Optical Properties of Complex Plasmonic Materials Studied with Extended Effective Medium

13 Pages·2017·4.36 MB·English

materials
Article
Optical Properties of Complex Plasmonic Materials
Studied with Extended Effective Medium Theories
Combined with Rigorous Coupled Wave Analysis
ElieNadal1,2,* ID,NoémiBarros1,2,HervéGlénat2andHamidKachakachi1,2
1 UniversityofPerpignanViaDomitia(UPVD),52AvenuePaulAlduy,66100Perpignan,France;
[email protected](N.B.);[email protected](H.K.)
2 Processes,Materials,andSolarEnergyLaboratory,CNRS(PROMES-CNRS,UPR8521),
RambladelaThermodynamique,66100Perpignan,France;[email protected]
* Correspondence:[email protected]
Received:5February2018;Accepted:22February2018;Published:27February2018
Abstract: In this study we fabricate gold nanocomposites and model their optical properties.
The nanocomposites are either homogeneous films or gratings containing gold nanoparticles
embeddedinapolymermatrix. Thesamplesarefabricatedusingarecentlydevelopedtechnique
making use of laser interferometry. The gratings present original plasmon-enhanced diffraction
properties.Inthiswork,wedevelopanewapproachtomodeltheopticalpropertiesofourcomposites.
WecombinetheextendedMaxwell–GarnettmodelofeffectivemediawiththeRigorousCoupled
WaveAnalysis(RCWA)methodandcomputeboththeabsorptionspectraandthediffractionefficiency
spectraofthegratings. Weshowthatsuchasemi-analyticalapproachallowsustoreproducethe
original plasmonic features of the composites and can provide us with details about their inner
structure. Suchanapproach,consideringreasonablyhighparticleconcentrations,couldbeasimple
andefficienttooltostudycomplexmicro-structuredsystembasedonplasmoniccomponents,such
asmetamaterials.
Keywords: goldnanoparticles;plasmon;nanocomposites;laserinterferometry;Maxwell–Garnett
theory;gratings;diffraction;RCWA
1. Introduction
Complex plasmonic systems, and in particular plasmonic nanocomposites, have emerged
as promising materials for numerous applications in photonics [1–3], photovoltaics [4–7], and in
environmental issues such as water remediation [8–10] or hydrogen production through water
splitting[11–13]. Indeed,duetotheirplasmonicfeatures,thesesystemsexhibitnovelopticalaswellas
electricalproperties. Thecontrolofthesefeatures,withthepurposetodesignfunctionalmaterials
ordeviceswithtailoredfunctionalities,oftenrequiresanorganizationofthemetallicnanostructures
into specific arrangements [14]. For instance, in photonics, the design of metamaterials, defined
as exotic materials producing non-natural optical properties, mostly relies on the ability to create
complexandregular3Dcompositesuperlattices[1,3,15]. Theinsertionofplasmonicnanostructures
in organic solar cells has also been demonstrated as an efficient way to improve the conversion
efficiencyofthesedevices. Onceagain,thedifferentscenariosusedtoenhancetheopticalproperties
ofthesystemstronglyrelyontheabilitytopreciselyinsertthemetallicparticles,actingasabsorbers
or diffusers, inside the device structure [4,16]. Finally, very recently, plasmonic circuits based on
well-defined nano and micro-metallic patterns have been proposed as a new benchmark to build
opticalcomputers[17,18].
Materials 2018,11,351;doi:10.3390/ma11030351 www.mdpi.com/journal/materials
Materials 2018,11,351 2of13
Materials 2018, 11, x FOR PEER REVIEW 2 of 13
Theopticalpropertiesofsuchorganizedplasmonicmaterialsarecomplexanddifficulttodescribe
theoreticaTllhyes ionpcteicbaol thprtohpeeirntitersin osifc spurcohp eorrtgieasniozfetdh epnlaasnmoosntriuc cmtuarteesriaanlsd athree lcoonmgp-rleaxn gaenodr gdaifnfiiczualtti otno must
betakdeenscirnibtoe athcecooruentitca[1ll9y] .sGinecne ebroatlhly ,thtwe oinmtrianisnica pprporpoearcthieess oafr ethues endantoosctraulccutulraetes tahned otphtei claolnpg-rroapnegret iesof
plasmoorgnaicniszyasttieomn ms.uTsht ebefi rtastkeanp pinrotoa cahcccoounnsti s[1ts9]i.n Gseonlverinalglyt,h tewMo maxawine lalpepqruoaatcihoenss afroer uasfeedw ton caanlocustlarutec tures
bydethfien ionpgtitchael iprrgoepoemrtieetsr yofe xpplalsicmitolyn.icT hsyisstaepmpsr. oTahceh frierslite aspopnroeaxcahc tcnonusmisetsr iicna lssoilmvinugla ttihoen Mstahxawterlel quire
equations for a few nanostructures by defining their geometry explicitly. This approach relies on
largecomputerresources,amongwhichthemostcommonlyusedarediscretedipoleapproximation
exact numerical simulations that require large computer resources, among which the most commonly
(DDA)[20,21],finitedifferencetimedomain(FDTD)[22]andboundaryelementmethod(BEM)[23,24].
used are discrete dipole approximation (DDA) [20,21], finite difference time domain (FDTD) [22] and
Thesemethodsareveryefficientforquitepreciselycomputingboththeopticalspectraandtheelectric
boundary element method (BEM) [23,24]. These methods are very efficient for quite precisely
field maps of any nanostructure placed in a given medium. However, the computing time rapidly
computing both the optical spectra and the electric field maps of any nanostructure placed in a given
increaseswiththesizeofthesystem,thuslimitingthesemethodstothestudyofverysmallnanoparticle
medium. However, the computing time rapidly increases with the size of the system, thus limiting
assemthbelsiee sm[2et5h].odTs hteo stehceo sntdudayp pofr ovaecrhy issmaanlla lnyatnicoaplaartnicdler ealsiseesmobnlietsh e[2e5f]f. eTchtiev esemcoenddi uampprthoaecohr ieiss [26],
the manoasltyftaicmalo aunsd breeilniegs othne thMe aexffwecetlilv–eG marendeiuttm( MthGeo)rtiehse o[2r6y], [t2h7e] .mUosnt lifkameothues bperienvgi othues Mapapxwroealcl–h, the
effectGivaern-metet d(MiuGm) tphheeonryo m[2e7]n. oUlongliikcea lththe eporreiveisomusa akpepirtopacohs,s itbhlee etfofetcatcivkel-emneadniuomco mphpeonsoimteesncoolongsiicsatli ngof
alargtheenourimesb merakoef nita pnoossstirbulec ttuo rteasc.kHle onwaneovceorm,tphoesyitepsr ococenesidstbinyga ovfe ar alagrigneg nsuizmebs,ers hoaf pneasn,oasntrducotruireenst. ation
However, they proceed by averaging sizes, shapes, and orientation distributions and thus usually
distributionsandthususuallysmoothouttheintrinsicfeaturesofthenanoparticles.
smooth out the intrinsic features of the nanoparticles.
Inthepresentwork,weproposeanewmethodfordescribingtheopticalpropertiesofplasmonic
In the present work, we propose a new method for describing the optical properties of plasmonic
systemswithamulti-scalespatialorganizationconsistingofensemblesofplasmonicnanostructures
systems with a multi-scale spatial organization consisting of ensembles of plasmonic nanostructures
organized at the micrometer range. As a benchmark, we use gold nanoparticle gratings (GNGs)
organized at the micrometer range. As a benchmark, we use gold nanoparticle gratings (GNGs)
fabricfaabteridcabtyedl asbeyr ilnasteerr feinretenrcfeerpenacttee rpnainttger.nIinngth. eIsne sthyessteem ssy,satesmsesm, basliseesmobflnieasn oofp anratnicolpesaratriceledsi satrrieb uted
inapdoislytrmibuertemd aint rai xpoolfy1mDerg mraattirnixg sofw 1iDth garaptienrgiso wdiothf 2a pµemrio(dse oef F2i µgmur e(se1ea )F.igure 1a).

FigurFeig1u.re( a1). G(ao) lGdonlda nnoanpoapratirctilceleg rgaratitninggss iinn ppoollyymmeerr ththinin filfimlms asnadn (db)( bm)omdeolidnegl ionfg thoef styhsetesmy sbtye mby
combining the RCWA and the effective medium theory.
combiningtheRCWAandtheeffectivemediumtheory.
We have prepared several gratings with a variable gold/polymer ratio and studied the effect of
Wehavepreparedseveralgratingswithavariablegold/polymerratioandstudiedtheeffectof
the gold volume fraction on the optical properties. Due to their specific structure, exact simulation of
thegsoulcdh vgoralutimnges ifsr aimctpioonssiobnle twhietho tphtei cuaslupalr aoppperrotaiecsh.esD suuecht oast DheDiArs, pFDecTiDfi,c osrt BruEcMtu. Irned,eeexda,c itt wsiomuuldl ation
ofsubceh ngercaestisnargys tois ciomnspidoesrs aib vleeryw liatrhget hneumubsuera olfa npapnroopaacrthicelsess (usecvhearasl DhuDnAdr,eFdDs) TtoD c,ororrecBtlEyM de.sIcnridbeee d, it
woultdhebire pneercioedssicaarly sptoaticaol ndsisidtreibruativoner ayt tlhaerg meincruommebteerr oscfanlea. nTohpe acrotmicpleusti(nsge tvimerea,l ahlounngd wreitdhs m)teomcoorryr ectly
descrailbloectahtieoinr preeqruioirdeimcaelnstsp, awtioaullddi sbterciboumteio pnroahtitbhiteivme.i cCroonmseeqteurensctlayl,e t.hTehree icso am rpeaul tninegedt itmo ed,eavleolnopg with
new methods in order to address such systems. For that, we adopt an intermediate approach
memoryallocationrequirements,wouldbecomeprohibitive. Consequently,thereisarealneedto
combining the semi-analytical MG theory and the so-called numerical method Rigorous Coupled
developnewmethodsinordertoaddresssuchsystems. Forthat,weadoptanintermediateapproach
Wave Analysis (RCWA) [28,29]. The periodic nature of the system is dealt with using the RCWA,
combiningthesemi-analyticalMGtheoryandtheso-callednumericalmethodRigorousCoupledWave
which makes use of a stratified description of the composites, each stratum being described by its
Analysis(RCWA)[28,29]. TheperiodicnatureofthesystemisdealtwithusingtheRCWA,which
dielectric permittivity. The plasmonic properties of the nanocomposites are then introduced by
makersepulsaecinogf athset rdaiteilfiecetdricd pesecrmripitttiivointyo offt heaechco smtraptousmit ebsy, aena cehffesctrtiavteu pmerbmeiitntigvidtye sccormibpeudtebdy friotsmd tiheele ctric
permeixttteivnidteyd. TMhGe pmlaosdmel.o Tnhice pmroodpeelrintige sproofctehdeurnea ins osckoemtchpeods iinte Fsiagrueret h1ebn. Tinhitsr omdeuthceodd balylorwesp luasc itno gthe
dieleccotrmicpputeer mthitet ivopittyicoalf eparcohpesrttriaetsu mof bthyea nfilemff eacntidv einp eprmartiitctuivlaitry tchoem dpiuffrteacdtiforno,m thteh epelaxstmenodneicd MG
modenla.nToshtreumctuordees lbineigngp irmocpelidciutlrye diesscsrkiebtecdh. e d in Figure 1b. This method allows us to compute the
optic alpropertiesofthefilmandinparticularthediffraction, theplasmonicnanostructuresbeing
implicitlydescribed.
Materials 2018,11,351 3of13
2. MaterialsandMethods
2.1. FabricationofGoldNanoparticleGratings
WebrieflypresentthefabricationapproachusedtosynthesizetheGNGs. Thedetailedfabrication
procedureisgivenin[30]andissummarizedinSectionA,FigureS1oftheSupplementaryMaterials.
Wehavepreparedthreegratingswithgold/polymerratiosof3wt%,5wt%,and10wt%. Apolyvinyl
alcohol(PVA)solutioncontainingtheappropriateamountofgoldprecursorsisspin-coatedonglass
substrates. Thefilmsthusobtainedarehomogeneouslydopedwithgoldions. Then,aMachZehnder
interferometerisusedtoirradiatethesamplewithaninterferencepattern,thusperformingaspatially
controlledphoto-reductionofthegoldsalt. Finally,nanoparticlegrowthistriggeredbyannealingthe
sample. Itturnsoutthatthenanoparticlesaremainlyformedintheirradiatedareas(brightfringesof
theinterferencepattern)andinducethedeformationofthepolymerfilm,leadingtotheappearanceof
sinusoidalsurfacereliefgratings. Amechanismexplainingthesurfacedeformationhasbeenproposed
in[31]. Asacomparison,anothersetofsamplesispreparedusingthesameprocedureexceptforthe
irradiationpart,whichisperformedwithahomogeneousGaussianbeaminsteadoftheinterference
pattern. Consequently,attheendoftheprocedure,thesamplesthusirradiatedareloadedwithgold
nanoparticleshomogeneouslydistributedinthefilms. Thissecondsetofsampleswillbedenotedas
homogeneousfilms(HFs).
Theobtainedfilmshaveanaveragethicknessof800nm. SincescanningElectronMicroscopy
imagingbecomesratherinvolvedwhendealingwithdielectricmediadepositedonglasssubstrates,
wehaveusedAtomicForceMicroscopy(AFM)tocharacterizethestructuralpropertiesofoursamples.
AFMimagesofthevariousGNGsandtheHFswithgold/polymerratioof3wt%,5wt%,and10wt%,
alongwiththesurfaceprofileofthegratingsaregiveninFigure2. Ascanbeseen,theheightofthe
surfacemodulationofthegratingsincreaseswiththegoldconcentration,varyingfrom25nmto80nm,
whereastheHFsremainflatatallconcentrations. Forlowgoldratios,thenanoparticlesareembedded
inthefilms,butbecomeclearlyvisibleatthefilmsurfaceasthegoldconcentrationincreases. Inthe
caseofthegratingwith10wt%gold,thenanoparticlesstartemergingatthetopofthegratingcrests,
whichresultsinanunevensurfaceprofile.
Absorption spectra have been measured on all samples by using standard spectroscopic
techniques. Adedicatedsetup[31]hasbeenusedtomeasurethediffractionefficiencyofthegratings,
detailsaregivenintheSupplementaryMaterials(SectionA,FigureS2).
2.2. AnalyticalandNumericalModels
Inthissection,wefirstintroduceourapproachforcomputingthedielectricpermittivityofthe
goldnanoparticles. WethendescribetheextensionsoftheMGmodelthatwehaveusedtocalculate
theeffectivepermittivityofthenanocomposites. Finally,weexplainhowtheHFsandtheGNGsare
parameterizedwithintheRCWAapproach.
WehaveusedtwodifferentMGmodelstocomputetheeffectivepropertiesofthecomposites.
Thematerialisdescribedasanensembleofinclusions(thegoldnanoparticles)randomlydistributed,
with a given volume filling fraction f, in a given host matrix (the polymer). The inclusions and
the matrix are described with the help of their respective dielectric permittivities (cid:101) and (cid:101) .
incl m
In the visible range, the permittivity of the polymer can be assumed to be constant and equal to
(cid:101) = n2 =2.25. On the other hand, the permittivity of the inclusions strongly depends on the
m PVA
wavelength. ThemostcommonwaytomodelthisbehavioristousetheDrudemodel[30]orthe
tabulated data measured for bulk gold [32]. The latter option is usually preferred as it offers the
possibilitytoaccountfortheinter-bandelectronictransitionsthattakeplaceingoldforwavelengths
below450nm[33]. Evenifthisapproachhasproventobefairlyreliable,ithasbeenpointedoutthatit
isnotfullyappropriatefordescribingthebehaviorofgoldatthenano-scale,especiallyinverysmall
nanostructures. Moreprecisely,whenthesizeofthenanoparticlesisreducedbelowthemeanfree
pathoftheelectrons,typically40nmingold[34],thelatterarestronglyscatteredbythenanoparticle
Materials 2018,11,351 4of13
surface, thusinfluencingtheirbehavior. Thiseffect, knownasconfinement[35], canbetakeninto
accoMuantetribalys 2i0n1t8r, o11d, ux cFiOnRg PaEEdRa mREpViInEWg t ermintheDrudemodel,dependingonthenanoparticlesrad4 iouf s13R
andaphenomenologicalparameter A. Basedonthisobservation,ithasbeenshownthatverygood
agreneamnoepnatrctiacnlesb reardeiaucsh (cid:1844)ed anbdy am pohdeinfyominegntohloegtiacbalu plaatreadmdetaetra (cid:1827)fo. Brabsuedlk ogno tlhdist oobtsaekrveaitnioton, aitc choaus nbetetnh e
shown that very good agreement can be reached by modifying the tabulated data for bulk gold to
effectofconfinement. Consequently,theexpressionobtainedin[36]forthepermittivityofnanometric
take into account the effect of confinement. Consequently, the expression obtained in [36] for the
metallicinclusionsisgivenby
permittivity of nanometric metallic inclusions is given by
(cid:101)in(cid:2035)c(cid:3036)l(cid:3041)=(cid:3030)(cid:3039) =(cid:101)b(cid:2035)u(cid:3029)lk(cid:3048)(cid:3039)−(cid:3038)−ω(cid:2033)2(cid:2870)++iω(cid:1861)(cid:2033)ω(cid:0)(cid:2033)γ(cid:4672)2p(cid:2011)(cid:3043)(cid:2870)++A(cid:1827)vR(cid:1874)(cid:1844)F(cid:3007)(cid:1)(cid:4673)++(cid:2033)ω(cid:2870)2(cid:2033)++ω(cid:3043)(cid:2870)(cid:1861)2pi(cid:2033)ω(cid:2011)γ，, (1)( 1)
whewrehe(cid:101)rbeu l(cid:2035)k(cid:3029)(cid:3048)is(cid:3039)(cid:3038) tihs ethtea btaubluatlaetdedp peremrmitittitviviittyy ooff bbuullkk ggooldld [3[23],2 ](cid:2033),(cid:3043)ω tphet hpelaspmlaosnm pounlspatuiolsna toifo gnolodf, g(cid:2011)o ald ,
γ apphheennoommeennoolologigciacla dladmampipnign gcoceoffeicffiiecniet n[3t3[]3, 3(cid:1874)],(cid:3007) vtFheth FeerFmerim vielvoecliotyc i[t3y3][ 3a3n]da n(cid:1827)d aA coaecffoiceifefincti ethnattt hisa t
is inintrtorodduucceedd ffoorr aaddjujustsitning gthteh eeffeefcfte ocft coofnfcionnemfinenemt. Venart.iouVsa vraioluuess voaf l(cid:1827)u ecsano fbeA focuannd bine tfhoeu lnitderainturthe e
liter[a3t7u,3re8][ a3n7,d3 8h]earen wdeh ehraevwe cehhoasevne c(cid:1827)h=os1en [3A9,=40]1. [39,40].

Figure2. AFMimagesoftheGNGs(a)andtheHFs(b)withgold/polymerratioof3wt%,5wt%,
andF1i0guwret %2.. ATFhMes iumrfaagcees porfo tfihlee GsoNfGths e(ag)r aantidn gthsea rHeFssh (obw) nwiinth( cg)o.ld/polymer ratio of 3 wt %, 5 wt %,
and 10 wt %. The surface profiles of the gratings are shown in (c).
Materials 2018,11,351 5of13
Equation (1) is then used to describe the effective permittivity of a nanocomposite material
accordingtothestandardMGmodel,whichwillbereferredtoasMGc(‘c’standsfor‘confinement’).
Foravolumefraction f ofinclusions,theeffectivepermittivitycanbecalculatedwiththehelpofthe
followingexpression
(cid:101) −(cid:101)
(cid:101) = (cid:101) +3f(cid:101) incl m . (2)
eff m m(cid:101) +2(cid:101) − f((cid:101) −(cid:101) )
incl m incl m
In fact, this model is only valid under the following conditions: (i) the concentration of the
nanocomposites is small enough, i.e., the volume fraction is typically less than 10% and (ii) the
nanoparticleradiusfallsintherangeof1–25nm. ThesecondconditionreflectsthefactthattheMG
model does not explicitly account for the nanoparticle size. However, experimentally it turns out
thatthenanoparticlesize,andmorepreciselythesizedistributionofthenanoparticlesassembly,may
greatlyaffecttheplasmonicresponse. Totacklethisissue,extensionsoftheMGmodel,basedonthe
Mietheoryhavebeenproposedinordertotakeintoaccounttheeffectofparticlesize. Amongthem,
theModifiedMie–Maxwell–Garnettmodel(MMMG),alsointroducestheeffectofthenanoparticles
sizedistribution[36,40]. Consequently,wecomparedtheMGcmodelwiththistheory,togetherwith
Equation(1)accountingfortheeffectofconfinement,andcomputedtheeffectivepermittivityofthe
goldnanocomposites. ThismodelisreferredtoMMMGcandisgivenby
(cid:101)eff −(cid:101)m = f Rmaxα (R)g(R)dR, (3)
(cid:101)eff +2(cid:101)m Rmax R3g(R)dR(cid:119)Rmin Mie
(cid:114)Rmin
where,g(R)isthenanoparticlesizedistribution,withR andR itslowerandupperbounds.Next,
min max
3iλ3
α (R) = a (R), (4)
Mie 16π2(cid:101)m32 1
is the nanoparticle polarizability with a (R) being the first Mie (electric dipole) coefficient [41].
1
Notethathereweignorethe(usually)weakmagneticcontribution.
WethenusetheRCWAapproachtomodelthegratingsasaperiodicdistributionofnanostructures.
The parameterization of the system is sketched in Figure 3. We introduce the parameter h as the
1
thickness of the nanocomposite layer; it can be smaller than the total thickness of the film h .
tot
Inotherwords,theparametersh determinesthelocalizationofthenanoparticlesinthefilmthickness.
1
Indeed,ScanningElectronMicroscopy(SEM)measurementsperformedonthecrosssectionofsamples
depositedonsiliconwafershaveshownthatinsomecases,thegoldnanoparticlesarelocatedonlyin
athinlayeronthepolymerfilmsurface(seeFigureS8,SectionBoftheSupplementaryMaterial).
TheHFsaredefinedasmultilayerstructurescomposedoftheglasssubstrate, alayerofpure
polymer (of thickness h −h ) and a layer of nanocomposite (of thickness h ), whose effective
tot 1 1
permittivity(cid:101) iscomputedusingeithertheMGcortheMMMGcmodelaspreviouslydescribed.
eff
Thevolumefraction f ofinclusionsinthenanocompositelayerisnormalizedtoensuretheconservation
ofthetotalmassofgold.
InthecaseofGNGs,weusethesameparameterizationexceptthatthenanocompositelayeris
nowregardedasasuccessionofverythinlayersinordertoreproducethesurfaceprofileofthegrating.
The surface profiles are assumed to be perfectly sinusoidal with an amplitude h (see Figure 3b),
G
sothatthetotalvolumeofthenanocompositelayeristhesameasthatofaflatfilmdefinedbythe
samevalueofh . Consequently,thenormalizationofthevolumefractionisthesameasforHFs.
1
Materials 2018,11,351 6of13
Materials 2018, 11, x FOR PEER REVIEW 6 of 13

Figure 3. Parameterization of (a) the HFs and (b) the GNGs in the frame of the RCWA method.
Figure3.Parameterizationof(a)theHFsand(b)theGNGsintheframeoftheRCWAmethod.
3. Results and Discussion
3. ResultsandDiscussion
We now compare the experimental spectra with the results of our calculations. In order to
Wenowcomparetheexperimentalspectrawiththeresultsofourcalculations. Inordertovalidate
validate our theoretical method, we used as benchmarks the HFs and GNGs previously described in
ourtheoreticalmethod,weusedasbenchmarkstheHFsandGNGspreviouslydescribedinSection2.1.
Section 2.1. It should be emphasized that the GNGs exhibit a novel plasmon-enhanced diffraction
ItshouldbeemphasizedthattheGNGsexhibitanovelplasmon-enhanceddiffractioneffectthatwas
effect that was previously reported in [30]. This effect was defined as a resonant increase of the
predvififoruascltyiorne peoffritceiednicny [3in0 ].thTeh ipsleafsfmecotnw aressdoenfiannceed adsomaraeinso, nwahnitcihn ccraena sebeo fqtuhaendtiiffiferdac tbioy npelfofittciinegn cy
indthifefrpalcatisomn oenffirceiseonncya nccuervdeosm. Tahine ,awbshoircphticoann abnedq duifafnraticfitieodn beyffipcileonttciyn gspdeicftfrraa chtaiovne beeffienci esinmcyulcauterdv es.
Thuesainbgs othrpe tRioCnWaAn dmdetihffordac atsio dneteafifilecdie innc Syecstpioenct 2r.a2,h tahve edbieeleecntrsiicm puerlmatietdtivuitsyin ogf tthhee cRomCWpoAsitmese btheiondg as
dectaoimlepduitnedS eucstiinogn e2it.2h,etrh tehed MielGecc t(rEicqupaetrimoni t(t2iv))i toyr othfet hMeMcoMmGpco (sEitqeusabtieoinn g(3c))o mmopduetle. dusingeitherthe
MGc(EWquea ftiirostn d(i2s)c)uosrs tthhee MresMulMts Gfocr( tEhqeu HatFiso.n Fo(3r) o)umr osdimelu.lations we use the experimental values for
(cid:1858) (Wcaelcfiurlsatteddi sfcruomss tthhee rAeusu/PltVsAfo rratthioe).H InFds.eeFdo,r tohue resxipmeruimlateinotnasl awbesourspetitohne sepxepcetrraim deon ntaolt vparleuseenstf or
f (tchael ccuhlaartaecdtefrriostmic tpheeakA ouf/ tPhVe Agorldat ipor)e.cIunrdsoere (da,t t3h2e0 enxmpe),r iinmdeicnattailngab tshoart pthtieo nlatstpere chtaras bdeoenn oetntpirreelsye nt
thecocnhvaerratcetde rtios timcepteaallkic ogfotlhde. gTohled epxrpeecruimrseonrta(al tsp32a0tianl md)is,tirnibduictiaotnin goft hthaet tnhaenolaptatertrichlaess bine etnhee nfitlimre ly
conthvieckrtneedsst ocomuledt anlolitc bge oclodn.fiTrmheede bxyp esrtrimucetunrtaall cshpaartaiactledriizsattriiobnust.i oHnowofevthere, onuarn osipmaurtlaictlieosnsi nfotrh HeFfisl m
show that the parameter ℎ has a non-negligible effect on the absorption spectra, especially in the
thickness could not be confi(cid:2869)rmed by structural characterizations. However, our simulations for
long-wavelength domain. More precisely, as ℎ increases, which is equivalent to having the
HFs show that the parameter h has a non-negli(cid:2869)gible effect on the absorption spectra, especially
1
nanoparticles distributed in a thicker layer, the agreement between the measured and simulated
inthelong-wavelengthdomain. Moreprecisely,as h increases,whichisequivalenttohavingthe
1
spectra improves, and the best fit is obtained for ℎ = ℎ , i.e., when the nanoparticles assembly is
nanoparticles distributed in a thicker layer, the a(cid:2869)greem(cid:3047)e(cid:3042)(cid:3047)nt between the measured and simulated
spread over the total layer thickness (see section B, Figure S6 of the Supplementary Materials). Based
spectraimproves,andthebestfitisobtainedforh = h ,i.e.,whenthenanoparticlesassemblyis
on this result, we may conclude that the nanop1articlesto tare evenly dispersed in the film. More
spreadoverthetotallayerthickness(seesectionB,FigureS6oftheSupplementaryMaterials). Based
generally, the effect of varying ℎ indicates that the nanoparticle organization within the hosting
(cid:2869)
onthisresult,wemayconcludethatthenanoparticlesareevenlydispersedinthefilm. Moregenerally,
matrix plays a crucial role in the optical response for it affects the various scattering processes and
theeffectofvaryingh indicatesthatthenanoparticleorganizationwithinthehostingmatrixplaysa
interactions among t1he nanoparticles. A more quantitative analysis and comparison between theory
crucialroleintheopticalresponseforitaffectsthevariousscatteringprocessesandinteractionsamong
and experiments would require, on one hand, a precise measurement of the nanoparticles depth, and
thetankainngo pacacrotiucnlet so.f Athem morueltqi-uscaanttteitraintigv epraoncaeslysessis oann tdhec ootmhepra. risonbetweentheoryandexperiments
wouldrCeoqnusiereq,uoenntolyn,e whea nhdav,ae purseecdi sℎem=eℎasur=em8e0n0t nomft,h aesnsuamnoinpga rtthicalte sthdee npathn,oapnadrtitcaleksin agrea cecvoeunnlyt of
(cid:2869) (cid:3047)(cid:3042)(cid:3047)
thedmisturilbtiu-stecdat tienr itnhge ptortoacl etshsiecsknoenssth oef otthhee fri.lms. For the MMMGc model, it is necessary to take into
accCoounnst etqhue esniztely d,iwsteribhuatvioenu osfe dtheh 1na=nohptoatrt=icle8s0 0(senem E,qausastuiomni n(3g)).t hIna tththe ecansaen oofp tahret iscalmespaleres wevitehn l y
dis5t rwibtu %te danind t1h0e wtot t%al tghoilcdk, neexspseorifmtehnetafill msizse. FdoisrtrtihbuetMionMs MhaGvce mbeoedne lb,uiitlti sbny emceesassaurryintgo ata lkaergien to
accnouumnbtetrh eofs inzaendoipsatrrtiibculetsio tnhaotf atrhee vnisainbolep oanrt itchlee sA(FseMe Eimqaugaetsio onf (t3h)e) .fIilnmt’hs esucarfsaecoe f(ttihpe esfafemctpsl ewsewrei th
5westt%imaatnedd a1n0dw tatk%en ginotlod a,cecxopuenrt iwmheennt aelvasliuzeatidnigs ttrhibe untainoonpsahrtaicvleesb seizeen). bTuhielyt hbayvme tehaesnu breineng faittleadr ge
nuwmibthe ra olfognnaonrompaalr tdiicsltersibtuhtaiotna rleeavdiisnibg letoo tnhet hseizAe FdMistriimbuatgioens ofufntchteiofinl m(cid:1859)(’(cid:1844)s)s uursfeadc ein( ttihpee MffeMctMsGwce re
estmimoadteeld. Taynpdictaalk eAnFiMnt oimaacgcoesu natnwd htheen ceovrarleusaptoinngditnhge dniasntroibpuatritoicnlse sfosriz teh)e.sTeh seaymhpalvese tahree nshboewennfi itnt ed
wiFthigaurleo 4g.n Iot wrmasa lnodti sptorsibsiubtlieo tno alepapdlyin tghet osatmhee psrizoeceddiusrter itbou tthieo nHFfu ant c3t wiotn %g b(eRc)auussee ndoi nnatnhoepaMrtMiclMesG c
were visible on the film’s surface in the AFM images. In the absence of experimental data, the size
model. Typical AFM images and the corresponding distributions for these samples are shown in
distribution was numerically optimized by fitting the absorption spectrum to obtain the best
Figure4. ItwasnotpossibletoapplythesameproceduretotheHFat3wt%becausenonanoparticles
agreement between the simulated and the experimental data. The size distribution used for the
were visible on the film’s surface in the AFM images. In the absence of experimental data, the
sample at 3 wt % is given in the Supplementary Materials (Section B, Figure S5). For the MGc model,
size distribution was numerically optimized by fitting the absorption spectrum to obtain the best
agreementbetweenthesimulatedandtheexperimentaldata. Thesizedistributionusedforthesample
Materials 2018,11,351 7of13
MMaatteerriaialsls 2 2001188, ,1 111, ,x x F FOORR P PEEEERR R REEVVIIEEWW 77 o off 1 133
at3wt%isgivenintheSupplementaryMaterials(SectionB,FigureS5). FortheMGcmodel,theeffect
tothhfeec oeenffffifeencctet moofef nccoto,nnwffiinhneiecmmheednnett,p, ewwnhdhiiscchhe x ddpeelpipceientnldydsso enexxtphpleliiccniittallyny o oopnna rttthhiece l ennasaninzoeop,pawarrtatiiscclilene tssrioizzdee,u, wcweadass b iinynttcrrooodndsuuicdceeeddr i nbbygy
ctchooennsmsiiddeeaerrniinnvgga t tlhuheee m moefeatanhn ev vapalaluurete io coflf et thhseie zp peaardrtitisicctllreei sb siuizzetei od dniiss.ttrMriibbeuuattsiiouonrn.e .M dMeaeanasdsuursreiemdd au anlnaddt es sidimmauublslaaotteredpd ta iabobsnsoosrrpppteticiootnrna s spopefecctthtrraea
onofaf nt thhoece o nnmaannpoooccsooimtmepspowossiiitttehessA w wuii/tthhP A VAAuu//PrPaVVtiAoA r orafatt3iioow o otff %3 3 w ,w5tt w% %t, ,5 %5 w,wattn % %d, ,1a a0nndwd 1 t10%0 wwatrt e% %g a iavrreee ng giiivnveenFni i ginnu F rFeiigg5uu.rree 5 5. .

FFiigguurree 44. . ((aa)) HHiissttooggrraamm aanndd ffiitttteedd ssiizzee ddiissttrriibbuuttiioonn o off tthhee HHFFss aatt 55 wwtt %% aanndd 1100 wwtt %%; ; ((bb)) 33DD vviieeww ooff
Figure4.(a)HistogramandfittedsizedistributionoftheHFsat5wt%and10wt%;(b)3Dviewof
ttyyppiiccaall A AFFMM i immaaggeess o off t thheessee s saammpplleess. .
typicalAFMimagesofthesesamples.

FFFiiiggguuurrreee 55 5.. .C CCooommmpppaaarrriiisssooonnn b bbeeetttwwweeeeeennn t tthhheee a aabbbsssooorrrppptttiiiooonnn s sspppeeeccctttrrraaa f ffrrrooommm e eexxxpppeeerrriiimmmeeennntttsss ( ((dddoootttttteeeddd ll liiinnneee))) a aannnddd s ssiiimmmuuulllaaatttiiiooonnnsss
(((cccooonnntttiininnuuuooouuusss ll ilininneee))) uu usssiininnggg tt hthheee MM MGGGccc mm mooodddeeelll (( a(aa))) aa annnddd tt hthheee MM MMMMMMMGGGccc mm mooodddeeelll (( b(bb)).). .
TTThhheee rrreeesssuuulltltstss s shshhooowww t ththhaatattt h ttheheep prperrdeedidciticictotiinoosnnsos f ootfhf tethhMee MGMcGGmcc ommdoeodldeaelrl e aarsrelei g sshlliitgglhyhtbtllylyu bebl-lusuhee-i-fssthehidiffttceeoddm ccpoomamreppdaartreoeddt h ttoeo
tethxhepe eerexixmppeeernriimtmaelendntataatlal .ddHaatotaaw.. eHHvoeowrw,etehvveeerrM,, MtthheMe GMMcMMmMMoGdGeccl wmmiotodhdeeslil z wewiditthihs t rssiiibzzeue t idodinissttlrreiibabudutstiiotoonn a llegeaoadodsds tatogo r aea e mggooeoonddt
waaggirtrheeeetmhmeeenentxt pw weiritthihm t thehnee te aexlxpdpeaertriaimm.eFeninnttaaalll ld yd,aattthaa.e. F Fgiionnoaaldlllyya,g, t trhheeee g mgooeoonddt a oagbgrsreeeeremvmeedenntft oo orbbpsselearrsvvmeedod nf foorrre p spollanassammnocoenn ar rmeesspoolnnitaaunndcceee
abamemtpwplleiitetuunddese i mbbeeuttwlwaeteieoennn sssiiammnudullaaettxiioponnesrs i amanneddn teesxxpcpoeenrrifiimmremennsttsst hccoeonnffafiicrrmtmtshs atththeet h ffeaaccttot ttthahlaatat mtthhoee u tntootttaaoll f aagmmooloduunnptt r eoocff u ggrosoollddr
pipnrrterecocudurursscooerrd iininnttrtrohodeduuscycesedtde miinn h tathhseeb essyeynssttereemmd u hchaeasds tbboeeemenne trareledldicuucsceteaddt e ttdoo u mrmineetgtaatlllhliicec fsastbtaarttieec a dtdiuournriinnpggr o tcthheede uffaraebb.rriiccaattiioonn
pprroocceedduurree..
Materials 2018,11,351 8of13
Materials 2018, 11, x FOR PEER REVIEW 8 of 13
Insummary,forsimplesystemssuchasHFs,ourapproachrendersfairlygoodresults,butitalso
showstIhna stuitmismnaercye, sfsoarr ysimtoptlaek esyasctceomusn stuocfht haes nHaFnso, poaurrt iacplepsr’osaizceh dreisntdriebrus tfioainrliyn gthooedc arlecsuullattsi,o bnuot fitt he
effeaclstoiv sehpowersm thitatitv iti tiys. necessary to take account of the nanoparticles’ size distribution in the calculation
of Ntheex etf,fwecetiavnea plyerzmeitthteivrietys.u ltsfortheGNGs. Asbefore,thetotalthicknessofthefilm,h =800nm,
tot
Next, we analyze the results for the GNGs. As before, the total thickness of the film, ℎ = 800
is the same for all samples and we have used values of the volume fraction f calculated(cid:3047)(cid:3042)(cid:3047)from the
nm, is the same for all samples and we have used values of the volume fraction (cid:1858) calculated from
experimentalgoldconcentrations. Thegratingsheights,inferredfromthesurfaceprofilesmeasured
the experimental gold concentrations. The gratings heights, inferred from the surface profiles
byAFM(seeFigure2b),areh =25nm,65nmand80nm,respectivelyforthesampleswithAu/PVA
G
measured by AFM (see Figure 2b), are ℎ = 25 nm, 65 nm and 80 nm, respectively for the samples
ratioof3wt%,5wt%,and10wt%. Inco(cid:3008)ntrastwithHFs,herewehavefoundthatthelocalization
with Au/PVA ratio of 3 wt %, 5 wt %, and 10 wt %. In contrast with HFs, here we have found that the
of nanoparticles in GNGs, described with the help of the numerical parameter h , plays a crucial
localization of nanoparticles in GNGs, described with the help of the numerical param1 eter ℎ , plays
(cid:2869)
roleinthesimulatedspectra,inparticularinwhatregardsthediffractionproperties. Indeed,asthe
a crucial role in the simulated spectra, in particular in what regards the diffraction properties. Indeed,
periodicsurfacemodulationisonlysuperficial(h ≈ h /10),theconcentrationofthenanoparticles
as the periodic surface modulation is only supGerficitaolt (ℎ ≈ℎ /10), the concentration of the
(cid:3008) (cid:3047)(cid:3042)(cid:3047)
in this region strongly affects the diffraction efficiency of the system. Consequently, for each gold
nanoparticles in this region strongly affects the diffraction efficiency of the system. Consequently, for
concentration,theparameterh hasbeenoptimizedinordertoobtainthebestagreementbetween
each gold concentration, the pa1rameter ℎ has been optimized in order to obtain the best agreement
(cid:2869)
thebesitmweuelna tetdhea nsdimeuxlpateerdim aenndta lexsppeercitmrae.nTtahle soppetcitmrai.z eTdhev aolupetism,sizuemd mvaarluizeesd, isnumthmeaSruizpepdl eimn etnhtea ry
MaStuepripallesm(Seencttairoyn MBa,tFeirgiaulrse (SSe9c)t,iaorne Ba,r Foiugnudre1 S090),n amre, awrohuicnhd i1n0d0i cnamte, swthhiacth, cinodnitcraatreys ttohatht, ecocnastreaoryf HtoF s,
thethnea ncaospea orft iHcleFss,a trhees ntraonnogplayrtlioccleasli zaered sntreoanrgtlhye lfioclmalizsuedrf anceea.r Fthroem filtmh esufarbfarcicea. tFioronmp othine tfaobfrvicieawtio,nit is
likpeloyintht aotf tvhieewlo, ciat liisz alitkioelny othfagto tlhdeo lcoccuarliszdatuiornin ogft ghoeldir roacdciuartsi odnuprirnogc ethsse. iArrsadthiaetigoonl dprioocnessse.x Apes rtiheen ce
thegolilgdh itoinnst eexnpseitryiegnrcaed thieen ltigohft tihneteinnstietyrf gerreadniceenpt oaft ttehren i,nttheerfyermenigcer aptaettteorwn,a trhdeyth meibgrriagteh ttofwrinargde sthaen d
arebrpihghott ofr-rinegdeusc aenddn aeraer pthhoetosu-rrefdauceceodf ntheaer fithlme ssu[r4f2a]c.e Aofs tfhoer fHilmFss, [t4h2e]. nAasn foopr aHrtFics,l ethseiz neadnoisptarirbtiuclteio n
usesdizein dthisetrMibuMtiMonG cusmedo dienl hthaes bMeeMnMdeGtce rmmoindeedl fhraosm bAeeFnM diemteargmeisnfeodr tfhroemna nAoFcMom impoasgietess faotr5 twhet %
andna1n0ocwotm%po(ssietees Faigt u5r ew6t) ,%an danndu m10e rwicta l%ly o(speteim Fiizgeudref o6r),t haennda nnoucmoemripcaolslyit eoaptti3mwizted% f(othr ethfien al
disntrainbouctoimonpoissigteiv aet n3 wint F%i g(tuhree fiSn5alo dfitshtreibSuutipopnl iesm geivnetna riny FMigautreer iSa5l so)f. tTheh eSuvpapluleemseonftahrya Mndatearlilaolst)h. er
1
The values of ℎ and all other simulation parameters for the GNGs are summarized in the
simulation parame(cid:2869)ters for the GNGs are summarized in the Supplementary Materials (Section B,
Supplementary Materials (Section B, Figure S9).
FigureS9).

FigFuigreur6e. 6(a. )(aH) Histisotgorgarmamssa nanddfi ftittetedds sizizeed diissttrriibbuuttiioonnss ooff tthhee GGNNGGss aat t55 wwt t%% anadn d101 0wwt %t;% (b;()b 3)D3 vDievwie w
oftoyf ptyicpailcaAl FAMFMim imagaegseos fotfh tehseeses asammppleless..
The experimental and simulated absorption and diffraction efficiency spectra are given in Figure 7.
TheexperimentalandsimulatedabsorptionanddiffractionefficiencyspectraaregiveninFigure7.
The first important result is the fact that our approach correctly accounts for the optical behavior of the
Thefirstimportantresultisthefactthatourapproachcorrectlyaccountsfortheopticalbehaviorofthe
GNGs, and in particular enables to reproduce the plasmon-enhanced diffraction effect. Upon closely
GNGs,andinparticularenablestoreproducetheplasmon-enhanceddiffractioneffect. Uponclosely
analyzing the details, we find that the simulations show that, except for low gold concentrations
analyzing the details, we find that the simulations show that, except for low gold concentrations
(3 wt %), the MGc model does not provide a quantitative agreement with the experimental data.
Materials 2018,11,351 9of13
Materials 2018, 11, x FOR PEER REVIEW 9 of 13
(3wt%), the MGc model does not provide a quantitative agreement with the experimental data.
Indeed, the simulated absorption curves for the samples with 5 wt % and 10 wt % gold exhibit
Indeed, the simulated absorption curves for the samples with 5 wt % and 10 wt % gold exhibit
plasmon resonance profiles that are both narrower and blue-shifted, as compared to the measured
plasmonresonanceprofilesthatarebothnarrowerandblue-shifted,ascomparedtothemeasured
ones. The same conclusions can be drawn for the diffraction efficiency spectra, which, even if they
ones. Thesameconclusionscanbedrawnforthediffractionefficiencyspectra,which,evenifthey
show the right tendency, do not allow for quantitative predictions. On the other hand, the results for
showtherighttendency, donotallowforquantitativepredictions. Ontheotherhand, theresults
the MMMGc model show that taking into account the particle size distribution qualitatively and
fortheMMMGcmodelshowthattakingintoaccounttheparticlesizedistributionqualitativelyand
quantitatively improves the results, in particular for the sample with 5 wt % gold. However, for
quantitatively improves the results, in particular for the sample with 5 wt % gold. However, for
10 wt % gold, even if there is a better qualitative agreement between theory and experiment than for
10wt%gold,evenifthereisabetterqualitativeagreementbetweentheoryandexperimentthanfor
the MGc model, the discrepancies are still large in both absorption and diffraction efficiency spectra.
theMGcmodel,thediscrepanciesarestilllargeinbothabsorptionanddiffractionefficiencyspectra.
In particular, with this approach, we cannot precisely predict the position of the plasmonic peaks at
Inparticular,withthisapproach,wecannotpreciselypredictthepositionoftheplasmonicpeaksat
this concentration.
thisconcentration.

Figure 7. Comparison between the absorption spectra and the diffraction efficiency (DE) spectra
Figure 7. Comparison between the absorption spectra and the diffraction efficiency (DE) spectra
measured experimentally and simulated using the MGc model (a,b) and the MMMGc model (c,d).
measuredexperimentallyandsimulatedusingtheMGcmodel(a,b)andtheMMMGcmodel(c,d).
The latter observation is, however, not quite surprising. Indeed, if we analyze the AFM images
Thelatterobservationis,however,notquitesurprising. Indeed,ifweanalyzetheAFMimages
of the GNG at 10 wt % gold (see Figure 6c), we notice a very high density of nanoparticles at the
of the GNG at 10 wt % gold (see Figure 6c), we notice a very high density of nanoparticles at the
grating crests emerging from the surface. This means that the nanoparticles are not fully embedded
gratingcrestsemergingfromthesurface. Thismeansthatthenanoparticlesarenotfullyembedded
in the polymer matrix anymore, so that our simulations based on the effective medium approach are
inthepolymermatrixanymore,sothatoursimulationsbasedontheeffectivemediumapproachare
not really suitable for describing the system. For a better description of the emerging nanoparticles,
notreallysuitablefordescribingthesystem. Forabetterdescriptionoftheemergingnanoparticles,
we proposed a new parametrization of the system (M2) sketched in Figure 8a. First, we increase the
weproposedanewparametrizationofthesystem(M2)sketchedinFigure8a. First,weincreasethe
grating height in order to include, at least partially, the emerging nanoparticles inside the simulated
gratingheightinordertoinclude,atleastpartially,theemergingnanoparticlesinsidethesimulated
nnaannooccoommppoossiittee llaayyeerr.. TThhee eeffffeeccttiivvee ggrraattiinngg hheeiigghhtt ℎh(cid:3008)e(cid:3032)(cid:3033)f(cid:3033)f hhaass bbeeeenn vvaarriieedd bbeettwweeeenn 8800 nnmm ((hℎ(cid:3008))) aanndd
130 nm, which corresponds to the maximal height thatG is reached only locally by some nanopaGrticles.
130nm,whichcorrespondstothemaximalheightthatisreachedonlylocallybysomenanoparticles.
We have found that this parameter strongly affects the simulated spectra, in particular the amplitude
Wehavefoundthatthisparameterstronglyaffectsthesimulatedspectra,inparticulartheamplitude
of the diffraction efficiency and the best agreement with the experimental spectra is obtained for
of the diffraction efficiency and the best agreement with the experimental spectra is obtained for
ℎ(cid:3032)(cid:3033)(cid:3033) =110 nm. Second, since the nanoparticles are partly covered by polymer on one side and by air
he(cid:3008)ff =110nm. Second, sincethenanoparticlesarepartlycoveredbypolymerononesideandby
oGn the other, they experience a different environment, which may be characterized by a smaller value
of the matrix permittivity. Numerical optimization leads to (cid:2035) =1.82 (i.e., (cid:1866) = 1.35 instead of 1.5).
(cid:3040)
Materials 2018,11,351 10of13
Maiarteorinalst 2h0e18o, t1h1,e xr ,FtOhRe yPEeExRp ReErVieIEnWce adifferentenvironment,whichmaybecharacterizedbyasm10 aolfl 1e3r
valueofthematrixpermittivity. Numericaloptimizationleadsto(cid:101) =1.82(i.e.,n=1.35insteadof1.5).
m
TThhee rreessuullttss oobbttaainineedd wwitihth ththisi snenwew mmodoedl e(lM(M2) 2a)rea rceomcopmapreadr ewditwh itthhet pherepvrioeuviso ounseos n(meso(dmelo Mde1l, Mℎ(cid:3008)1,
=h G80= n8m0,n (cid:2035)m(cid:3040), (cid:101)=m 2=.252).2 i5n) FinigFuirgeu 8rbe,8cb. ,c.

FFiigguurree 88.. SSppeeccifiifcicc ocnosnisdiedreartaiotinonfo rfothr ethGeN GGNatG1 0atw 1t0% .w(at )%P.a r(aam) ePtaerrasmfoerttehres nfoewr tmheo dneeliwn gmapopdreoliancgh
a(Mpp2r)oaancdh t(hMe2p)r aenvdio uthseo pnree(vMio1u).s (obn)eA (bMso1r).p (tbio)n Aabnsdor(pc)tiDonif farnacdt i(ocn) Defififfcriaecntciyon(D eEff)icsipeencctyra (DofEt)h sepGecNtrGa :
ocfo mthpe aGriNsoGn: bcoetmwpeaernistohne beextpwereiemne tnhtea lexdpaetariamnedntthale dtwatoa manodd tehlse. two models.
It is clear that the new set of parameters, which corresponds to a more plausible physical
It is clear that the new set of parameters, which corresponds to a more plausible physical
description of the GNG, improves the agreement between experiments and theory. We see in
descriptionoftheGNG,improvestheagreementbetweenexperimentsandtheory. Weseeinparticular
particular a better prediction regarding the resonances position and amplitude in both absorption
abetterpredictionregardingtheresonancespositionandamplitudeinbothabsorptionandDEspectra.
and DE spectra. These two effects are mainly due to the change of environment (modified (cid:2035) ), since
These two effects are mainly due to the change of environment (modified (cid:101) ), since the p(cid:3040)lasmon
m
the plasmon resonance of nanoparticles becomes more blue-shifted and weaker in magnitude when
resonanceofnanoparticlesbecomesmoreblue-shiftedandweakerinmagnitudewhentherefractive
the refractive index of their surrounding medium decreases. It can be seen that, even with this
indexoftheirsurroundingmediumdecreases. Itcanbeseenthat,evenwiththisimprovedmodel,we
improved model, we cannot reproduce the shoulder appearing on the experimental spectra around
cannotreproducetheshoulderappearingontheexperimentalspectraaround750–800nm.Thisfeature,
750–800 nm. This feature, which is not observed for the other samples, may be attributed to plasmonic
whichisnotobservedfortheothersamples,maybeattributedtoplasmoniccouplingbetweenstrongly
coupling between strongly packed nanoparticles [43]. Indeed, at the grating crests, the nanoparticle
packednanoparticles[43]. Indeed,atthegratingcrests,thenanoparticleconcentrationcanbelocally
concentration can be locally very high. As a consequence, aggregates may appear and involve complex
very high. As a consequence, aggregates may appear and involve complex multi-polar coupling
multi-polar coupling among the nanoparticles. Unfortunately, such effects cannot be described
amongthenanoparticles. Unfortunately,sucheffectscannotbedescribedproperlybytheeffective
properly by the effective medium approach used here, which only includes the dipolar coupling.
mediumapproachusedhere,whichonlyincludesthedipolarcoupling.
4. Conclusions
4. Conclusions
In conclusion, we have fabricated nanocomposites in the form of homogeneous films (HFs) and
Inconclusion,wehavefabricatednanocompositesintheformofhomogeneousfilms(HFs)and
gold nanoparticle gratings (GNGs) by using an in situ synthesis approach under laser irradiation. We
gold nanoparticle gratings (GNGs) by using an in situ synthesis approach under laser irradiation.
have measured and simulated both the absorption and the diffraction efficiency spectra of these
Wehavemeasuredandsimulatedboththeabsorptionandthediffractionefficiencyspectraofthese
systems with a variable gold/polymer ratio. We have shown that the combination of RCWA and
systems with a variable gold/polymer ratio. We have shown that the combination of RCWA and
(extended) effective medium theories is a promising means for computing the optical properties of
(extended)effectivemediumtheoriesisapromisingmeansforcomputingtheopticalpropertiesof
complex plasmonic systems. In particular, our simulations reproduce the previously observed effect
complexplasmonicsystems. Inparticular,oursimulationsreproducethepreviouslyobservedeffectof
of plasmon-enhanced diffraction in GNGs. For polydisperse nanoparticles, it has been shown that
the size distribution must be taken into account in order to reach a quantitative agreement with
experiment. Finally, we have speculated how the present model may be adapted so as to describe the
specific configuration of GNGs at 10 wt %. This demonstrates the versatility of this approach and