SOFIforPlasmonics:ExtractingNear-fieldIntensityintheFar-FieldatHighDensity

RobertC.Boutelle1,XiyuYi1,DanielNeuhauser1,2,ShimonWeiss1,2,3,4

1DepartmentofChemistry&Biochemistry,2CaliforniaNanoSystemsInstitute,and3DepartmentofPhysiology,UniversityofCaliforniaLosAngeles,LosAngeles,California90095,UnitedStates

4DepartmentofPhysics,BarIlanUniversity,RamatGan,52900,IsraelIntroductionSuper-resolutionmicroscopy is the classification of techniques that allow imaging belowthediffractionlimitfacedbyconventionalopticalmicroscopy.Overthepastdecade,super-resolution imaging has rapidly grown and greatly impacted the field of biology, asevidencedbythe2014NobelPrizeinchemistry[1].Itsrapidgrowthhasstemmedvariousmethods,includingtheearlySTORM,PALM,STEDandnewlydevelopedPAINT,GSDIM,andSOFI[2-7].Additionally,super-resolutiontechniqueshavegainedpopularityinthefieldofmaterials, influencing polymers and catalysis [5, 8-12]. These far-field super-resolutiontechniquesarebasedon individualemitters thataremodulatedbetweenemissive (“on”)and non-emissive (“off”). From this modulation, one can spatially separate two emitterpointspreadfunctions(PSFs)intime,capturedinthefar-fieldasastreamofimages,suchthat a single emitter PSF can be fit to a model function, such as a 2D-Gaussian.Superimposingthepositionsoftheindividualemitterscreatesacompositereconstructedimage[2, 13, 14]. Recently, there has been a push to utilize super-resolution imaging forplasmonics[15]. However, there are many technical challenges that must be overcomebeforesuper-resolutionforplasmonicsbecomesfeasible.Plasmonics and super-resolution imaging naturally compliment each other. Plasmonicsprovides a simple strategy to achieve subdiffraction excitation volumes using a far-fieldexcitation source. Additionally, plasmonic nanostructures are by their very naturenanoscale in dimension, requiring subdiffraction-limited imaging tools to measure thecomplex relationship between structure, resonance frequencies, and local fieldenhancement[16].Withthedevelopmentofplasmonics-baseddevicesandcircuitsthereisa growingneed fordetectingand characterizingplasmonic effects.At first glance, super-resolutionimagingappearstobethebestmethodtocharacterizeplasmonicsystemsinthefar-field. When applied to plasmonic nanostructures, dye emission intensity is typicallyusedasa far-fieldreporterof thenear-field intensity[17].Due to thestrongelectric fieldneartheplasmonicnanostructure,thedyehasenhancedemissionwhentheexcitationoremission frequencymatches theplasmonresonance.Unfortunately therearedetrimentalproblemswithprobingthenear-fieldintensitywithfar-fieldemitters.First, the diffraction limited emission is affected via a combination of mechanisms,includingplasmon-moleculecoupling,pointspreadfunctiondistortions,andimagedipoleformation[15]. These mechanisms lead to erroneous error in localization. Second,fluorescenceenhancement changesnon-monotonically as a functionofdistance from the

metallicsurface.Whentheemitteristooclosetothesurface(<10nm),thefluorescentratedrops sharply due to quenching effects[17]. Thus fluorescent emission intensity is not agood candidate for measuring plasmon near-field intensity in close proximity to themetallic surface. In this report, we focus on a new method to measure the near-fieldplasmonicfieldsusingafar-fieldreporterthatisinvarianttoquenchingeffects.MethodstomitigatethePSFdistortionanderrorinlocalizationarebeyondthescopeofthisworkbutareoutlinedbyothers[15].Futurereportswillintegratemethodstoallowmoreaccuratecharacterizationoftheplasmonicnear-field.Specifically,we previously created amethod tomeasure plasmonic near-field intensitiesdubbedCharacterizingOpticalFieldIntensitybyBlInkingNanoparticleS(COFIBINS).[18]This method extracts plasmonic near-field intensity in the far-field using QD stochasticblinking field sensitivity. COFIBINS demonstrated that in low areal density (< 1.8QDs/µm2),individualQDtime-intensitytrajectorycouldbeusedtomeasurethechangeinblinking rate as a measure of optical field intensity. COFIBINS was applied to silvernanowires (AgNWs) and accurately extracted the propagation length and penetrationdepth of the plasmonic waveguides. The downside is that COFIBINS had low spatialresolution. The QDs had to be well separated to obtain their individual time-intensitytrajectoryforaccuratecharacterizationoftheplasmonicnear-field.

Recently, we developed a method to extract photo-physical properties of QDs at highlabeling densities. A variant of superresolution optical fluctuation imaging (SOFI)methodology [4, 7, 19-21] is used to spatially resolve features at high density and, in amethodsimilartobSOFI[22]thatutilizesmultipleordersofcumulantanalysis(dubbedasMOCA-SOFI),extractthephoto-physicalinformationofQDsathighlabelingdensity.Whencombined with COFIBINS, this method creates a crucial development for true far-fieldsuper-resolutiondetectionofplasmonicnear-fields.

A direct demonstrate of high spatial resolution measurement of SOFI-COFIBINS onplasmonicnear-field intensity inthe far-field isdonehereonsilvernanowires(AgNWs).Ag NW waveguides have an inhomogeneous (decaying) field distribution both in thesurface plasmon polariton (SPP) propagation direction (along the long direction of thewire) and penetration depth direction (perpendicular to the long direction of thewire).SOFI isusedincombinationCOFIBINStoextracttheQDblinkingparameter inhigharealdensitiesalongtheseAgNWs.QDswerespin-coatedathigharealdensity(>30QDs/µm)ontopofAgNWs.TheseexperimentstesttheefficacyofthenewlydevelopedSOFI-COFIBINSmethod.Themethodextractsvaluescomparabletothefluorescenceintensityyetcontainssuper-resolvedinformation.

ResultsandDiscussionHighDensityQDPhoto-PhysicalParameterExtractionPrevious studies have already demonstrated that QD blinking is relatively invariant toenhancementandquenchingeffects,yettheirblinkingrateissensitivetoopticalnear-fieldintensity. Optical field intensities affect the stochastic switching ofQDs between an “on”statewithahighphotonemissionrateandan“off”lowemissionstate.Stochasticswitching,also known as “intermittency”, or “blinking”, has been studied extensively, both

experimentally and theoretically. Auger recombination is commonly invoked to explainblinking, but other processes, such as surface and heterointerface charge trapping, havealso been shown to contribute to the switching. Auger recombination is a three-particleprocess that results inanonradiative transitiondue to theabsorptionofenergy fromanexcitonbyaspectatorparticle,leavingtheQDcharged,andina“dark”,or“off”,state.OnlyoncethechargedQDisneutralizeddoestheemissive“on”stateresume.BlinkinginQDsisinherentlystochasticandindependentofothernearbyQDemitters.Traditionally,emissionfromasingleQDisrecordedintimebinstoanalyzetheblinkingphenomena.Athresholdisusedtodiscern“on”and“off”timeperiodsinthetelegraphnoise-liketimetrajectoryandhistograms are constructed for the “on” and “off” periods. At low excitation power, thehistogramsexhibitanearperfectpowerlawdistributionforboththe“on(+)”and“off(−)”states,describedby𝑃± 𝑡 = 𝑡!!.Forhigherexcitationenergies,the“on”timedistributionstarts to bend at long “on” times (𝑃! = 𝑡!!𝑒!!" , where Γ is the intensity bendingparameter). Here,m is the slope of the on/off-time probability distribution in a log−logplot.Thus,thestrongertheexcitationintensity,theshorterthe“on”periodsandthemorelikelytheQDwillbetoenteran“off”state.Thebendingparameter,Γ,yieldsinformationontheexcitationfieldviatheblinkingstatisticsofindividualQDs.

Theautocorrelationfunction(ACF)of aQD’s individual time-intensitytrajectory can also extract theoptical intensity bendingparameterΓbyfitting:1− 𝐺 𝜏 = 𝛽 𝑚 𝜃!!!𝛤!!!𝜏!!!where𝜃 is the minimum capturewindow and𝛽 𝑚 is a numericalfunction (product of𝛤 -functions)of𝑚.TheQDblinkingparameter𝛤shows a linear trend for powerdependent parameter over threeordersofmagnitudeopticalpowerdensity. Thus, by taking theautocorrelation of the time-intensity trajectory of a blinkingQD, the optical field strength canbe measured. This method hassuccessfully been applied to AgNW waveguides. The largestdrawbackistheinabilitytoresolvethe individual time-intensity

trajectory at high densities. The solution is to use SOFI to extract out the blinkingparametersandsimultaneouslysuper-resolvetheimageathighdensity.

Figure 1: Extracting intensity values from a defocused PSF. (a)Average fluorescence intensityper pixel. (b) ExtractedΓ valueperpixel via SOFI-COFIBINS. (c) Cross section of (a) (green) and (b)(blue) plotted against the reflected PSF Intensity. SOFI-COFIBINSagrees well with both the average fluorescence intensity andreflectedPSFintensity.

In SOFI, the temporal autocorrelation amplitude of pixels with signal contribution frommultipleQDsislowerthantheautocorrelationamplitudeofpixelswithsignalcontributionfromonlyoneQD,yieldinganimagewithadipbetweenQDs.Thisdipleadstoshrinkageofthe individual PSF as a function of1/ 𝑛, where𝑛is the SOFI order, and is the basis forincreasedresolution.Wehave taken thismethoda step further toextractout thephoto-physical properties of QDs at high density. Briefly, the fluctuation signal within a givenpixelwilldependontheemitterPSF,emitterbrightness,anditsfluctuationprofile,whichcontainsan“on-”/”off-time”ratio,suchthat:

𝐹 𝑟, 𝑡 = 𝑈 𝑟 − 𝑟! ∙ 𝜖! ∙ 𝑆! 𝑡!

where𝐹 𝑟, 𝑡 is thesignalacquired intime 𝑡 onasinglepixel 𝑟 ,𝑘is theemitter index,𝑈 𝑟 − 𝑟! is the model PSF (in this case 2D-Gaussian),𝜖! is the emitter brightness, and𝑆! 𝑡 is the fluctuation profile. Then, in MOCA-SOFI we extract out the individualparameters.Detailsonthemethodisbeyondthescopeofthisreportandwillbepresentedinasubsequentindependentpaper.

The key conclusion is that the fluctuation signal in a single pixel containingmultipleQDfluctuationprofilescanbedecoupledandresolved.Specifically,weacquirethe“on-”/”off-time”ratioofeachquantumdotcontributingtothesignalofasinglepixelsuchthat:

𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑛 𝑡𝑖𝑚𝑒𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓𝑓 𝑡𝑖𝑚𝑒 + 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑛 𝑡𝑖𝑚𝑒 =

𝑡𝑃! 𝑡 𝑑𝑡!!

𝑡𝑃! 𝑡 𝑑𝑡!! + 𝑡𝑃! 𝑡 𝑑𝑡!

!

where𝑃! 𝑡 and𝑃! 𝑡 are the probability distribution function of the on/off lifetimesrespectively:

𝑃! 𝑡 = 𝐴𝑡!!𝑒!!"

𝑃! 𝑡 = 𝐵𝑡!!where𝐴and𝐵are the normalization constant,𝑚is the power law slope, and𝛤is theexcitationintensitybendingparameter.Combiningequations[EQUATIONS],weget:

𝛤!!!𝛽𝜃!!!2−𝑚 + 𝛤!!!𝛽

where𝛽isaplaceholderforthegammafunction𝛤(2−𝑚).Thus,wecanextractoutthe𝛤intensity parameter and,when combinedwith COFIBINS,mapwith super-resolution theopticalfieldintensity.

A proof of principle demonstration is illustrated in Figure 1with a defocused laser PSF.800nmemissionQDsweredepositedviaspincoatonacoverslipinhigharealdensity.NextathicklayerofPMMAwasdepositedviaspincoattoprotecttheQDs.TheQDswerethenilluminatedwith a defocused 642nmCW laser. An EMCCD camera captured the far-field

emission time-trajectoriesusing a conventionaldiffraction-limited wide-fieldopticsanda750longpassfilter(Edmund optics). 20K frameswith exposure of 30ms werecapturedforanalysis.An image constructed fromfitted bending parameters 𝛤 for each pixel maps thelocalized electric field andsuper-resolve the defocusedPSF illumination. We can seethat the SOFI-COFIBINS resultagrees well with both theaverage fluorescence intensityand thereflectedPSF intensity.Thisresultillustratesaproofofprinciple that the optical fieldstrength can be extracted athighdensitythroughblinkingstatisticswithSOFI-COFIBINS.

Figure 2: Superresolved PlasmonicsQDswere drop- castedon glassconverslipcontainingrandomlyorientedAgNWs.SPPswereexcitedwitha confocal 642nm CW laser at one end of AgNWs (top right of eachimage).TheSPPsevanescentfieldexcitestheQDsdownstreamthewire.(a)Averagepixelintensity.(b)Zoom-intoboxedareain(a).(c)QDon-offratioextractionviaSOFI-COFIBINS. (d)Zoom-in toboxedarea in(c)All heat-maps are log scale (to allow visualization of the plasmonpropagationexponentialdecay).

Figure3: Cross Section analysis of SOFI-COFIBINS(a)Averagepixel intensity.(b)QDon-offratioextractionviaSOFI-COFIBINS. (c) FDTD simulations illustrating the modes visualized are due to a 45˚ polarization angle ofexcitation. (d)Normalized cross section for SPPpropagation of averagepixel intensity from (a) (green) and SOFI-COFIBINS(b)(blue)plottedtogether.(e)NormalizedcrosssectionforSPPpenetrationofaveragepixelintensityfrom(a)(magenta)andSOFI-COFIBINS(b)(teal)plottedtogether.ThetwoshowsimilartrendsyettheSOFI-COFIBINShassuper-resolvedinformation.

SOFI-COFIBINSforPlasmonicsA direct application of our merged SOFI-COFIBINS to the characterization of plasmonicwaveguide is demonstrated next. QDs were drop-casted at high concentration onto a220nmAgNW. Upon confocal excitation of the SPPs at one end of thewire (642nmCWlaser), the QDs excite and emit (800nm) downstream due to the SPP’s evanescent field.Figure 2a shows the average (sum image) of 10k acquired frames. Figure 2c shows thesuperresolved image using SOFI-COFIBINS. The two methods give similar trends to theplasmonicSPP.However,SOFI-COFIBINShassuperresolvedinformation.This is further verified by taking cross sections for the propagation and penetrationdirectionoftheSPP(Figure3).Heretheaveragefluorescenceintensityagainshowssimilartrend to the SOFI-COFIBINS super-resolved image to extract the SPP propagation lengthandpenetrationdepth.ConclusionOur initial implementation of SOFI-COFIBINS shows promise for simultaneous fieldintensity extraction with the1/ 𝑛spatial resolution enhancement factor, where𝑛is theSOFI order, typical of SOFI analysis. However, we need to investigate our method’slimitations such as large electromagnetic field gradient, time resolution, and dynamicrange.OptimizationwillbemadebysimplesimulationoffakeQDemitterswithgeneratedintensitytrajectoriesandusingknownblinkingprofiles,spreadalongaplasmonicsystemofsimulation.FDTDsimulationswilldictatethefieldsexperiencedbythesefakeQDs,andthereforetheir intensitytrajectoriesandPSFprofile.Theemissionprofile,generatedasamovie,willbeanalyzedbySOFI-COFIBINSandtheerrorsintheoutputcomparedwiththepreassigned locations will yield a measure of the method’s accuracy. We will use thisinformation to optimize under what conditions SOFI-COFIBINS best performs. Theoptimized conditionswill guide our experimental protocol andwhat we learn from ourexperimental measurements will help optimize our theoretical simulations and SOFI-COFIBINSanalysis.

ContributionsRobertC.Boutellewasresponsibleforexperimentalmeasurement/analysis,applicationofMOCA-SOFI,andFDTDsimulations.XiyuYiwasresponsiblefordevelopmentandcodingofMOCA-SOFI in addition to advising Robert on the SOFI algorithm. Daniel NeuhauseroversawthetheoreticalFDTDresults.ShimonWeissmanagedtheprojectandscience.

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