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Lineshape of harmonic generation on metal nanoparticles and metallic Photonic Crystal slabs

We study the linear- and nonlinear-optical lineshapes of metal nanoparticles (theory) and metallic photonic crystal slabs (experiment and theory). For metal nanoparticle ensembles, we show analytically and numerically that femtosecond second- or third-harm

Lineshapeofharmonicgenerationbymetalnanoparticles

andmetallicphotoniccrystalslabs

M.W.Klein, T.Tritschler,andM.Wegener

Institutf¨urAngewandtePhysik,Universit¨atKarlsruhe(TH),D-76131Karlsruhe,Germany

arXiv:cond-mat/0503284v2 [cond-mat.mtrl-sci] 14 Oct 2005

S.Linden

Institutf¨urNanotechnologie,ForschungszentrumKarlsruheinderHelmholtz-Gemeinschaft,D-76021Karlsruhe,Germany

Westudythelinearandnonlinear-opticallineshapesofmetalnanoparticles(theory)andmetallicphotoniccrystalslabs(experimentandtheory).Formetalnanoparticleensembles,weshowanalyt-icallyandnumericallythatfemtosecondsecond-orthird-harmonic-generation(THG)experimentstogetherwithlinearextinctionmeasurementsgenerallydonotallowtodeterminethehomogeneouslinewidth.Thisisincontrasttoclaimsofpreviousworkinwhichweidentifyatechnicalmistake.Formetallicphotoniccrystalslabs,weintroduceasimpleclassicalmodeloftwocoupledLorentzoscillators,correspondingtotheplasmonandwaveguidemodes.Thismodeldescribesverywellthekeyexperimentalfeaturesoflinearoptics,particularlytheFano-likelineshapes.Thederivednonlinear-opticalTHGspectraareshowntodependontheunderlyingsourceoftheopticalnonlin-earity.WepresentcorrespondingTHGexperimentswithmetallicphotoniccrystalslabs.Incontrasttopreviouswork,wespectrallyresolvetheinterferometricTHGsignal,andweadditionallyobtainahighertemporalresolutionbyusing5fslaserpulses.IntheTHGspectra,thedistinctspectralcomponentsexhibitstronglydi erentbehaviorsversustimedelay.Themeasuredspectraagreewellwiththemodelcalculations.

(SubmittedtoPhys.Rev.BonFebruary28,2005;publishedinPhys.Rev.B72,115113onSeptember15,2005;resubmittedtoarXivonFebruary2,2008)c2005TheAmericanPhysicalSociety

PACSnumbers:42.70.Qs,73.20.Mf,78.47.+p,42.50.Md

I.INTRODUCTION

Thelinear-opticalpropertiesofmetallicphotoniccrys-talslabs(MPCSs)haverecentlyattractedconsiderable

attentionbecausetheycanbeviewedasasimplemodelsystemoftwocoupledoscillators:(i)aLorentzoscillatorelectronicresonancecouplesto(ii)anelectromagneticresonance.(i)Theelectronicresonancecomesaboutfromchargeswhichaccumulateatthesurfaceofthemetalnanostructureswhenexposedtotheelectric eldoftheincidentlight.Thesechargesinduceadepolariza-tion eldthatcaneithercounteractorenhancetheex-ternalelectric eld,dependingonthepermittivityofthemetal,hencedependingonthefrequencyoflight.Theresultingresonanceatthetransitionpointisthewell-knownparticleplasmonorMieresonance.1(ii)Theelec-tromagneticresonanceistheBraggresonanceofthepe-riodicarrangementwithlatticeconstanta.Importantly,anappreciablecouplingbetweenthesetwooscillatorsre-quiresanadditionalslabwaveguide,e.g.,underneaththemetalnanoparticles.Therefore,thephysicsofmetal-licphotoniccrystalslabsisdistinctfromthatofusualmetallicgratings,whichhavebeendiscussedextensivelymanyyearsago.2Tailoringthewaveguideparametersal-lowsonetocontrolthecouplingstrength,sincethecou-plingarisesfromthespatialoverlapoftheplasmon-andwaveguide-mode elds.

Two-dimensionalMPCSswere rstdiscussedinRef.3employinggoldnanoparticlesonadielectricwaveguide.

Later,4goldnanowiresshowedevenmorepronouncedef-fects.Inthelatterstructures,thecouplingoftheinci-dentlighttotheparticleplasmonresonancecanconve-nientlybeswitchedonando viathepolarization.Iftheelectric eldvectorisorientedperpendiculartothenanowires(TMpolarization),apronounceddepolariza-tion eldarises,givingrisetoastrongopticalresonance.Incontrast,iftheelectric eldvectorisalongthewireaxis(TEpolarization),thedepolarizationfactoriszeroandonerathergetsaDrude-typeresponseofthemetal.Morerecently,nonlinear-opticalexperimentsonMPCSshavebeenpresented.5Thesewereinterpretedalongthelinesofsimilar6performedonmetalnanoparticleensemblesonasubstratesurfacewith-outaslabwaveguide.Thus,ourinitialmotivationwastocontinuewithexperimentsalongtheselinesandob-tainadditionalinformationfromnonlinear-opticalexper-iments.

Thispapercontainsboththeoryandexperimentsandisorganizedasfollows.InSec.IIwestartbydis-cussingthenonlinearopticsofmetalnanoparticleen-sembleswithinhomogeneouslybroadenedplasmonreso-nances.WederiverigorousanalyticresultsforexcitationwithδpulsesandLorentzianinhomogeneousbroadening.Furthermore,wepresentnumericalresultsforaGaus-sianinhomogeneousbroadeningand nite-durationopti-calpulses.Forsecond-(SHG)andthird-harmonicgener-ation(THG),we ndthattheinterferometricnonlinearresponseexclusivelydependsonthetotallinear-opticallinewidthoftheparticleplasmon,i.e.,onecannotob-

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