUniversityofAuckland,PrivateBag92019,Auckland1142,NewZealand
4 ∗Correspondingauthor:[email protected]
1
0
CompiledMarch17,2014
2
We experimentally and numerically study dispersive wave emission, soliton fission and supercontinuum generation in a

r silicon wire at telecommunication wavelengths. Through dispersion engineering, we experimentally confirm a previously
a reportednumericalstudy[1]andshowthattheemissionofresonantradiation fromthesolitonscanleadtothegeneration of
M
asupercontinuum spanningover500nm.Anexcellent agreementwithnumericalsimulations isobserved. © 2014 Optical
SocietyofAmerica

4 OCIScodes: (130.4310)Integratedoptics,Nonlinear;(190.5530)Nonlinearoptics,Pulsepropagationandtemporalsolitons
1

]
s Supercontinuum generation has been the subject of many ing. Previous experiments reporting dispersive wave emis-
c studies,particularlysincetheadventofphotoniccrystalfibers sionin siliconattelecomwavelengthdisplayedverylimited
i
t (PCFs) [2]. The low losses and high confinement, leading spectralbroadeningandtheimpactofthewaveguidegeome-
p
to high nonlinearities, as well as the possibility to tailor the try was notinvestigated[13]. Here we reportwhatis, to the
o
. zero-dispersionwavelength(ZDW)hasledtothegeneration best of our knowledge,the first experimentalobservationof
s
c ofsupercontinuaspanningovermorethananoctave[3].Such abroadsupercontinuumbyengineeringtheemissionofdis-
i widespectrabenefitmanyapplicationssuchashigh-precision persivewavesinasiliconwirewaveguidepumpedintheC-
s
y frequencymetrology[4], opticalcoherencetomography[5], band.Wefindanexcellentagreementwithsimulations,con-
h ortelecommunication[6]. firming early predictions [1] that the nonlinear Schrodinger
p As on-chip generation of ultrashort pulses is becoming a equation with a complex nonlinear parameter correctly de-
[
reality[7,8],thefullintegrationofsupercontinuum-basedap- scribesbroadsupercontinuumgenerationattelecommunica-

2 plicationscanbeenvisioned.On-chipsupercontinuumgener- tionwavelengths.Moreover,thegoodagreementwithsimu-
v ationwasperformedinchalcogenide [9],Si N [10],amor- lationsgivesmoreinsightintohigh-ordersolitondynamicsin
3 4
3
phous silicon [11] and silicon waveguides [12,13]. On the siliconinthatwavelengthrange.
1
silicon platform, previous experiments have reported a rel- Weconsider7mm-longsilicon-on-insulator(SOI)waveg-
7
5 atively limited spectral broadening in the 1550 nm telecom uides with a standard 220nm silicon thickness. To achieve
. band. Other studies have focused instead on mid-IR pump- anomalous group velocity dispersion at the pump wave-
1
0 ing, and most of the broadening,up to 3.5 m m wavelength, length,whichisrequiredforefficientfemtosecondsupercon-
4 was in that wavelength range[14,15]. At the 1550nm tele- tinuum generation [2], such waveguides must be no wider
1 com wavelength in a silicon wire, losses are not dominated than 800 nm. Here we report results for waveguides with
v: byTPA butbythe subsequentfreecarrierabsorption(FCA)
i andthese lossestypically preventthe observationofnonlin-
X
eareffects[16].Notethatpicosecondsolitoncompressionhas
r neverthelessbeenveryrecentlydemonstratedinsiliconpho- 1
a
toniccrystals[17].Onewaytocircumventthefreecarrierin- m) 0.5
ducedlossesistouseveryshortfemtosecondpulsessuchthat 2s/
p
thecarrierdensityremainsnegligible[1].Inthatregime,the on ( 0
dynamics of supercontinuum generation is known to occur si
er Si h = 220 nm
through fission of higher-order solitons and the subsequent p
s −0.5
Di W = 700, 750 nm
emissionofresonantdispersivewaves(DWs)[2,18–20].This BOX
processiswelldescribedbythewellknowngeneralizednon- −1
linear Schro¨dinger equation (GNLSE) and excellent agree- 1200 1300 1400 1500 1600 1700
mentbetweenthismodelandexperimentshasbeenreported Wavelength (nm)
inPCFs[21].Usingasimilarmodel,Yinetalpredictedthat
the same mechanismsshouldgiverise to a 400nmwide su- Figure 1. Simulated wavelength dependence of the second-
percontinuum in a silicon wire at telecommunication wave- order dispersion coefficientb 2 of 220 nm-thickSOI waveg-
lengths [1] but an experimental demonstration is still miss- uideswith700nm(dotted)and750nm(solid)width.Thever-
ticaldottedlineindicatesthepumpwavelength.
1
Theyappearinthenormaldispersionregimearound1350nm
and1200nm, respectivelyforthe 750nm and 700nm-wide
Wavelength (nm) guide. In the latter, the DWs allow for the generation of
1100 1200 1300 1400 1500 1600 1700 a supercontinuum with a -30dB bandwidth spanning from
(a) 1160nm to 1700nm, almost twice what was previously re-
w = 750 nm
ported in silicon at telecom wavelength [12]. We can also
v)
B/di noticea clearsaturationofthespectralbroadeningwhenin-
0 d creasing the pump peak power beyond 14W, which can be
4
y ( explainedbyincreasedtwo-photonabsorptionbasednonlin-
nsit earlosses.
e
d
er In order to gain further insights in the observed spectral
w
o broadening,wehaveperformednumericalsimulationsbased
P
on the GNLSE describing the propagation of the temporal
envelopeE(z,t)oftheelectricfieldofshortpulsesalongthe
lengthzofanonlinearmedium.Theequationreads[1,22],
(b)
div) w = 700 nm ¶ E¶(zz,t) =i(cid:229) ikbk!k¶¶ktEk −a2lE−a2c(1+im )E
B/ k≥2
d
0 i ¶ t
sity (4 +ig (cid:18)1+w 0¶ t(cid:19)EZ−¥ R(t−t′)|E(z,t′)|2dt′. (1)
n
e
er d Here the b k are the Taylor series expansioncoefficientsthat
ow fitthechromaticdispersioncurvesofFig.1intermsofangu-
P
larfrequencyaroundthepumpcentralangularfrequencyw .
0
a anda account,respectively,forlinearandfreecarrierab-
l c
1100 1200 1300 1400 1500 1600 1700 sorptionlosses.Wehavea =s N whereN isthefreecar-
c c c
Wavelength (nm) rier density and s =1.45×10−21m2 for silicon [22]. The
parameter m accounts for the free carrier dispersion and is
Figure2.Experimentalspectrameasuredattheoutputof(a) takenasm =2k w /(s c)withcthespeedoflightinvacuum
c 0
the750nm-wideand(b)the700nm-widewaveguideforon- and k =(8.8×10−28N +1.35×10−22N0.8)/N [22,23].
c c c c
chip peak powers of 0.15W, 1.5W, 3.5W, 7W, 14W and Notethatk isdependentonthecarrierdensity.g isestimated
c
32W.Thespectrahaveeachbeenshiftedby40dBforclarity.
from experiments on similar waveguides [24] and scaled
throughtheeffectivemodeareaA =0.2m m2.Wefindg =
eff
(234+44i)W−1m−1.R(t)isthenonlinearityresponsefunc-
two differentwidths,respectively,700and750nm.Thedis- tiondefinedasinfibers,R(t)=(1−fR)d (t)+fRhR(t)where
persive propertiesof these waveguideshave been calculated fR is thefractionalRaman contributionandhR(t) isthe Ra-
with a full vectorial mode solver, and the wavelength de- manresponsefunction.Bothcanbededucedfromtheknown
pendence of their second-order dispersion coefficient b is spectral Lorentzian shape of the Raman response of sili-
2
showninFig. 1. Ascan beseen,the dispersionissmalland con[22].Weusetherelation fR=gR(w 0)G R/[W RAeffRe(g )]
anomalous at the 1565 nm pump wavelength used in our withgR(w 0)=3.7×10−10m/W[25],W R/(2p )=15.6THz
experiments. The pump pulses of 150 fs full-width at half- andG R/p =105GHz[22]whichyields fR=0.026.Finally,
maximum (FWHM) duration at an 82 MHz repetition rate thecarrierdensitycanbecalculatedbysolving
aregeneratedwithanOPO(SpectraphysicsOPAL)pumped ¶ N (z,t) 2p Im(g ) N (z,t)
by a Ti-Saphire laser (Spectra physics Tsunami) running at c = |E(z,t)|4− c , (2)
¶ t hw A t
722nm wavelength. We use the horizontally-polarizedidler 0 eff c
output, exciting only the quasi-TE mode of the waveguide. wherehisPlanck’scontantandt isthecarrierlifetime,esti-
c
The light is coupled into the waveguide with a x60 micro- matedtobe1ns[26].
scope objective (NA=0.65) and coupled out with a lensed Equations (1) and (2) have been solved with a split-step
fiber(NA=0.4).Thecorrespondingcouplingefficienciesare Fourieralgorithm[20,27].Thetaylorexpansioncoefficients
17dB and 7dB. The propagationlosses are estimated to be are computed up to the 10th order. Results for a hyperbolic
2dB/cmbycutbackmeasurementsonsimilarwaveguides. secantinputpulsewith150fsduration(FWHM)andapeak
The optical spectra measured at the output of the two powerof32Wcorrespondingtotheexperimentalparameters
waveguidesforincreasingpumppeakpower(upto32W)are areshowninFigs.3and4forourtwodifferentwaveguides.
shown in Figs. 2(a) and (b). We can readily observe a clear The top-left panel of each figure reveals a good agreement
differencebetweenthe two sets ofmeasurements,whichre- betweenmeasuredandsimulatedoutputspectra.Inparticular
vealsthestronginfluenceofthewaveguidewidth,hencethe thepositionoftheDWsandtheoverallspectralwidtharewell
dispersion,onspectralbroadeninginsiliconwires.Resonant predictedbysimulations.TheDWsrelatetoCˇerenkovradia-
DWs areobservedwith pumppeakpowersas lowas 3.5W. tionemittedbysolitonsperturbedbyhigher-orderdispersion
2
Wavelength (nm) Time (ps) Wavelength (nm) Time (ps)
1200 1400 1600 −0.5 0 0.5 1200 1400 1600 −0.5 0 0.5
density (dB) −200 23 wer (W) Density (dB) −200 23 wer (W)
er 1 Po er 1 Po
w w
o o
P −40 0 P −40 0
7 7
6 6 6 6
m) 5 m) m) 5 m)
Distance (m 234 24 Distance (m Distance (m 234 24 Distance (m
1 1
0 0 0 0
1200 1400 1600 −0.5 0 0.5 1200 1400 1600 −0.5 0 0.5
Wavelength (nm) Time (ps) Wavelength (nm) Time (ps)
Figure4.SameasFig.3butforthe700nm-widewaveguide.
−60 −40 −20 0 0 10 20 30
Power density (dB) Power (W)
these characteristics are well predicted analytically [2]). In
Figure 3. Pseudocolor plots of the simulated spectral (left)
contrast, while our input soliton number is N =19 for the
andtemporal(right)evolutionalongthe750nm-widesilicon
700nm-widewaveguide,we only observefoursubpulsesat
waveguidefora150fs(FWHM)32Wsechinputpulse.Top
the output of that waveguide, and they all have roughly the
plots(red)highlightthewaveguideoutputatz=7mm.The
same temporal duration and peak power (note that N =33
dashed curve is the measured output spectrum for compari-
for the 750nm-wide waveguide). We believe that the TPA-
son.
inducedpeak-powerlimitationduringtheverystrongtempo-
ralcompressionisresponsibleforthesedifferences.Previous
andtheirspectralpositioncanbeanalyticallypredictedwith theoreticalresultsbroadlyagreewiththishypothesis[28,29].
thephasematchingrelation[18] Inparticular,thoseworkshavehighlightedthatTPA can in-
w w ducesolitonfissionevenintheabsenceofRamanscattering
b (w DW)− DW =b (w s)− s +(1−fR)g Ps, (3) orhigher-orderdispersion,andthatthesplitpulseshavevery
v v
g,s g,s
close characteristics. Only the cases of N = 2 and N = 3
where b (w ) designates the frequency-dependentwavenum- have been considered in details however, and more theoret-
berofthewaveguide,w andw arethefrequenciesofthe icalworkisneededtofullyunderstandthesolitonfissiondy-
s DW
solitonandtheemittedDWrespectively,whileP andv are namicsoftheGNLSEinpresenceofTPAinthecaseofhigh
s g,s
the soliton peak power and group velocity. By using a soli- solitonorders.Wealsoemphasizethatoursimulationspredict
tonpeakpowerP =10Wextractedfromthesimulations,we pulsecompressiondownto20fs(seeFig.4),highlightingthe
s
findthatforthe750nm-wide(700nm-wide)waveguidethe potentialuseofsiliconforthemanyapplicationsrequiringul-
DWs should be emitted at 1300nm (1150nm), which is in trashortpulses.
goodagreementwithourexperimentalandnumericalresults. In conclusion we have experimentally and numerically
Thisconfirmstheoriginofthesespectralpeaks. studiedhigh-ordersolitonfission,dispersivewavegeneration,
Additional information can be gained by examining the andsupercontinuumgenerationinasiliconphotonicwire.We
simulated evolution of the temporal intensity profiles of the have reported a supercontinuum spanning from 1200nm to
pulses along the waveguide, which are plotted in the right 1700nm.Itisobtainedfrom150fsinputpulsesat1565nm
panels of Figs. 3 and 4. These figures reveal the tempo- wavelength,i.e.,intheC-bandoftelecommunications,andto
ral compression and subsequent splitting (or fission) of the the best of our knowledge it constitutes the widest reported
input pulse that is typical of supercontinuum generation in supercontinuum in silicon in htis wavemength range. Our
PCFs[2].Thetheoreticalfissionlength[2]is4.5mmforthe work also highlights that the high-order soliton dynamics,
750nm-wide waveguide and 2.6mm for the 700nm waveg- andinparticularthe solitonfissionprocess,ofthenonlinear
uide which agrees reasonably well with our results despite Schro¨dingerequationisstillmostlypreservedinthesecondi-
strong nonlinear losses. We can note however some differ- tions,despitethestronginfluenceofTPA.Letusnotethatwe
enceswiththesolitonfissiondynamicreportedinPCFs.Fis- havecheckedthatbothRamanscatteringandfreecarrieref-
sion of a soliton of order N in PCF leads to N fundamental fectsplayverylittleroleinoursimulationsandcaninpractice
solitonswithdifferentpeakpowersandtemporalwidths(and beneglected.Thisresultsfromoperatinginthefemtosecond
3
regime and confirms the findings of Refs. [1]. We therefore 19. M.Erkintalo,Y.Q.Xu,S.G.Murdoch,J.M.Dudley,andG.
believe that the goodagreementbetween our numericaland Genty,Phys.Rev.Lett.109,223904(2012).
experimentalresultsclearlyshowsthatthesimpleNLSEwith 20. I.Cristiani,R.Tediosi,L.Tartara,andV.Degiorgio,Opt.Ex-
acomplexnonlinearparameterissufficienttodescribeshort press12,124(2004).
pulsepropagationinasiliconwireattelecomwavelength. 21. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A.
Diddams, K.Weber,andR.S.Windeler,Phys.Rev.Lett.90,
ThisworkissupportedbytheBelgianSciencePolicyOf-
113904(2003).
fice (BELSPO) Interuniversity Attraction Pole (IAP) pro-
22. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15,
gramme under grant no. IAP-6/10 and by the FP7-ERC-
16604(2007).
MIRACLE project. The participation of S. Coen to this
23. R.A.SorefandB.R.Bennett,IEEEJournalofQuantumElec-
project was made possible thanks to a Research & Study
tronics23,123(1987).
Leave granted by The University of Auckland and to a vis-
24. J.Matres,G.C.Ballesteros,P.Gautier,J.-M.Fe´de´li,J.Mart´ı,
itingfellowshipfromtheFNRS(Belgium).BartKuykenac-
andC.J.Oton,Opt.Express21,3932(2013).
knowledges the special research fund of Ghent University
25. R.Claps, D.Dimitropoulos, V.Raghunathan, Y.Han, andB.
(BOF)forafellowship. Jalali,Opt.Express11,1731(2003).
26. O.Boyraz,P.Koonath,V.Raghunathan,andB.Jalali,Opt.Ex-
press12,4094(2004).
References 27. J.M. Dudley andJ.Taylor (ed.).Supercontinuum generation
inopticalfibers.CambridgeUniversityPress,2010.
1. L.Yin,Q.LinandG.P.Agrawal,Opt.Lett.32,391(2007). 28. Y.Silberberg,Opt.Lett.15,1005(1990).
2. J.M.Dudley,G.Genty,andS.Coen,Rev.Mod.Phys.78,1135 29. V.V.Afanasjev,J.S.Aitchison,andY.S.Kivshar,Opt.Comm.
(2006). 116,331(1995).
3. J.K.Ranka,R.S.Windeler,andA.J.Stentz,Opt.Lett.25,25
(2000).
4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.
Windeler, J. L. Hall, and S. T. Cundiff, Science 288, 635
(2000).
5. I.Hartl,X.D.Li,C.Chudoba, R.K.Ghanta,T.H.Ko,J.G.
Fujimoto,J.K.Ranka,andR.S.Windeler,Opt.Lett.26,608
(2001).
6. S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M.
Kobtsev,S.Kukarin,andS.K.Turitsyn,Opt.Fib.Technol.12,
122(2006).
7. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R.
Johnson,M.A.Foster,M.R.E.Lamont,M.Lipson,andA.L.
Gaeta,Opt.Express21,1335(2013).
8. T.Herr,V.Brasch,J.D.Jost,C.Y.Wang,N.M.Kondratiev,
M.L.Gorodetsky,andT.J.Kippenberg,NatPhotonadvance
onlinepublication,(2013).
9. M.R.Lamont,B.Luther-Davies,D.-Y.Choi,S.Madden,and
B.J.Eggleton,Opt.Express16,14938(2008).
10. R.Halir,Y.Okawachi,J.S.Levy,M.A.Foster,M.Lipson,and
A.L.Gaeta,Opt.Lett.37,1685(2012).
11. J. Safioui, F. Leo, B. Kuyken, S-P. Gorza, S. Selvaraja, R.
Baets, Ph. Emplit, G. Roelkens and S. Massar, Opt. Express
22,3089(2014).
12. I.-W.Hsieh,X.Chen,X.Liu,J.I.Dadap,N.C.Panoiu,C.-Y.
Chou,F.Xia,W.M.Green,Y.A.Vlasov,andR.M.Osgood,
Opt.Express15,15242(2007).
13. W.Ding,A.V.Gorbach,W.J.Wadswarth,J.C.Knight,D.V.
Skryabin,M.J.Strain,M.Sorel,andR.M.DeLaRue,Opt.
Express18,26625(2010).
14. B.Kuyken,X.Liu,R.M.OsgoodJr.,R.Baets,G.Roelkens,
andW.M.J.Green,Opt.Express19,20172(2011).
15. M.R.Lamont,R.K.Lau,A.Griffith,Y.H.Wen,Y.Okawachi,
M.Lipson,andA.L.Gaeta,inCLEO:2013(OpticalSociety
ofAmerica,2013),p.CW3H.1.
16. H.Rong,Y.-H.Kuo,S.Xu,A.Liu,R.Jones,M.Paniccia,O.
Cohen,andO.Raday,Opt.Express14,6705(2006).
17. A.Blanco-Redondo,C.Husko,D.Eades,Y.Zhang,J.Li,T.F.
Krauss,andB.J.Eggleton,Nat.Comm.5,3160(2014).
18. N.AkhmedievandM.Karlsson,Phys.Rev.A51,2602(1995).
4
References 17. A.Blanco-Redondo,C.Husko,D.Eades,Y.Zhang,J.Li,T.F.
Krauss,andB.J.Eggleton,”Observationofsolitoncompres-
1. L.Yin,Q.LinandG.P.Agrawal,”Solitonfissionandsuper-
sioninsiliconphotoniccrystals”,Nat.Comm.5,3160(2014).
continuum generation in silicon waveguides”, Opt. Lett. 32,
18. N.AkhmedievandM.Karlsson,”Cherenkovradiationemitted
391(2007).
bysolitonsinopticalfibers”,Phys.Rev.A51,2602(1995).
2. J.M. Dudley, G. Genty, and S.Coen, ”Supercontinuum gen-
19. M.Erkintalo,Y.Q.Xu,S.G.Murdoch,J.M.Dudley,andG.
eration in photonic crystal fiber”, Rev. Mod. Phys. 78, 1135
Genty, ”Cascaded Phase Matching and Nonlinear Symmetry
(2006).
Breaking in Fiber Frequency Combs”, Phys. Rev. Lett. 109,
3. J.K.Ranka,R.S.Windeler,andA.J.Stentz,”Visiblecontin-
223904(2012).
uumgenerationinair-silicamicrostructureopticalfiberswith
20. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, ”Dis-
anomalousdispersionat800nm”,Opt.Lett.25,25(2000).
persivewavegenerationbysolitonsinmicrostructuredoptical
4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.
fibers”,Opt.Express12,124(2004).
Windeler, J. L. Hall, and S. T. Cundiff, ”Carrier-Envelope
21. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A.
PhaseControl of Femtosecond Mode-Locked Lasersand Di-
Diddams,K.Weber,andR.S.Windeler,”FundamentalNoise
rectOpticalFrequencySynthesis”,Science288,635(2000).
Limitations to Supercontinuum Generation in Microstructure
5. I.Hartl,X.D.Li,C.Chudoba,R.K.Ghanta,T.H.Ko,J.G.Fu-
Fiber”,Phys.Rev.Lett.90,113904(2003).
jimoto,J.K.Ranka,andR.S.Windeler,”Ultrahigh-resolution
22. Q. Lin, O. J. Painter, and G. P. Agrawal, ”Nonlinear optical
opticalcoherencetomographyusingcontinuumgenerationin
phenomenainsiliconwaveguides:modelingandapplications”,
an air?silica microstructure optical fiber”, Opt. Lett. 26, 608
Opt.Express15,16604(2007).
(2001).
23. R.A.SorefandB.R.Bennett,”Electroopticaleffectsinsili-
6. S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M.
con”,IEEEJournalofQuantumElectronics23,123(1987).
Kobtsev, S. Kukarin, and S. K. Turitsyn, ”Optical spectral
24. J.Matres,G.C.Ballesteros,P.Gautier,J.-M.Fe´de´li,J.Mart´ı,
broadening and supercontinuum generation in telecom appli-
andC.J.Oton,”Highnonlinearfigure-of-meritamorphoussil-
cations”,Opt.Fib.Technol.12,122(2006).
iconwaveguides”,Opt.Express21,3932(2013).
7. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R.
25. R.Claps, D.Dimitropoulos, V.Raghunathan, Y.Han, andB.
Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, and
Jalali,”ObservationofstimulatedRamanamplificationinsili-
A. L. Gaeta, ”Modelocking and femtosecond pulse genera-
conwaveguides”,Opt.Express11,1731(2003).
tion in chip-based frequency combs”, Opt. Express 21, 1335
26. O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, ”All
(2013).
opticalswitchingandcontinuumgenerationinsiliconwaveg-
8. T.Herr,V.Brasch,J.D.Jost,C.Y.Wang,N.M.Kondratiev,M.
uides”,Opt.Express12,4094(2004).
L.Gorodetsky,andT.J.Kippenberg,”Temporalsolitonsinop-
27. J.M. Dudley andJ.Taylor (ed.).Supercontinuum generation
ticalmicroresonators”,NatPhotonadvanceonlinepublication,
inopticalfibers.CambridgeUniversityPress,2010.
(2013).
28. Y.Silberberg,”Solitonsandtwo-photonabsorption”,Opt.Lett.
9. M.R.Lamont,B.Luther-Davies,D.-Y.Choi,S.Madden,and
15,1005(1990).
B.J.Eggleton,”Supercontinuumgenerationindispersionen-
29. V.V.Afanasjev, J.S.Aitchison,andY.S.Kivshar,”Splitting
gineeredhighlynonlinear(? =10/W/m)As2S3chalcogenide
of high-order spatial solitons under the action of two-photon
planarwaveguide”,Opt.Express16,14938(2008).
absorption”,Opt.Comm.116,331(1995).
10. R.Halir,Y.Okawachi,J.S.Levy,M.A.Foster,M.Lipson,and
A.L.Gaeta,”Ultrabroadbandsupercontinuumgenerationina
CMOS-compatibleplatform”,Opt.Lett.37,1685(2012).
11. J. Safioui, F. Leo, B. Kuyken, S-P. Gorza, S. Selvaraja, R.
Baets, Ph. Emplit, G. Roelkens and S. Massar, ”Supercon-
tinuumgenerationinhydrogenatedamorphoussiliconwaveg-
uides at telecommunication wavelengths”, Opt. Express 22,
3089(2014).
12. I.-W.Hsieh,X.Chen,X.Liu,J.I.Dadap,N.C.Panoiu,C.-Y.
Chou,F.Xia,W.M.Green,Y.A.Vlasov,andR.M.Osgood,
”Supercontinuum generation in silicon photonic wires”, Opt.
Express15,15242(2007).
13. W.Ding,A.V.Gorbach,W.J.Wadswarth,J.C.Knight,D.V.
Skryabin,M.J.Strain,M.Sorel,andR.M.DeLaRue,Opt.
Express18,26625(2010).
14. B.Kuyken,X.Liu,R.M.OsgoodJr.,R.Baets,G.Roelkens,
andW.M.J.Green,”Mid-infraredtotelecom-bandsupercon-
tinuumgenerationinhighlynonlinearsilicon-on-insulatorwire
waveguides”,Opt.Express19,20172(2011).
15. M.R.Lamont,R.K.Lau,A.Griffith,Y.H.Wen,Y.Okawachi,
M. Lipson, and A. L. Gaeta, ”Mid-Infrared Supercontinuum
Generation in SiliconWaveguides”, in CLEO: 2013 (Optical
SocietyofAmerica,2013),p.CW3H.1.
16. H.Rong,Y.-H.Kuo,S.Xu,A.Liu,R.Jones,M.Paniccia,O.
Cohen, and O. Raday, ”Monolithic integrated Raman silicon
laser”,Opt.Express14,6705(2006).
5