Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators

0.68 MB·English

by  Serge Rosenblum

Cavity ring-up spectroscopy for ultrafast sensing with optical
microresonators
Serge Rosenblum1†, YuliaLovsky1†, LiorArazi1, Frank Vollmer2 andBarak Dayan1⋆
5
1
0
2
Spectroscopy of whispering-gallery mode propagating modes)4,8 or a shift (due to modification of
n
a (WGM)microresonatorshasbecomeapowerfulscien- theopticalpathlength)5,11. Thetypicalscaleofallthese
J tifictool,enablingdetectionofsingleviruses,nanopar- spectralvariationsisoftheorderofafew MHzormore,

7 ticles, and even single molecules. Yet the demon- inprincipleallowingtheirdetectiononatimescaleofless
strated timescale of these schemes has been limited thanamicrosecond.

]
s so far to milliseconds or more. Here we introduce However,althoughtherearefastmethodstosepa-
c a novel scheme that is orders of magnitude faster, ratelymeasuresplitting6,12, broadening10 orashift13, the
i
t capable of capturing complete spectral snapshots of only method for obtaining the full spectrum had so far
p
WGM resonances at nanosecond timescales: cavity beenlaser scanning. Laserscanningis slow notonlybe-
o
. ring-upspectroscopy(CRUS).Basedonsharply-rising cause of technical reasons. It is inherently slow since in
s
c detuned probe pulses, CRUS combines the sensitivity orderto accuratelycapturethe cavity spectrum, the laser
i ofheterodynemeasurementswiththehighestpossible, mustscanoverthecavityresonance(ofwidth2κ)duringa
s
y transform-limited acquisition rate. As a demonstra- timelongenoughfortheintracavityfieldtocontinuously
h tion we capture spectra of microtoroid resonators at maintain a steady state. The timescale for this duration
p time intervals as short as 16 ns, directly monitoring is determined by the cavity lifetime τ (=1/4πκ), mean-
[
sub-microseconddynamicsoftheiroptomechanicalvi- ingthatthescanrateneedstobesignificantlyslowerthan

1 brations, thermorefractiveresponse and Kerr nonlin- κ/τ. Accordingly,to acquirea spectralscan overa total
v earity. CRUS holds promise for the study of fast bio- bandwidthB,thetotalscantimeneedstoexceedNτ,with
3 logicalprocessessuchasenzymekinetics,proteinfold- N =B/κrepresentingtheeffectivenumberoffrequency
2
ing and light harvesting, with applications in other pointsacquiredduringthescan. Yetthisscantimeisnot
4
1 fieldssuchascavityQEDandpulsedoptomechanics. optimal: the fundamental limit for the duration of such
0 aspectralmeasurementisdefinedbythetime-bandwidth
1. Introduction uncertaintyrelation(ortheFourierlimit),andissetbythe
0 desired spectral resolution (κ) to be roughly τ. In other
5 The remarkable sensitivity of WGM microresonators1,2 words,ascanmeasurementisatleastN timesslowerthan
1 stems from their small mode volume (V ∼ 100 µm3), aFourier-limitedone.
: which enhances the electric field associated with every
v Here we presentCRUS as an ultrafast methodfor
Xi photon, and their ultra-high quality factor (Q ∼ 108), acquiringcompletespectralsnapshotsofWGMresonators
which enables very long cavity lifetimes. This leads to
at the minimaltimescale set by the Fourierlimit. CRUS
r enhancementoftheinteractionwithanyobjectwithinthe
a relies on the abrupt turn-on of far-detuned probe laser
mode3–7 byafactorproportionaltoQ/V. Asaresult,the
pulses(δ ≫ 2κ),thatarecoupledtotheWGMmicrores-
presenceofevennanoscaleobjectswithintheevanescent
onator(amicrotoroid14inourcase)throughataperedop-
field of the WGM can lead to detectable variationsin its
tical fibre15 (Fig. 1a). At such a large detuning, most of
spectrum8. Specifically, these variations include broad-
thelightistransmittedthroughthefiberwithoutentering
ening(dueto shorteningof the cavity lifetime)9,10, split-
the cavity. However, the short rise time t of the pulse
r
ting (due to induced cross-talk between its two counter-
correspondstoabroadspectraldistributionofbandwidth
B ∼1/t .Accordingly,ifthecavityresonancelieswithin
r
1DepartmentofChemicalPhysics,WeizmannInstituteofScience, thisbandwidth(δ < B),thisturn-onleadstothebuildup
76100 Rehovot, Israel, 2Laboratory of Nanophotonics & Biosensing, ofasmall,transientfieldinthecavity.Thisfieldthenradi-
Max Planck Institute for the Science of Light, D-91058 Erlangen,
Germany; †These authors contributed equally to this work. ⋆e-mail: atesbackintothefibre,whereitinterfereswiththetrans-
[email protected] mittedfield, creatinga ring-upsignal. Thespectrumcan
1
nowberetrievedwitharesolutionof∼κ(orbetter)byac- a
quiringthisring-upsignalduringatimeofτ (orlonger).
CRUS therefore enables monitoring kinetics and
events in the nanosecond regime, drastically expand-
ingthecapabilitiesdemonstratedinpreviousschemes3–6,
whichhavefocusedonslowdetectionoflong-termevents,
suchasbindingofvirusesornanoparticlesto thesurface
ofthemicroresonator.
b c
This situation is reminiscent of the well-known
method of cavity ring-down spectroscopy (CRDS), in
which the field emitted from a cavity is directly mea-
sured by abruptly turning off a resonantprobe16. CRDS
iswidelyusedasasensitivemethodforabsorptionspec-
troscopy of gaseous samples in Fabry-Pe´rot resonators.
Since CRDS captures only the intensity of the ring-
down signal, it providesno knowledgeof the center fre-
quency of the resonance, and therefore cannot be used
Figure 1: Outline of the principles of CRUS. a, SEM-
todetectspectralshifts(nordoesitenablereconstruction
image of a tapered-fibre coupled microtoroid. Sharply-
of asymmetric spectra). Accordingly, its application to
risingdetunedprobepulses(leftinset)leadtothebuildup
WGMmicroresonatorshadsofarbeenlimitedtoQ-factor
ofacavityfield. Asthisweakfieldleaksbackintothefi-
measurements14.
bre,itinterfereswiththeprobe,resultinginabeatingsig-
Incontrast,inCRUSthefar-detunedprobe,which
nalattheoutput(rightinset). b, Thering-upsignals(t).
continuesinthefibre,servesasalocaloscillatorasitinter-
Thedetuningδ fromtheprobeisexhibitedbythefastos-
fereswiththeemittedcavityfield.Theresultisthereforea
cillations, the resonancewidth2κ is exhibitedbythe ex-
robustheterodynemeasurementofboththeamplitudeand
ponentialdecayenvelope,andtheslowbeatnoteindicates
the phase of the cavity field, which allows unambiguous
the splitting of the resonance 2g. c, Fourier transform-
extraction of the complete spectrum, including its center
ings(t) allowsretrievalof the completespectrum(black
frequency. The difference between CRUS and CRDS is
curve),showingexcellentagreementwiththefourorders
thereforeanalogoustothedifferencebetweenahologram,
ofmagnitudeslowerscanmeasurement(bluecurve).Both
which captures both the amplitude and the directionality
spectra were taken with similar peak intracavity energy
oftheobjectwavefront,toapicture,whichcapturesonly
(∼100fJ,setbelowthevisibleonsetofnonlineareffects).
itsintensity. Inthisview, thelargedetuningbetweenthe
probe and the resonance is analogous to the large angu-
cavity,i.e. Y(ω) = X(ω)+X(ω)H(ω),whereH(ω)is
larseparationbetweenthe referencebeamandthe object
thecavity’stransferfunction.ByFouriertransformingthe
inanoff-axishologram,whichpreventsoverlapbetween
ring-upsignals(t)andusingthefactthatduetothelarge
positiveandnegativefrequencies(theobjectandits con-
detuningH(ω)containsonlypositivefrequencies,weget
jugate)duringthereconstruction.
H(ω)=S(ω)/X(ω),finallyyielding(seeMethods)
2
T(ω) = |1+S(ω)/X(ω)| .
Results Figure 1c presents the spectrum obtained from a single-
shot, 500 ns pulse performed on a resonance with Q =
Figure 1b presents the measured ring-up signal, defined 1×108at780nm,showingexcellentagreementwiththe
ass(t) = |y|2−x|x|2, wherexandy aretheinputandout- much slower (5 ms) single-shot scan measurement. The
put fields, respectively. The main features of the WGM fundamentalorigin of the drastic difference between the
resonancealreadyappearinthissignal. Accordingly,s(t) speedsofCRUSandaregularscanisclearlyillustratedin
enables complete retrieval of the transmission spectrum Fig. 2, which simulates scans of the spectrum of Fig. 1c
T(ω) = |Y(ω)/X(ω)|2, which by the final value theo- at various speeds. The fact that CRUS is a transform-
rem is identical to that obtained by frequency scanning limitedmeasurementwhereasascanmeasurementisnot,
(where X,Y are the Fourier transformsof x, y). This is is clearly exhibited by the ringing effects that appear at
donebynotingthattheoutputfield resultsfrominterfer- shortscantimes17.
ence between the input field and the emission from the
2
a b c
Figure 2: Comparison of scanning spectroscopy and CRUS. Simulated scan measurements (black curves) of the
spectrum of a resonatoridentical to that of Fig. 1 (red curves), with scan times of a, 2 µs, b, 20 µs and c, 100 µs,
assumingatotalscanrangeof500MHz(notentirelyshowninfigure).Thebluecurveincshowsthesimulatedresult
ofaCRUSmeasurementusinga200nsring-upsignal.
a b c
pump on
pump on
pump off
Figure 3: Thermal and Kerr nonlinearities measured by CRUS. The graphs show the center frequency of the
probedWGM(reddots,interpolationinblue)asextractedfromCRUSspectrafor:a,Thermaloscillationsinducedby
theturn-onofapumpbeammodulatedat300kHz. Theoscillationsaresuperimposedonadriftingcentralfrequency
whichreflectsthegradualincreaseinthemicrotoroid’saveragetemperature. Thespectrawerecapturedevery200ns.
Theinsetshowsthephaselagbetweentheinducedoscillationsandthepump(blackcurve). b, Therelaxationofthe
resonantfrequencyfollowingtheturn-offofthepump. Thecoolingofthecavitycanbeseparatedintoa slowdecay
(correspondingto a cutofffrequencyof Ω1 = 5.1kHz) anda fast decay(cutofffrequencyΩ2 = 210kHz). c, Kerr
oscillationsinducedby the turn-onof a pumpbeammodulatedat5.5MHz. The spectrawere capturedevery37ns.
TheinstantaneousresponseoftheKerreffectisexhibitedbynearlyzerophaseshiftwithrespecttothepump(inset).
The ability to rapidly capture the entire spectrum ities.
also makes CRUS more resilient to various noise mech- As a first demonstrationof the potentialof CRUS
anisms (such as amplitude noise) that typically occur at for capturing ultrafast phenomena, we applied it to fully
lower frequencies and can distort a scan measurement, characterizethenonlinearitiesofthemicrotoroid.Forthis
whichsamplesdifferentpartsofthespectrumatdifferent purposeweusedamodulatedpumplaser(seeMethods)to
times. Indeed,asevidentfromFig.1c,thesignal-to-noise inducespectralvariationsin theprobedWGM resonance
ratio of CRUS is comparable to that of the much slower throughthermal21,Kerr22,23andoptomechanicaleffects25.
scan. CRUS also has the inherent advantage of hetero-
Figure3ashowstheresponseofthemicrotoroidto
dynemeasurements,whichreadilyenableshot-noiselim-
anabruptturn-onofa300kHzmodulatedpump,asexhib-
itedsensitivities(aswasdemonstratedforheterodynede-
itedbythevariationsinthecenterfrequencyofa54MHz
tection of cavity ring-down by Levenson et al.18,19, and
WGM resonance(fullwidth at halfmaximum), captured
forprobingofWGMnonlineardynamics20).Sensitivede-
byCRUSatintervalsof200ns. Asdemonstratedinpre-
tectionofweakfieldsis extremelyimportantwithWGM vious works21,26, for modulation frequenciesbelow ∼ 1
microresonators, in which the intracavity power must be
MHzthenonlinearityofthemicrotoroidisdominatedby
keptverylow,topreventtheonsetofundesirednonlinear-
itsthermalresponse,whichisgovernedbytwoprocesses
3
with different timescales21,26. The short timescale is set oscillationsbycontinuousmonitoringoftheentireWGM
by the conduction rate of heat from the optical mode to spectrum-ataskfarbeyondtheabilityoflaserscanning.
the rest of the cavity, and the longer corresponds to dis-
sipation of heat from the entire cavity to the silicon sub-
strate through the pillar. The high rate of CRUS allows
accurate extraction of these timescales directly from the Discussion
cavity’stemporalresponsetoabruptturn-offofthepump,
By acquiringmaximalknowledgeon the spectrumat the
asshowninFig.3b.
shortestpossibletimescale,CRUSintroducesthepromis-
The CRUS measurements also reveal a phase lag
ing field of optical sensing with WGM microresonators
of50◦±1◦ betweenthecavityoscillationsandthepump intothenanosecondregime.Asaspecificexample,Fig.4c
modulation(insetof Fig. 3a), which is a resultof the in-
terplay between the two capacitive thermal mechanisms
and the much weaker, frequency-independentKerr non- a
linearity. By measuring this phase shift as a function of
modulation frequency we find that the heating rates are
≈ 6,700K/W/100nsfortheslowmechanismand≈ 700
K/W/100 ns for the fast mechanism, in good agreement
withtheory27.
Figure 3c shows the cavity’s center frequency re-
sponse to abrupt turn-on of a pump laser modulated at
5.5 MHz, extracted from spectral snapshots taken every
b
37ns. Atthishighfrequencythenonlinearityofthecav-
ityisdominatedbytheKerreffect22,26 (superimposedon
the slower thermal drift), with the corresponding instan-
taneous response exhibited by a nearly zero phase shift
(4◦±1◦)withrespecttothepumpmodulation(seeinset).
As a final demonstration of the capabili-
ties of CRUS we directly monitor optomechanical
oscillations24,25,28ofthemicrotoroidataratemuchfaster c
thantheoscillationfrequency.Suchpulsedmeasurements
are of particular interest in the context of quantum
non-demolition measurements of mechanical motion29.
Forthis purposewe tuned the pumpto excite the second
ordercrownmodeofthemicrotoroid(insetofFig.4a).
Figure 4a presents the measured time-varying
spectrum of a 90 MHz WGM resonance, captured at
intervals of 25 ns. The graph clearly displays the varia-
tions of the resonance resulting from the oscillations of
Figure 4: CRUS measurements of optomechanicalos-
the microtoroid’s circumference at 8 MHz. Figure 4b
cillations. a, Measured spectra of a microresonator os-
displaysthe center frequencyshift extractedfrom CRUS
cillatingmechanicallyat8MHz,ascapturedbyCRUSat
spectraofanothermicrotoroid,inwhichthefrequencyof
intervalsof25ns. b,Thecenterfrequencyshift(reddots,
the second-order crown mode was 12.5 MHz. Here the
interpolationinblue)ofa microresonatoroscillatingme-
spectra were taken at intervals of 16 ns. The extracted
chanicallyat12.5MHz,extractedfromCRUStakenevery
phasedifferencebetweenthemechanicaloscillationsand
16ns. The oscillationsdisplaya π/2 phaseshiftrelative
the pump is 89◦ ± 1◦, in agreement with the expected
tothepump(blackcurve)andcontinueafterthepumpis
valueofπ/2foraresonantlydrivenoscillator. Thereso-
turnedoff,asexpectedfromaresonantlydrivenoscillator.
nantbehavioroftheseoscillationsisalsoexhibitedbythe
c,SimulatedCRUSperformedevery150ns, fora75nm
fact that they continue after the pump is abruptly turned
radiusnanoparticlewithrefractiveindexn=1.5crossing
off. Bymeasuringthedecayrateoftheseoscillationswe
the evanescent field of a 10 MHz WGM at a speed of 1
obtain a mechanical quality factor of 300. These results
m/s, with distance of closest approach of 150 nm (mea-
provide the first direct observation of optomechanical
suredfromtheparticlecentertotheresonatorsurface).
4
presentsanumericalsimulationofananoparticlewithra- gallery microlasers. Nature nanotechnology 6, 428–432
diusof75nmflyingbythemicrotoroid.Asevidentinthis (2011).
example, CRUS enables simultaneousobservationof the
7. Dantham,V.R.etal. Label-freedetectionofsingleprotein
shift, splitting and broadeninginducedby the interaction usingananoplasmonic-photonichybridmicrocavity. Nano
with the nanoparticle. Looking forward, these abilities Letters13,3347–3351(2013).
openthepathforthestudyofultrafastphenomenainvar-
8. Mazzei,A.etal.Controlledcouplingofcounterpropagating
iousfields, suchasmicromechanicalvibrations29,30, cav-
whispering-gallery modes byasingle rayleigh scatterer: a
ity QED31 and fast biological processes such as enzyme
classicalprobleminaquantumopticallight.Physicalreview
kinetics32,lightharvesting33andproteinfolding34. letters99,173603(2007).
Methods 9. Shao, L. et al. Detection of single nanoparticles and
lentiviruses using microcavity resonance broadening. Ad-
Theprobelaser(at780nm)wasintensitymodulatedwith vancedMaterials25,5616–5620(2013).
a LiNbO3 electro-optic modulator, yielding pulses with
10. Truong,G.-W.etal. Frequency-agile,rapidscanningspec-
risetimestypicallybelow1ns. Thepulselengthwasset
troscopy. NaturePhotonics7,532–534(2013).
bytherequiredspectralresolution,andthecavitylifetime
wastunedtobesignificantlyshorterbyincreasingthecou- 11. Arnold, S., Khoshsima, M., Teraoka, I., Holler, S. &
Vollmer, F. Shift of whispering-gallery modes in micro-
pling to the tapered fibre. To allow separation from the
spheres by protein adsorption. Opticsletters28, 272–274
probe,thepumplaserwastunedtoaWGMresonanceat
(2003).
770 nm (differentfrom the probed resonance) and set to
becounterpropagatingtotheprobe. 12. Knittel,J.,Swaim,J.D.,McAuslan,D.L.,Brawley,G.A.&
Bowen,W.P. Back-scatterbasedwhisperinggallerymode
Duetothelargedetuning,thetermquadraticinthe
sensing. Scientificreports3(2013).
cavityemissionisneglectedintheretrievalalgorithm,as
it is much weaker than the probe. Additionally, it was 13. Keng, D., McAnanama, S.,Teraoka, I.&Arnold, S. Res-
assumed that the input field x has a constant phase, and onancefluctuationsofawhisperinggallerymodebiosensor
byparticlesundergoingbrownianmotion. AppliedPhysics
accordinglyit was treated as real. This assumption typi-
Letters91,103902–103902(2007).
callyholdsexcept,insomecases,duringthepulserise. If
thepulserisetimeissignificantlyshorterthanδ−1,thisef- 14. Armani,D.,Kippenberg,T.,Spillane,S.&Vahala,K.Ultra-
fectcanstillbeneglected.Otherwise,accurateretrievalof high-qtoroidmicrocavityonachip. Nature421, 925–928
the spectrum requires knowledge of this transient phase, (2003).
whichdependsonthespecificmodulationtechniqueused 15. Knight, J., Cheung, G., Jacques, F. & Birks, T. Phase-
(inourcaseaZ-cutmodulatorwithachirpfactorof0.7). matchedexcitationofwhispering-gallery-moderesonances
byafibertaper. Opticsletters22,1129–1131(1997).
References
16. O’Keefe, A. & Deacon, D. A. Cavity ring-down opti-
calspectrometerforabsorptionmeasurementsusingpulsed
1. Braginsky, V., Gorodetsky, M. & Ilchenko, V. Quality- laser sources. Review of Scientific Instruments 59, 2544–
factorandnonlinearpropertiesofopticalwhispering-gallery 2551(1988).
modes. PhysicsLettersA137,393–397(1989).
17. Matone, L. et al. Finesse and mirror speed measurement
2. Vahala, K.J. Opticalmicrocavities. Nature424, 839–846 forasuspendedFabry–Perotcavityusingtheringingeffect.
(2003). PhysicsLettersA271,314–318(2000).
3. Vollmer, F.,Arnold, S.&Keng, D. Singlevirusdetection 18. Levenson,M.D.etal. Opticalheterodynedetectionincav-
fromthereactiveshiftofawhispering-gallerymode. Pro- ityring-down spectroscopy. Chemical physicsletters290,
ceedingsoftheNationalAcademyofSciences105,20701– 335–340(1998).
20704(2008).
19. Levenson, M. D. et al. Frequency-switched heterodyne
4. Zhu,J.etal. On-chipsinglenanoparticledetectionandsiz- cavity ringdown spectroscopy. Optics letters25, 920–922
ingbymodesplittinginanultrahigh-qmicroresonator. Na- (2000).
turePhotonics4,46–49(2009).
20. Lin,Q.,Johnson,T.J.,Michael,C.P. &Painter,O. Adi-
5. Lu, T. et al. High sensitivity nanoparticle detection using abatic self-tuning in a silicon microdisk optical resonator.
opticalmicrocavities.ProceedingsoftheNationalAcademy Opticsexpress16,14801–14811(2008).
ofSciences108,5976–5979(2011).
21. Ilchenko, V. &Gorodetskii, M. Thermal nonlinear effects
6. He, L.,O¨zdemir, S¸.K.,Zhu, J.,Kim, W.&Yang, L. De- inoptical whisperinggallerymicroresonators. LaserPhys
tecting single viruses and nanoparticles using whispering 2,1004–1009(1992).
5
22. Rokhsari,H.&Vahala,K.J. Observationofkerrnonlinear-
ityinmicrocavitiesatroomtemperature. Opticsletters30,
427–429(2005).
23. Vukovic, N. et al. Ultrafast optical control usingtheKerr
nonlinearityinhydrogenatedamorphoussiliconmicrocylin-
dricalresonators. Scientificreports3,02885(2013).
24. Kippenberg,T.&Vahala,K. Cavityoptomechanics: back-
actionatthemesoscale. Science321,1172–1176(2008).
25. Rokhsari, H., Kippenberg, T., Carmon, T. & Vahala, K.
Radiation-pressure-drivenmicro-mechanicaloscillator.Op-
ticsExpress13,5293–5301(2005).
26. Schliesser,A.,Del’Haye,P.,Nooshi,N.,Vahala,K.&Kip-
penberg,T. Radiationpressurecoolingofamicromechani-
caloscillatorusingdynamicalbackaction. PhysicalReview
Letters97,243905(2006).
27. Schliesser,A. Cavityoptomechanicsandopticalfrequency
comb generation with silica whispering-gallery-mode
microresonators (Thesis, Ludwig-Maximilians-Universita¨t
Mu¨nchen,2009).
28. Aspelmeyer,M.,Kippenberg,T.J.&Marquardt,F. Cavity
optomechanics. arXivpreprintarXiv:1303.0733(2013).
29. Vanner,M.R.etal. Pulsedquantumoptomechanics. Pro-
ceedingsoftheNationalAcademyofSciences108,16182–
16187(2011).
30. Krause,A.G.,Winger,M.,Blasius,T.D.,Lin,Q.&Painter,
O.Ahigh-resolutionmicrochipoptomechanicalaccelerom-
eter. NaturePhotonics6,768–772(2012).
31. Aoki,T.etal. Observationofstrongcouplingbetweenone
atomandamonolithicmicroresonator.Nature443,671–674
(2006).
32. Yasuda, R.,Noji,H.,Yoshida,M.,Kinosita, K.&Itoh,H.
Resolutionofdistinctrotationalsubstepsbysubmillisecond
kineticanalysisoff1-atpase. Nature410,898–904(2001).
33. Perman, B. et al. Energy transduction on the nanosecond
timescale: earlystructuraleventsinaxanthopsinphotocy-
cle. Science279,1946–1950(1998).
34. Mayor,U.etal. Thecompletefoldingpathwayofaprotein
fromnanoseconds tomicroseconds. Nature 421, 863–867
(2003).
AuthorContributions
Y.L.,S.R.,andB.D.conceivedtheidea.Y.L.andS.R.conducted
theexperimentsandanalysedthedata. B.D.,Y.L.,S.R.andF.V.
wrotethemanuscript. Allauthorscontributedtothedesignand
construction of theexperiment, discussed the resultsand com-
mentedonthemanuscript.
Additionalinformation
Theauthorsdeclarenocompetingfinancialinterests.Correspon-
denceandrequestsformaterialsshouldbeaddressedtoB.D.
6