Optical trapping and polarization-controlled scattering of dielectric spherical nanoparticles by femtosecond laser pulses

ContentslistsavailableatSciVerseScienceDirect

Journal

of

Photochemistry

and

Photobiology

A:

Chemistry

j o u r n al hom ep age : w w w. e l s e v i e r . c o m / l o c a t e / j p h o t o c h e m

Optical

trapping

and

polarization-controlled

scattering

of

dielectric

spherical

nanoparticles

by

femtosecond

laser

pulses

Anwar

Usman

∗

,

Wei-Yi

Chiang,

Hiroshi

Masuhara

∗

DepartmentofAppliedChemistryandInstituteofMolecularScience,NationalChiaoTungUniversity,Hsinchu30010,Taiwan

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received23October2011 Receivedinrevisedform 19November2011 Accepted21November2011 Available online 12 January 2012 Keywords:

Opticaltrapping Dielectricnanoparticles Lorentzforce

a

b

s

t

r

a

c

t

Wepresentopticaltrappingbehaviorof50-nm-sizedpolystyrenebeads,suspendedinwatermedium, byfemtosecondpulsedlaserbeam.Inadditiontoahighernumberofnanoparticlestrappedatthefocal spotbytheultrashortlaserpulsescomparedwiththatbycontinuous-wavelaser,thenanoparticlesare scatteredoutofthefocalspotbythelaserpulsestothesurroundingarea.Thescatteredparticlesform apartiallyopenedfoldingfan-shapedbrightlocusintwooppositedirections,inanalternatingmanner, perpendiculartothelaserpolarization.Tounderstandthosephenomena,weanalyzedradiation(gradient andscattering)forceoffemtosecondlaserpulsesandtheirtemporalforceexertedonthedielectric sphericalnanoparticlesbytakingintoaccounttheimpulsivepeakpowerandtheaxialcomponentof electriclightfieldproducedbyhighnumericalapertureofobjectivelens.Weshowthattheaxialelectric fieldisresponsibleforlateralcomponentsofthescatteringandtemporalforces,andhence,controlsthe scatteringdirectionsoftheRayleighparticles.Thesefindingsprovideimportantinformationaboutthe dynamicopticaltrappingoftheRayleighparticlesbyhighlyfocusedultrashortlaserpulses.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Oneofthesuccessfulapplicationsofmode-lockedlasersisthe ultrafasttime-resolvedspectroscopies,whichprovidethe absorp-tion,vibrational, or emission spectraofatoms or molecules on extremelyshorttimescalesaftertheirexcitationwithultrashort laserpulses.TheresearchgroupofProf.M.Martinisoneofpioneers whohaveutilizedtransientabsorptionspectroscopytodecipher thedynamicsandmechanismsoffundamentalphoto-induced pro-cesses [1]. Their reports on the insights of driving forces and primaryoccurringeventsinthephoto-induceddynamicsofvarious chromophores,photoactiveproteins,orbiomimeticsareimportant advancesinourunderstandingofthephoto-processes,particularly thefunctionalityofthebiomaterialsinrelationwiththeirelectronic structures[2–7].

Anotherimportantlaser application is opticaltrapping (also calledopticaltweezers),exploitingtheopticalgradientforce,which canconfinemicrometertosubmicrometer-sizedobjectsinthefocal spot[8,9]. Inthis phenomenon, a highnumericalaperture lens

∗ Correspondingauthorsat:DepartmentofAppliedChemistryandInstituteof MolecularScience,NationalChiaoTungUniversity,1001TaHsuehRd.,Hsinchu 30010,Taiwan.Tel.:+88635712121x56595.

E-mailaddresses:[email protected](A.Usman), [email protected](H.Masuhara).

isnecessarilyrequiredtofocustightlythecontinuous-wave(cw) laserbeamsintoa diffraction-limitedspotsize[10,11].Withits potentialabilityofnon-destructivetool toimmobilize,reorient, andtransferthemicro-to-submicrometersizeddielectricor metal-licparticles,thistechniquehasbeenwidelyappliedinvariousfields ofscienceswithtargetmaterialsrangingfromsmallparticles[12], polymers[13,14],clustersof amino acids[15–19], tobiological substances[20],andhasbecomeindispensableinsingle-molecule measurements[21,22].

Recently,theopticaltrappingtechniqueisfurtherdevelopedby utilizingultrashortlaserpulses.Bythefemtosecondlaserpulses, opticaltrappingofmicrometer-sizedsilicasphereswasfoundtobe aseffectiveascwopticaltweezers,andtrapstiffnesswasrelated toaveragepowerofthelaserpulses[23].Withtheultrashortlaser pulses,however,severalphenomenahavebeenrevealed, includ-ingopticaltrappingofassmallasafewnm-sizedCdTequantum dotsorthedepositionsofCdSnanoparticleswithgrainsizedown to25nm[24,25].Forthetrappingofgoldnanoparticlesbylaser pulses,thetrappingsite splitsupintotwoequivalentpositions aroundthefocalcenter,demonstratingthathighnonlinear opti-calsusceptibilityofthetargetmaterialscanmodifytheshapesof gradientforceandtrappingpotential[26].Morerecently,the fem-tosecondlaserpulseswiththepowerlessthan200mWhasbeen successfullyappliedtoconfineanindividualpolystyrenebeadwith adiameterofafewtensofmicrons(theparticlesizeswithinthe frameworkofgeometricalopticsregime),butthemicroparticlewas 1010-6030/$–seefrontmatter © 2012 Elsevier B.V. All rights reserved.

LorentzforceoffundamentalGaussianbeamexertedonRayleigh particles[10,28],andbyapplyingscatteringcrosssectionvalueof thenanoparticlesobtainedbasedonMietheory[29].We demon-stratethattheaxialelectricfieldproducedbythehighnumerical aperture objective lens is responsible for the present novel phenomenon.

2. Experimental 2.1. Opticalsetup

To experimentally exemplify the trapping behavior of the nanoparticlesbyfemtosecondlaserpulses,wedevelopedan exper-imentalsetupbasedonaninvertedmicroscope(OlympusIX71), as shown in Fig. 1. We used a 800-nm fundamental mode of Ti:sapphire(Tsunami;SpectraPhysics)laserbeam,whichcanbe operatedincworfemtosecond-pulsemode,actingasthetrapping beam.Whenitwasoperatedinthepulsemode,thepulse dura-tionwascompressedbyapairofprismstobeabout90fs,andthe repetitionratewas80MHz.Thepolarizationdirectionofthelaser beamwascontrolledbyahalf-waveplatebeforethebeamwas col-limatedandexpandedto∼5mmindiameterbyapairofpositive lenseswithfocallengthbeing100and200mm,respectively.The beamthenwasfocusedthroughanobjectivelens(60×,NA=0.90) atnormalincidenceintoasamplecell,whichwasplacedonthe samplestageofthemicroscope.Thelightpoweraftertheobjective lenswascontrolledintherangeof0.10–0.35W.Thebeamwaist, ω0,atthefocalspotwascalculatedtobe460nm,equivalenttothe

calculatedradiuswhenthebeamintensityofitsfirstAirypattern fallsto1/e2_{ofthemaximumvalue.}

lamppassingthroughacardioidimmersiondarkfieldcondenser lens(Olympus;U-DCWNA=1.4–1.2).Theelasticlightscattering originatedfromthelasertrappingbeamwascompletelycutbya shortwave-passfilterwithtransmissionat380–720nm(Semrock; Brightline750/SP)infrontofcharge-coupleddevice(CCD) cam-era(JAI;CV-A551RE).Withsuchasetuponlythescatteringlight fromhalogenlampbythenanoparticleswascollectedbythe objec-tivelens,andwasdetectedbyusingtheCCDcamerarunningat30 interlacedframespersecond.Thus,thedetectedlightintensitycan berelatedmainlytothescatteringlightintensity,althoughthere ispossiblyaveryminorcontributionofthree-photonexcited flu-orescenceofthebarepolystyrenebeadsduetononlinearoptical effectsifsuchthefluorescencewavelengthislongerthan380nm topasstheshortwave-passfilter.Thepositionsofthenanoparticles wereassociatedwiththeimageofthescatteringlightdetectedby theCCDcamera.Theresolutionoftheimageinthelateral direc-tionwas94nmperpixel,andourobservationlayerwaslimited withintheaxialresolutionoftheobjectivelens(calculatedtobe approximately1.8␮m).

3. Results

Withthelasertrappingbeamoperatedinthefemtosecondpulse modeattheaveragepowerof350mW,weobservedabrighter scat-teringlightatthefocalspotcomparedwiththesurroundingarea. Weshouldnotethatsuchbrightscatteringlightwasneverobserved inaneatsolvent.Inadditiontoscatteringlightatthefocalspot, brightlocusofscatteredpolymerbeads,justlikemultipleshooting stars,fromthefocusspottothesurroundingareawasalsoobserved. Thebrightlocuswasshapedlikeapartiallyopenedfoldingfanalong twooppositedirections,inanalternatingmanner,perpendicular

Fig.1.Schematicdiagramoftheexperimentalset-up;/2ishalfwaveplate,BSisbeamsplitter,andLPFislowpassfilter.Insetisaschematicillustrationofthesamplecell containingthecolloidalsolutionofnanoparticles.

Fig.2. Acombinationoftwohalvesoftwodifferentimageframesshowingopticaltrappingandscatteredpolystyrenenanoparticlesbyfemtosecond-pulsemodesand showingtheiropticaltrappingbycwTi:sapphirelaserbeams(=800nm).(a)–(c)Asharpscatteringlightatthefocalspotandbrightlocusofscatteredpolymerbeads fromthefocusspottothesurroundingareatowardstwooppositedirectionsinanalternatingmannerperpendiculartothelaserpolarizationdirectionoffemtosecondlaser pulses,indicatingtheopticaltrappingofpolystyrenenanoparticlesatthefocalspotandnanoparticleflowsalongthetwooppositedirections.Thelaserpowerforeach caseis350mWaftertheobjectivelens.Arrowineachpanelindicatespolarizationdirectionofthelaserbeam.Thelineprofilesineachpanelweretakenfromonecursor passingthroughthefocalcentertotheoppositecursor,parallelandperpendiculartothepolarizationdirection.Thetwolineprofiles(solidanddottedlines)perpendicular tothepolarizationdirectionarerelatedtothetwoalternatingdirectionsofthescatteringlight.(d)Anunstableandlowscatteringlightintensityfromthefocalspotofcw laserbeamatthesamelaserpower.Arrowinthepanelindicatespolarizationdirection,andthelineprofilesweretakenfromparallelandperpendiculartothepolarization direction.

tothepolarizationdirection.Suchtheeventoccurredrandomly, andsimultaneousbrightlocusalongthetwooppositedirections likeapairoftwopartiallyopenedfoldingfanswasneverobserved. Thus,weshowthebrightlocusalongthetwooppositedirectionsby combiningtwohalvesofdifferentvideoframesinFig.2(a)–(c)(the originalvideosaregiveninVideosS1−S3inSupportinginformation formoredetails).Sincethescatteringlightsdetectedinthevideo imagerepresentthepositionsofthenanoparticles,wetherefore extractedtheprofilesofscatteringlightintensitypassingthrough thefocalcenterasshownineachpanel.Suchlineprofileparallelto thepolarizationdirectionshowsclearlyasinglesharppeakwithan approximately1.6␮mfullwidthathalfmaximumatthefocalspot, whereasthatperpendiculartothepolarizationdirectionindicates theadditionalbrightlocusofscatteredpolymerbeadsalongthetwo oppositedirectionsinanalternatingmanner.Theintensityofthe

brightlocusiscomparabletoeachother.Whenthelaserbeamwas operatedinthecwmodeatthesamelaserpower,onlyatiny scat-teringlightatthefocalspotwasobservedunderthesimilar experi-mentalconditions,buttherewerenoanyobservablebrightlocusof scatteredpolymerbeadsfromthebeamcentertothesurrounding area.Animageframeunderthecw-modelaserirradiationisshown inFig.2(d)(theoriginalvideoisgiveninVideoS4inSupporting information).Thelineprofilespassingthroughthefocalcenter par-allelandperpendiculartothepolarizationdirectionrevealthatthe scatteringlightatthelaserfocalspotofthecwmodeisverylow.

Byvaryingthelaserpower,thethresholdofthefemtosecond laserpulsestoinduceobservablescatteringlightatthefocalpoint andbrightlocusalongthetwooppositedirectionswasobserved at264mWforthehighlyconcentratednanoparticlesolution.We also found that the concentration of the nanoparticles was a

120 100 80 60 40 20 0 0

Light Scattering Intensity/ a.u.

Trapping Time/ s

(b)

0 40 80 120

Time/ s

Scattering Direction Probability

1 0

1

Right

Left

Fig.3.(a)Time-dependentlineprofileintensityunderfemtosecond-pulse(black line)andcwmode(grayline).(b)Thetypicaltime-dependenteventwhenbright locusofscatteredpolymerbeadsfromthefocusspotisalongthetwo alternat-ingleftandrightdirectionswithintheobservationwindowof120s.Experimental informationfordatashowninthefigures(a)and(b)arerelatedtothoseinFig.2(a).

crucialparametertoobservethebrightlocus.Underthelaserpulses attheaveragepowerof350mW,thebrightlocuswasnotobserved whenthecolloidalsolutionwasdilutedbyafactorof4, equiva-lenttotheconcentrationof0.95×1014_{particles/mL.Weconsider}

that,underthesameopticalconditions,thefourfolddilutionled toseverereductionsinthetrappingrate,sizeoftrappedassembly, andnumberofscatterednanoparticles,givingnoimagesofbright locus.

Thetemporalevolutionsofscatteringlightintensityatthefocal spotwhenthelaserbeamwasoperatedinfemtosecond-pulseor cwmodeareshowninFig.3(a).Incontrasttohighintensityof scatteringlight whenthelaserbeamwasoperatedin thepulse mode,lowintensity,unstable,andfluctuatedscatteringlight inten-sitywasobservedunderthecwmode.Incomparison,thescattering lightintensityisaboutoneorderhigherwhenthelaserbeamwas operatedinthepulsemodethanthatundercwmode.

Further,inFig.3(b)weshowtheplotofthetemporalrandom distributionoftheevent,wherethebrightlocuswasobservedalong oneofthetwoalternatingdirectionsperpendiculartothe polariza-tionofthefemtosecondlaserpulses,fortheobservationwindow about120s.Thebrightlocusemergedinonedirectiononthe time-scaleofsecondsbeforetheychangedintotheoppositedirection, andtheycontinuedinthesameway.Theprobabilityandtotal dura-tionofthebrightlocusalongthetwoalternatingdirectionsalmost balancedeachother.

caltrappingexperiments[8,32],butitisincontrasttothetrapsplit of60-nmsizedgoldnanoparticlesbythefemtosecondlaserpulses onthesamelevelofaveragelaserpower[26].Itisnoteworthythat sincethethird-ordernonlinearopticalsusceptibilityis responsi-bleandsensitivetosplitthetrapsiteintotwoequivalentpositions shiftedfromthebeamaxis,thelowerthird-ordersusceptibilityof polystyrenenanoparticles(0.8×10−8esu)[33]ascomparedwith thatofgoldnanoparticles(5_{× 10}−8esu)[34]isthereasonforthe polymernanoparticleshavingnoclearobservablenonlinearoptical effectonthetrapsite.

Here,weinterpretourexperimentalresultsasfollows.Whena nanoparticleenterstheeffectivetrappingareabydiffusion, gradi-entforceduetoasteepgradientofopticalintensityofthehighly focusedultrashortlaserpulsesisexertedonthenanoparticle,and theforcedrags thenanoparticletowardsthesingletrapsite at thefocal center. A stable trapping can only beachieved when thegradientforceovercomesscatteringforce,andthe character-isticstiffness ofopticaltrapshouldbeproportionaltothelaser intensity, as it has been reportedfor the trapping laser in cw mode[21,35].For theultrashort opticalpulses,in particular,in additiontothegradientandscatteringforces,wealsohaveto con-sidertemporalforcewithinthepulseduration,whichisdefined asinstantaneousLorentzforceatthetimeovertheentireduration ofthepulseenvelope[36–38].Inthiscase,thegradientforceof thelaserpulsesshouldovercomesthescatteringandtheir tem-poralforcestoachieveastabletrapping.Consideringthesizesof thenanoparticlesandbeamwaist,multiplenanoparticlescanbe trappedin thesinglepotentialminimum atthefocal spot,and thescatteringlightintensityisproportionallyenhancedwiththe numberoftrappednanoparticlesatthetrapsite.Thus,monitoring suchthescatteringlightintensity,similarlytomonitoringa step-wisebehavioroffluorescenceintensityincreaseinopticaltrapping of100-or200-nm-sizeddye-dopedpolystyrenenanoparticlesby cwlaserbeam[39],wouldprovidetheinformationonthenumber ofnanoparticlesenteringthetrapsite.However,thevideoframes inourexperimentaresaturatedwithinthefirstintegratingtime, hinderingapreciseobservationontheexactnumberofthe opti-callytrappednanoparticles.Nevertheless,basedonthescattering lightintensityatthefocalspot(Fig.3(a))wecouldroughly esti-matethenumberoftrappednanoparticlestobeatleastoneorder higherwhenthelaserisoperatedinthefemtosecondpulsemode comparedwiththatundercwmodeonthesameaveragedlaser power.

Sincetheopticaltrappingpotentialcanonlyfilledbyacertain number of nanoparticles, additional nanoparticles entering the trappingsiteshouldpushandreplacethenanoparticlesoccupying thetrappingsite.Thetrappednanoparticlescanalsoescapeand release themselves from the trapping site by diffusion during theintervalperiodbetweentwolaserpulses. Thenanoparticles escapedfromtheopticaltrappingsitearereadilypushedfarther away from the focal center by scattering or temporal forces. Althoughonesinglepulsemaynotbeableinducethemigrationof

nanoparticlesalongthewayastheyareobservedinthispresent work, but since the laser pulses are repeatedly introduced at thepulserepetitionrateof80MHzintothehighlyconcentrated nanoparticles,we considerthatmultiplenanoparticlesare scat-teredwiththehighfrequency onthesamedirection.Withthis mechanism,thestablequantityofnanoparticlesatthetrapping siteismaintained,resultingintheconstantintensityoflineprofiles observed at thetrapping site, while multiple nanoparticlesare continuouslyscatteredoutofthefocalspotmakingtheirmotions asakindofnanoparticleflow,whichisobservedasthemultiple shootingstarsfromthefocalspottothesurroundingareaforming apartiallyopenedfoldingfan-shapedbrightlocus.Interestingly, thenanoparticle flowsarealong two opposite directions, inan alternating manner,controlledby the laser polarization.In the following,weshowthatsuchthepolarization-controlled nanopar-ticleflowscanbeattributedtotheexistenceoflateralcomponent ofscatteringandtemporalforces.

4.2. Radiationandtemporalforcesactingonadielectricspherical nanoparticle

LetusconsiderthefundamentalmodeofGaussianbeam prop-agating without distortion in a medium containing dielectric spheres.Thebeamis tightlyfocusedbya highnumerical aper-tureobjectivelens,convergingtoanear-diffraction-limitedsize withafocalwaistbeingω0,andthenreexpanding.Here,we

con-siderthatLorentzforceactsonadielectricsphericalnanoparticle duetointeractionsbetweenlightelectricfieldandinduceddipole momentofthepolarizabledielectricsphere.Theinduced polar-izationcanbeapproximatelyexpressedas,P=E,whereisthe electricsusceptibility.Forauniformdielectricsphere,the suscep-tibilityis isotropicand thepolarizationPis paralleltoE. Thus, thegradientforce,relatedtospatialLorentzforce,exertedonthe nanoparticlescanbeexpressedas[28]

Fgrad=[P· −→

∇

]E= 1 2˛− →

_∇

_|E|2 ₍₁₎ where˛=4n2 mε0a3[(m2−1)/(m2+2)]isthepolarizabilityofan

individualnanoparticleintheRayleighregime,ε0isvacuum

per-mittivity, ais theradiusof thenanoparticle, and m=np/nm is

therelativerefractiveindexoftheparticle(np)tomedium(nm).

Anothercomponentintheradiationforceisthescatteringforcedue tomomentumtransferoflightexertingonthedielectricsphere,as givenby Fscatt=



_n mp c



E×Ht (2)

wherepisthescatteringcrosssectionofananoparticle,cdenotes thespeedoflight invacuum,and E×Ht isthetime-averaged

energy flux ofthe laser pulses. The temporal forceis given by [36–38]

Ftemp=0∂tP×H=˛0∂tE×H (3) where0isvacuumpermeability.Thecharacterandmagnitudeof

thistemporalforcedependstronglyonthepulseduration[40],and thisforceisobviouslyzeroforthecwlaserbeams.

Itisnoteworthythatinourexperimentalcase,forwavelength oflaserbeam=800nmandbeamwaistω0=460nm,beam

diver-gencehalf-angle(definedas=/nmω0)iscalculatedtobe∼24◦.

Consequently,theaxialvectorfieldoftheplane-polarized Gaus-sianbeamstightlyfocusedbysuchanobjectivelenscannotbe neglected[41,42].Ifweassumethefocalplaneislocatedatthe xy-plane(z=0),andthecarrierfrequencyandpulsedurationofthe laserpulsesis_ωand_,respectively,thelinearlypolarizedelectric fieldparalleltothex-axiscanbeexpressedasEx0=E0exp[iωt−

2_]exp[−˜t2_{](where=x/ω}

0and ˜t=t/).Wenotethattheelectric

fieldalongthey-axisiszerointhelowestorderapproximationof theparaxialGaussianbeam[41,43],andtheaxialelectricfieldalong thez-axiscanbederivedusingEz0=(−i/k)∂xEx0,andoneobtains

Ez0=−iKE0exp[iωt−2]exp[−˜t2] (4)

wherek=2/andK=2/kω0.Byconsideringthattheaxial

com-ponentisaphasequadrature,theelectricfieldonthex-axisisgiven by[26],E_=E0(ˆx cosωt+ ˆzKsinωt)exp[−2]exp[−˜t2](where ˆx is

theunitvectoralongthex-axis,and ˆz istheunitvectorofz-axis oralongthebeampropagatingdirection).Withthe correspond-ingmagneticfieldofthelaserpulses,H=nmε0c(ˆxEz0+ ˆyEx0),the

gradient,scattering,andtemporalforcesexertingona nanoparti-cleatthefocalplane,aspresentedinEqs.(1)–(3),canbetherefore expressedasfollows: Fgrad=−ˆx˛E_x02



 ω0 − 1 2 K2 ω0 + K23 ω0



(5) Fscatt= ˆz



n2 mpε0 2



E2 x0+ ˆy



K22_n2 mpε0 2



E2 x0 (6) Ftemp=−ˆz 4˛nmE2x0 ˜ t c − ˆy4˛nmEx02K22 ˜ t c (7)

Wenotethatthegradientforcehasonlyalateralcomponent, whereasthescatteringandtemporalforceshavetwoorthogonal componentsperpendiculartotheelectricfieldEx0direction;along

thebeampropagationdirectionandinthelateraly-axis.The magni-tudesofthegradient,scattering,andtemporalforcesdependonthe laserbeamintensityandonthespatialpositioninthetrappingarea, andinparticular,thetemporalforceisalsoinverselyproportional topulseduration.Theeffectoftheaxialcomponentfieldproduced bythehigh-numericalapertureobjectivelensarisesclearlyinthe gradient,scattering,andtemporalforcesinthetermK2_.Itis

there-foreinteresting tocalculatetheforcesin ourrealexperimental case.

From knowledge of the size and refractive index of an individual polystyrene nanoparticle we calculated ˛ to be 3.85×10−34Nm3_V−2_{, and based on the Mie scattering theory}

[29]weobtainedptobe3.5×10−19m2.Byadoptingthevalues

ofK≈1.6/foranobjectivelenswithNA≈0.9[26,43]andE0=

(4P/ω2 0nmε0c)

1/2

=24.4V/␮m,(where P=350mW isthe aver-agepowerofthefemtosecondlaser,correspondingtolaserpower intensityof1.05×1012_W/m2_{atthefocalcenter),inFig.4(a)and}

(b)weshowtheplotsofthecalculatedtime-averagedgradientand scatteringforcesexertingonasphericalpolystyrenenanoparticle asafunctionofthepositionx/ω0.Thelateralgradientforcewith

themaximumbeing0.14pNatx=0.56ω0(showninFig.4(a))acts

asarestoringforce,whichdirectsthenanoparticletowardsthe beamcenterascommonlyobservedinconventionaloptical trap-pingexperiments[8,32].Themaximumvalueofaxialscattering forceis1.6fNatx=0,andthatoflateralscatteringforceis0.08fN atx=0.71ω0,asshowninFig.4(b).Suchthegradientandscattering

forcesofthetime-averagedpowerofthemode-lockedlaserbeam shouldalsobeappliedforthecwlaserbeam.Thecalculatedaxial andlateraltemporalforces,whichapplyonlyforthelaserpulses,as afunctionofthetimet/isplottedinFig.4(c).Theplotrevealsthat thetemporalforcesfluctuatewithinthepulseenvelope(=90fs), similarlytothetheoreticalapproachreportedbyGordon[36]and WangandChai[40].Atthefirsthalfofthepulse,theaxialand lateralcomponentofthetemporalforcepushesthenanoparticles alongthebeampropagationandalongy-axis,respectively,parallel tothoseofthescatteringforce.Atthesecondhalfofthepulsethe temporalforcepushesthenanoparticlesalongtheopposite direc-tions.Interestingly,themaximumaxialandlateraltemporalforces wereestimatedto12.3fNand1.7fN,respectively,whichareabout 8and20timeslargerthantherespectivecomponentofscattering

(b)

(d)

2 1 0 -1 -2 0.0 0.4 0.8 1.2 1.6

F

scatt

[fN]

x/

ω0

x5

z

x

y

ω ₀ F _x F _z F _y E_Z0 EX0

Fig.4.Plotsofcalculatedtime-averagedgradient,scattering,andtemporalforcesactingonapolystyrenenanoparticlelocatinginthefocalplane(z=0)asafunctionofeither thenormalizedlateralpositionofx/ω0ornormalizedtimet/.(a)Lateralcomponentofthegradientforce,Fgrad,paralleltoEx0.(b)Axial(black)andlateral(red)components ofthescatteringforce,Fscatt.(c)Axial(black)andlateral(red)componentsofthetemporalforce,Ftemp.Note:forthesakeofclarity,thelateralcomponentsofthescattering andtemporalforceshavebeenmultipliedbyafactorof5.(d)Aschematicillustrationofthegradient,scattering,andtemporalforces.Note:Fx=Fgrad,Fy=Ftempyˆ+Fscattˆy, Fz=Ftempzˆ+Fscattˆz.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthearticle.)

force.Thosegradient,scattering,andtemporalforcesareillustrated withadiagrammaticsketchinFig.4(d).

Consideringthattheopticaltrappingreliesonthelateral gra-dientforce,andthatthemagnitudeofthelateralgradientforce atthefocalplaneovercomesthoseofthescatteringandtemporal forces,theopticaltrappingof50-nmdiameterpolystyrenespheres bythe ultrashortlaser pulses is realized.Such optical trapping ofthe nanoparticlesis also supportedby theestimated poten-tialenergytobe13.8kBT(at300K)atthebeamcenter,whichis

abovetheminimumcriterionofanecessarypotentialenergyto overcomethermalenergeticforastableopticaltrapping(10kBT)

[8,28].Whenthepolymernanoparticlesescapefromtheoptical trappingpotential,theyarereadilyscatteredoutofthefocalspot bytheresultantofaxialandlateralcomponentsofbothscattering andtemporalforces.Inparticular,thelateralscatteringand tem-poralforces,whicharemuchlargerinthefrontofthegravityofthe nanoparticle(6.9×10−4fN),shouldcontrolthenanoparticleflows inthedirectionsperpendiculartothelightfieldpolarization. 4.3. Comparisonbetweenradiationforcesonthenanoparticlesin femtosecondlaserpulsesandinCWlaser

Ifthenecessarypotentialenergyofpulsedlaserbeamstotrap thenanoparticlesisrelatedtotheiraveragepower,similarlytothe caseofcwlaserbeams,weestimatedthat,underourexperimental condition,theaxialopticaltrappingcanbeachievedatminimum laserpowerof250mW.Thisisinagreementwithourobservation (264mW).However,theopticaltrappingbehaviorofthe nanopar-ticlesbylaserpulsesdramaticallydiffersfromthatbycwlaserbeam intermsofthenumberoftrappednanoparticlesandtheexistence ofscatterednanoparticlestowardsthedirectionscontrolledbythe

laserpolarization.Thehighernumberofnanoparticlestrappedat thefocalspot(Fig.3(a))bythelaserpulsesincomparisonwiththat bycwmodeindicatesthehigheropticaltrappingefficiencyofthe laserpulses,althoughthefluctuationofscatteringlightintensity atthefocalspottakesplaceduetothedynamicparticlemotions duringthepulseirradiationandpulseintervalperiod.Toclarify thisissue,weconsiderthenumberofphotonsofthe800-nmlaser beamtransferredintothesample.Forthelaserpulseswithan aver-agepowerof350mW,thepeakpowerofasinglepulseis4.9nJ andthenumberofphotonspersecondis1.11×1023_,almostfive

ordershigherthanthatofcwmode(1.41×1018_{)forthesamelaser}

power,highlightingtheimpulsivepeakpowerofthelaserpulses inthefrontofcwmode.However,weshouldnotethatsuchapeak powerinourexperimentismuchsmallerthanthattoinduceoptical breakdowninwater,whichrequires0.1␮Jperpulsefor100fslaser pulses[44],generatingshockwaveemissionand cavitation bub-ble[44–47].Unlikethepolystyreneparticlescontainingfluorescent dyes[38],thebarepolymernanoparticlesinourexperimentsdoes notabsorbefficientlytwo-photonexcitationofthelaserpulses, thus,theyarenotablatedbythelaserpulses.Weshouldalsonote thatthepolystyrenenanoparticlesizeistoomuch smallerthan thebeamwaisttoinducesecondaryconvergenceofthe femtosec-ondlaserpulsesthatcanreducetheopticalbreakdownthreshold asobservedforpolystyrenebeadswitha fewtensofmicronin diameter [27]. Thus, under ourexperimental conditionwe can ruleoutthepossiblecontributionsofshockwave,cavitationbubble (relatedtoopticalbreakdown),orablation,inthemechanismofthe nanoparticleflowscontrolledbythelaserpolarization.Instead,as weproposedinSection4.2,thelateralcomponentsofboth scatter-ingandtemporalforcesduringtheshortpulseirradiationplayan importantroleinthepolarization-controllednanoparticleflows.

Thetemporal force,which is notavailable incwmode, pushes thenanoparticlesinthefluctuatingmanneroutofthefocal cen-ter,inducingthedynamicsofnanoparticlemotionduringthepulse duration.Theparticlemotionsmayalsoinduceconvectionofthe liquidmedium.Thus,combinationofattractiveandrepulsiveforces bytheimpulsivepeakpower,resultingindynamicmotionsand diffusionsof nanoparticlesaroundthefocalspot,makesoptical trappingoflaserpulsesismoreefficientthanthatofcwmode.In otherwords,undercwmode,thelaserbeamwithoutmodulation resultsinflatpower,lesscontrollableflows,lessdynamicmotions anddiffusionsofnanoparticlesaroundthefocalspot,andhence, lessefficiencyinopticaltrapping.

Inordertoevaluatewhetheratrappednanoparticlecanescape fromthetrapsite bythermal motionduring thepulseinterval period between two pulses, we have considered the diffusion of a polystyrene nanoparticle in water. With 12.5ns interval betweentwolaserpulses(relatedto80MHzrepetitionrate)and diffusioncoefficientintheorderof∼10−10_m2_s−1_for57-nm

diam-eterpolystyreneparticle[48],we estimatedthediffusionofthe nanoparticleswithinthepulseintervalperiodtobe∼4nm2_,which

is much smaller than the focal spot size. We therefore could excludetheseveredestabilizationoftheopticaltrappingdueto thenanoparticlediffusion.Nevertheless,thediffusionduringthe intervalbetweenpulses maybeattributedtothefluctuationof accumulatednanoparticlesatthefocalspotasindicatedbythelight intensityfluctuationinFig.3(a).Sincetheexistenceof nanoparti-cleaggregateatthefocalspotcandistortthelightelectricfield, weproposedthatacertainmacroscopicshapeoftheaccumulated nanoparticlesallowsthenanoparticleflowsinonedirectionand theothershapeinanotherdirection.Inthiscurrent experimen-talcase,suchatransitionfromonetoanothermacroscopicshape oftheaccumulatednanoparticlestakesplaceonthetime-scaleof seconds,notonthetime-scaleofthepulseduration.Thisalso indi-catesthatthechangeordestabilizationofmacroscopicshapeof theaccumulatednanoparticlesismuchslowerthanthefluctuation inthenumberoftheopticallytrappednanoparticles.Thediscrete probabilitydistributionofthenanoparticleflowsinoneofthetwo oppositedirectionscanbeconsideredasaPoissondistribution.

Further,weinterpretthatpulsedurationandrepetitionrateof laserpulses willbeimportantparameters governingand bring-ingabouttheefficientopticaltrappingandpolarization-controlled scatteringofthedielectricsphericalnanoparticles.This interpreta-tionisincontrasttotheopticaltrappingof0.78or1.28␮msilica spheres,inwhichtheopticaltrappingofthesubmicro-or micro-particlesbyfemtosecondlaserpulseswerereportedtobejustas effectiveasthosebycwlaser mode,andtheopticaltrappingis independentonpulseduration within12–40fsoverthe repeti-tionrateof80MHz[23,38].Thiscanbeunderstoodaswehave interpretedourresultsbasedoninstantaneousforceonthe 50-nmsized Rayleighparticlesinsteadoftotal impulsetransferby thelaserovertherepetitioncycleonsuchmicron-sizedparticles, whicharemuchlargerthanthebeamwaistimplementedinthose reports[23,38].Finally,experimentswithvaryingrepetitionrate andpulsedurationoflaserpulses,inadditiontoanisotropy,the concentrationofthecolloid,andtheintrinsicpolarizabilitiesofthe Rayleighcolloidalparticlesasextensionsofourcurrentstudyare inprogressinourlaboratory,pursuinggeneralityofthetrapping andpolarization-controlledscatteringofdielectric nanoparticles bythetightlyfocusedlaserpulses,andtheresultswillbereported elsewhereinnearfuture.

5. Conclusion

Wehavepresentedopticaltrappingbehavior of50-nmsized dielectricsphericalnanoparticlesbythetightlyfocusedultrashort laserpulses.Inadditiontothesingleopticaltrapatthefocalspot,

thenanoparticleswerealsoscatteredfromthefocusspottothe sur-roundingareaformingapartiallyopenedfoldingfan-shapedbright locusintwooppositedirections,inanalternatingmanner, perpen-diculartothelaserpolarization.Wehaveshownthatascompared withthecwmode,thelaserpulsescanconfinealargernumberof theRayleighdielectricparticlesaroundthefocalspot,highlighting theimpulsivepeakpoweroftheultrashortlaserpulses.The tem-poralforcesofthelaserpulses,inadditiontothescatteringforces, readilypushthenanoparticlesoutofthefocalspot.Inparticular,the lateralscatteringandtemporalforces,whicharisefromtheaxial componentoftheelectricfieldproducedbythehighnumerical apertureofobjectivelens,cancontrolthenanoparticleflowsfrom thefocalspottothesurroundingarea.Thecontrollabledirections ofthescatterednanoparticlesbythepolarizationoflaserpulses willopenanewvistaforcontrollingdynamicalmotionof nanopar-ticleassemblyaswellasforseparationandsortingofnanoparticles witheitherdifferentpolarizabilitiesorscatteringcrosssections. Acknowledgements

ThefinancialsupportsfromtheMinistryofEducationofTaiwan (MOE-ATUProject;NationalChiaoTungUniversity),theNational ScienceCouncilofTaiwan(GrantNo.NSC100-2113-M-009-001), andFoundationoftheAdvancementforOutstandingScholarship ofTaiwantoH.M.aregratefullyacknowledged.

AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,atdoi:10.1016/j.jphotochem.2011.11.015. References

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