Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas

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1 SUPPLEMENTARY INFORMATION DOI: /NPHOTON Probing the mechnisms of lrge Purcell enhncement in plsmonic nnontenns Gleb M. Akselrod 1,, Christos Argyropoulos 1,, Thng B. Hong 1,3, Cristin Circì 1,,*, Cho Fng, Jini Hung 1,3, Dvid R. Smith 1,,3, Miken H. Mikkelsen 1,,3, 1 Center for Metmterils nd Integrted Plsmonics, Duke University, Durhm, NC 7708, Deprtment of Electricl nd Computer Engineering, Duke University, Durhm, NC Deprtment of Physics, Duke University, Durhm, NC Simultion Methods The commercil finite-element simultion softwre (COMSOL Multiphysics) ws used to model the NPA. We creted sphericl domin round single NPA nd scttering boundry conditions were employed to mimic n open boundry. The permittivity of the silver nnocube nd the gold film substrte were modeled bsed on the dispersive prmeters 1. The corners of the nnocube were smoothed, with rdius of curvture of 8 nm. The nnocube s dimensions were vried in order to lwys fix the plsmon resonnce of the NPA plsmonic system to λ = 650 nm np. A thin 3 nm insulting shell ws plced to surround the metllic nnocube with refrctive index n = 1.4. The thickness of the spcer lyer chnged from nm to 1 nm in order to simulte the different number of polymer lyers plced in the nnogp. These lyers were modeled s dielectrics with n index of refrction equl to n = 1.4. The glss substrte ws ssumed to be semi-infinite with refrctive index of n = 1.47 which ws plced beneth the gold film substrte. We used COMSOL simultions to clculte the scttering signture of the NPA nd the electric field distributions induced t the nnogp both t excittion (535 nm) nd resonnt (650 nm) frequencies. The scttered-field formultion ws employed, which uses the * Current ddress: Istituto Itlino di Tecnologi (IIT), Center for Biomoleculr Nnotechnologies, Vi Brsnti, I Arnesno, Itly e-mil: m.mikkelsen@duke.edu NATURE PHOTONICS Mcmilln Publishers Limited. All rights reserved.

2 nlyticl solution for n incident plne wve in the bsence of the nnocube s the bckground field. Trnsverse-mgnetic (TM) polriztion nd norml incidence is ssumed for the impinging plne wve to compute the scttering. However, the scttering response is firly independent of the ngle of incidence nd polriztion of the plne wve excittion, s it ws demonstrted erlier in Lssiter et l. nd Moreu et l. 3. The Ru dye ws modeled s monochromtic point-dipole emitting t λ sp = 650 nm. The Green's function of the system, from which the locl density of sttes, spontneous decy rte nd rditive quntum efficiency cn be derived 4, ws evluted by vrying the position of the dipole emitter on discrete 15x15 grid plced beneth the nnocube. The surfce formed by this rry ws plced in different positions long the z-xis inside the spcer lyer in order to tke into ccount in our clcultions the entire volume of the nnogp. The four-fold symmetry of the NPA ws used to reduce the necessry number of simultions. Note tht the sme simultion domin for the scttering clcultions ws used to compute the emissive properties of the system. The rditive nd non-rditive rtes were obtined by integrting the totl power rdited out of the entire domin nd bsorbed from the plsmonic system, respectively. Seprte simultions were performed for dipoles oriented long ll three Crtesin coordintes. However, it ws found tht the dominnt field component tht cn couple efficiently to the plsmonic mode t the nnogp of the NPA is the one ligned long the z-xis. The x nd y components cnnot couple efficiently to the plsmonic mode formed in the nnogp nd their contribution to the totl spontneous emission cn be sfely neglected. The time-dependent emission decy curves were clculted bsed on the fct tht the emitted power t n rbitrry position r is proportionl to the number of the excited molecules nd their emitted intensity: γ sp ( r, nˆ )t ˆ ex γr I(, r θ,t) E (r) n () r e, where E ex (r) is the field distribution t the excittion wvelength (535 nm). Only the emitters oriented long the z-xis rdite significntly nd, s result, contribute to the spontneous emission rte, which cn now be written: γ sp (r, ˆn) = γ sp (r,ẑ)cos θ, where θ is the ngle between the emitter orienttion ˆn nd the z-xis. Assuming distribution of emitter orienttions C(θ) = exp (θ θ 0 ) / σ, which is determined experimentlly in section 6, the verged emitted power over ll possible directions is equl to: 014 Mcmilln Publishers Limited. All rights reserved.

3 1 π / γsp ( r)cos θt I( r, t) Eex( r) cos θγ ( ) ( θ)sinθ θ 0 r r e C d. (1) The emission curve s function of time is then obtined by summing up the contribution of ech emitter, or eqully integrting I(r,t) over the volume of the emitters V nd multiplying by the emitter density, N/V, with N being the number of the emitters. Hence, the finl formul to compute the emission decy rte from the NPA is given by: I np (t) = N V I(r,t)dV () V This integrl cn be computed numericlly nd the obtined results hve excellent greement with the computed experimentl rtes for ll different nnogps.. Extrcting the cube enhnced fluorescence The excittion spot (~300 nm dimeter) is much lrger thn the cube size nd consequently dye fluorescence is collected from regions outside the nnogp. To obtin the contribution to the time-resolved fluorescence originting from the nnogp I () t, we mesured time-resolved fluorescence from ~10 spots on ech smple tht contined no cubes I off (t). Due to quenching from the Au film, the totl fluorescence from ech of these spots ws <10% of the fluorescence obtined from spot contining resonnt nnocube. The nnocube fluorescence contribution ws then obtined from the totl collected fluorescence I () t by tot np 3. Distribution of rtes nlysis 1 = N n I t I t I t ( ) np () tot () off () N n= 1 (3) The electric field in the nnogp is not uniform, nd consequently molecules t different positions will experience different emission rtes. In such cse, the mesured time-resolved emission curve cn be expressed generlly s the sum of exponentil decy terms F(t) = H(k) e kt dk (4) 0 where F(t) is the fluorescence intensity nd H(k) is the distribution of rte constnts. Recovering H(k) from the experimentlly obtined emission curve F(t) is in generl difficult Mcmilln Publishers Limited. All rights reserved.

4 becuse extrcting H(k) from Eq. (4) is n ill-defined problem. The pproch commonly used to recover H(k), 5 is to ssume mthemticl function describing the temporl dynmics. Here we will use the modified stretched exponentil function to model F(t) β t Ft ( ) = A exp (5) τ 0 The shpe prmeter 0 < β 1 determines how sub-exponentil the decy curve is, with β = 1 describing purely exponentil decy. We note tht other functions cn be used to model nonexponentil decy, s described below. In the experimentl system, the mesured time-resolved fluorescence from the NPA I () t is convolution of the instrument response function of the detector I () t with the underlying emission intensity from the cube I () t em I () t = I () t I () t (6) np em irf The instrument response function for our experimentl system hs full width t hlf mximum of 35 ps, s shown in Supplementry Figure S1. The mesured emission decy curves re fit to function I () t = F() t I () t which is convolution of the stretched exponentil nd the fit irf instrument response, from which the prmeters of the stretched exponentil re obtined. Such fit for single NPA for ech gp thickness is shown in Supplementry Figure S. irf np Supplementry Figure S1. Instrument response function of the fluorescence detection system, showing 35 ps FWHM response time, mesured by scttering smll mount of excittion lser light onto the detector Mcmilln Publishers Limited. All rights reserved.

5 Supplementry Figure S. Mesured emission decy curves from single NPA for ech gp thickness long with fit to the stretched exponentil function convolved with the instrument response function. To extrct the distribution of rtes underlying the stretched exponentil, we first consider the decy dynmics of system with time-dependent decy constnt tht cn be described by the first order differentil eqution dn dt = k(t)n (7) where N is the number of excited stte molecules. The mesured intensity is then ssumed to be proportionl to N F(t) = N N 0 (8) The time-dependent rte constnt is then given by k(t) = d ln F(t) (9) dt For the stretched exponentil function, the time-dependent rte constnt is then k(t) = β 1+ t τ 0 τ 0 β 1 (10) Mcmilln Publishers Limited. All rights reserved.

6 A number of prmeters chrcterizing the stretched exponentil decy cn be clculted 5. The ensemble verge rte constnt is while the ensemble verged time constnt is τ = k = kh(k)dk = k(0) = β (11) τ F(t) / F(0)dt = e β Γ 1, 1 β τ (1) 0 where Γ(x,) is the incomplete gmm function. The rte distribution function H(k) for stretched exponentil cn only be expressed in terms of elementry functions for discrete vlues of β. Berbern-Sntos et l. 5 hve found stble nd ccurte numericl solution for H(k) for rbitrry β, H β/(1 β) B (1 ββ ) ( k) = τ exp 1 kτ f( k) (13) β 0 (1 β/)/(1 β) 0 β/(1 β) ( kτ0) ( kτ0) where the uxiliry function f (k) is given by 1 β(1 / β), δ =, for β 1/ 1 + δ Ck ( τ0) 1 β f( k) = δ β( β 1/ ) 1 + Ck ( τ0), δ =, for β > 1/ 1 β (14) The prmeters B nd C re clculted numericlly nd re given for discrete vlues in Supplementry Tble 1. Intermedite vlues re obtined by cubic interpoltion. β B C Supplementry Tble 1. Prmeters for the rte distribution uxiliry function. The rte distribution obtined from fit of the experimentl dt to stretched exponentil for ech gp thickness is shown in Supplementry Figure S3 nd shown in Figure 3b in the min Mcmilln Publishers Limited. All rights reserved.

7 text. Also shown here re the rte distributions obtined directly from the simultions, showing good greement with the experiment without ny fit prmeters. Supplementry Figure S3. Emission rte distributions for ech gp thickness obtined from simultions nd from fit of the experimentl dt to stretched exponentil. We note tht the problem of extrcting distribution of rtes from time-dependent signl is not well-defined problem. A number of different functions hve been used to model nonexponentil decys 5-8, with the stretched exponentil being the most common. To show the effect of the choice of fitting function on the extrcted rte distribution, we show in Supplementry Figure S4 the nlysis from Figure e-f for both stretched exponentil nd the Lplce trnsform of the Γ distribution 8 The rte distribution corresponding to this decy is the Γ distribution 1 Ft () = (14) α 1 (1 + + κt) 1 k H( k) = exp( k / κ ) Γ ( α + 1) κ Supplementry Figure S4 shows fits of the time-resolved fluorescence from single NPA with n 8 nm gp to stretched exponentil nd to Γ distribution, with both functions resulting in good fits. The corresponding rte distributions (Supplementry Figure S4b) show more vrition, prticulrly in the tils of the distributions. While the stretched exponentil gives better greement with simultions for the pek of the distribution, the Γ distribution gives better 7 α (14) 014 Mcmilln Publishers Limited. All rights reserved.

8 greement in the tils of the distribution. Neither function is justified bsed on the underlying physics of the system since the non-exponentil decy from the NPAs is due to sptil inhomogeneity rther thn the kinetics of the molecule emission. However, we note tht the criticl prmeter of mximum rte is not determined by the prticulr function used. Rther it is obtined from the initil slope of the time-resolved fluorescence, which is nerly the sme regrdless of the choice of fitting function (Supplementry Figure S4). Supplementry Figure S4. () Time- resolved fluorescence decy from single NPA with n 8 nm gp nd fits to two types of functions: (i) stretched exponentil nd (ii) Γ distribution, long with the simultion results. (b) Distribution of rte constnts obtined from fits to stretched exponentil nd Γ distribution. The rte distribution from the simultion results is lso shown. 4. Fluorescence enhncement fctor Experimentlly, the verge time-integrted fluorescence enhncement fctor for NPA, EF, is the rtio of emission per unit re from the NPA divided by the emission per unit re from n equivlent lyer of dye molecules on glss, given by EF I = np c I c A A np (15) Mcmilln Publishers Limited. All rights reserved.

9 where I is the emission contribution from the NPA s determined from Eq. (3), I np c is the emission intensity from the glss control smple, A is the re under the nnocube, nd np A c is the re of the lser spot on the control smple. The re under the nnocube is given by Anp = l where l is the cube side length without the PVP lyer. This length is inferred from the gp thickness nd plsmon resonnce wvelength bsed on previously described methods. The side length depends on gp thickness in order for the resonnce to remin fixed t 650 nm. The reltionship between nnocube size nd gp thickness is given in Supplementry Tble. Emission from the control smple origintes from the entire excittion spot size, which is Gussin spot. To good pproximtion, the effective re of emission is from circle with dimeter equl to the FWHM of the excittion spot, such tht A = (350 nm). The imged spot of the control smple emission nd the NPA emission is smller thn the APD sensor re (50 µμm 50 µμm) such tht ll collected emission is detected nd Eq. (15) is vlid. The mesured EF is shown in Figure 4c in the min text. c Cube size, l (nm) Gp thickness, d (nm) Number of PE lyers 66 nm PE film nd 3 nm PVP shell nm PE film nd 3 nm PVP shell nm PE film nd 3 nm PVP shell nm PE film nd 3 nm PVP shell 9 Supplementry Tble. Nnocube nd gp prmeters for constnt plsmon resonnce of λ = 650 nm. To ensure proper control smples, it is criticl tht the density of Ru dye on the control smple is equl to the density of dye in the NPA smples. However, we find tht the polyelectrolyte (PE) lyers grow differently on glss nd gold substrtes. Using ellipsometry we show how the thickness of the PE lyers depends on the number of depositions on the two substrtes (Supplementry Figure S5). As glss substrtes re not suitble for ellipsometry mesurements of such thin films, Si with ntive oxide ws used insted. A Cuchy model for the refrctive index of the polymer film is used in the nlysis of the ellipsometry dt. For exmple, to obtin polymer lyer thickness of ~5 nm, 5 PE lyers re grown on gold while 9 PE lyers re grown on glss. The polymer films on gold nd glss re incubted in the Ru dye solution s Mcmilln Publishers Limited. All rights reserved.

10 described in the Methods, obtining the sme density of Ru dye on both the NPA nd control smples. Supplementry Figure S5. Thickness of PAH/PSS polymer film s function of number of PE lyers on Si with ntive oxide surfce (red) nd on gold surfce (blue) mesured by ellipsometry. The PE lyer number is defined s the totl number of polymer solution dips, including PAH nd PSS. 5. Simulted enhncement fctor The fluorescence enhncement fctor from simultions t prticulr position nd dipole orienttion is defined s η γ (, r θ) QE() r EF() r (15) ex = 0 η0 γex ( θ) QE0 where η is the emission collection efficiency, is the excittion rte nd θ is the polr orienttion of the dipole. Ech of these vlues for the NPA is normlized by the sme quntity clculted for equivlent dipoles on glss. The excittion rte enhncement cn be rewritten in terms of the field enhncements 1 γ E r + E r θ + E r γ θ θ (, θ) () ( ) sin ( ) cos z ex r x y = 0 ex( ) E0 sin Here we hve used the fct tht the incident field is in the plne of the smple, nd hence inplne molecules will be excited more efficiently in the control smple. The excittion field in the NPA is dominted by the z component, s shown in Supplementry Figure S6. γ ex θ (16) Mcmilln Publishers Limited. All rights reserved.

11 Supplementry Figure S6. Field enhncement for ech component in the NPA gp under off- resonnt excittion t λ ex = 535 nm, with the incident electric field in the plne. The white outline indictes the boundries of the nnocube. The dominnt field component is in the z direction. The collection efficiency of emission for the NPA system is clculted using full-wve simultions in CST with the fr-field rdition pttern shown in Figure 1d in the min text nd in Supplementry Figure S7b below. The collection efficiency using n NA = 0.9 objective lens is η = 84%, with the collection efficiency, CE, given by θ mx d S CE = π sinθ dθ (16) dω 0 where d S / dω is the emission per unit solid ngle, θ is the emission ngle, nd θ mx is the mximum collection ngle of the objective, relted to the NA by θ mx = rcsin(na). We note tht since emission from the dipoles is coupled to single plsmonic mode, the rdition pttern from the NPA is not sensitive to the emission dipole orienttion. The collection efficiency of emission from control smples consisting of dipoles situted on glss surfce is clculted nlyticlly using the pproch of Enderlein et l. 9. For the clcultion of collection efficiency the dipoles re situted t the interfce between ir nd glss, nd the emission is verged over the ngulr distribution s determined experimentlly below. The clculted rdition pttern is shown in Supplementry Figure S7. With the NA = 0.9 objective, the collection efficiency from the control smple emission, s defined by Eq. (16) is η 0 = 15% Mcmilln Publishers Limited. All rights reserved.

12 Supplementry Figure S7. Rdition pttern of dipoles on glss () nd from the NPA (b). The distribution of dipole orienttions, s determined experimentlly, ws used to clculte () nd (b). The collection efficiency for the control smple on glss is η 0 = 15% while for the NPA it is η = 84%. 6. Distribution of Ru dye dipole orienttions Following the technique of Brritult et l. 10, the distribution of dipole orienttions for Ru dye embedded in the PE lyers ws determined using n ngulr resolved fluorescence setup (Supplementry Figure S8). The Ru dye is deposited on 5 nm thick PAH/PSS polymer film on top of substrte consisting of SiO therml oxide (100 nm) on silicon wfer (Supplementry Figure S9). The intensity emitted s function of polr observtion ngle θ nd zimuthl ngle φ, with incidence ngle θ inc is where I ( θ, θ, φ) = µ E S( θ, φ) C( θ )sinθ dθ dλ (16) em inc ex e θ λ e µ E is the excittion rte nd S ( θφ, ) is the emission term. C ( θ, φ ) is the ex distribution of dipole orienttions, which is the quntity we re interested in extrcting. The mesured emission in prticulr direction is n integrtion over ll possible emission dipole orienttions nd emission wvelengths, determined by the emission spectrum of the Ru dye. The integrtion over dipole zimuthl ngle is left out since the zimuthl distribution is ssumed to be isotropic. The excittion rte is given by the interction of the bsorption dipole moment nd the incident electric field for ech polriztion Mcmilln Publishers Limited. All rights reserved.

13 ex s sn i (θ )cos ( φ )1 + rs ( θinc )exp( jψ ) µ E ex p sin ( θ)sin ( φ )cos ( θinc) 1 rp ( θinc)exp( jψ ) µ E cos ( θ)sin ( θinc) 1 rp ( θinc)exp( jψ ) sin ( θ)cos( θ)sin( φ)sin( θinc) 1 rp θinc ( ) (17) where φ is the bsorption dipole zimuthl ngle, r s nd r p re the complex reflection coefficients of the substrte for s nd p polriztion t the bsorption wvelength. These reflection coefficients re clculted using trnsfer mtrix formlism. The phse fctor is ψ = π / λ zcosθ inc, where λ is the bsorption (excittion) wvelength, nd z is the verticl position of the emitters bove the top surfce of the substrte. This phse fctor is ssumed to be zero becuse the polymer film in which the Ru dye is embedded is ~5 nm thick. The emission term for ech emission polriztion is obtined by decomposing the electric field from dipole in terms of plne wves in the presence of plnr interference lyers S s (θ,φ) = sin (θ e )sin (φ e φ) 1 r s e (θ)exp( jψ e ) S p (θ,φ) = sin(θ e )cos(φ e φ)cos(θ) 1 r e p (θ)exp( jψ e ) cos(θ e )sin(θ) 1+ r e p (θ)exp( jψ e ) where θ e nd φ e re the polr nd zimuthl ngles of the emission dipole, r s e (18) nd r p e re the complex reflection coefficients of the substrte for s nd p polriztion t the emission wvelength, nd ψ e = 0 is the emission phse fctor. The emission ngles θ e nd φ e re ssumed to be equl to the bsorption dipole ngles in the bsence of more detiled moleculr structure informtion bout the Ru dye. This ssumption does not mke substntil effect on the finl extrcted dipole orienttion distribution Mcmilln Publishers Limited. All rights reserved.

14 Supplementry Figure S8. Schemtic of experimentl setup for mesuring the distribution of moleculr dipoles. TL indictes Thorlbs. Supplementry Figure S9. () Schemtic of pproch for mesuring trnsition dipole orienttion of fluorescent molecules. (b) Schemtic of the relevnt orienttion of ngles of the trnsition dipoles on the surfce. The ngle nd polriztion resolved emission from the Ru dye smples on therml oxide substrtes re mesured using the system shown in Supplementry Figure S8. Bsed on the theory presented bove, we expect tht s polrized emission should be independent of the Mcmilln Publishers Limited. All rights reserved.

15 orienttion distribution function. Indeed we find tht mesurements of the ngle resolved emission under p polrized excittion nd s polrized emission show excellent greement with clcultions from Eq. (16) (Supplementry Figure S10). Supplementry Figure S10. S polrized fluorescence intensity s function of ngle under p polrized excittion of the Ru dye on therml oxide substrte, with fit to clcultions from Eq. (16). The informtion bout dipole orienttions is encoded in the ngulr dependence of the p polrized emission. Supplementry Figure S11 shows the p polrized emission under four different incidence ngles with p polrized excittion. In ddition we mesure the p polrized emission t two constnt observtion ngles while vrying the incidence ngle. To extrct the dipole orienttion distribution function, C (θ ), we perform simultneous fit of the clculted ngle resolved emission to ll the mesured curves from Supplementry Figure S11, using C (θ ) s the fitting prmeter. The function which is minimized is given by min Imes ( θi nc, θ) Isim( θinc, θ, θ) C ( θ ) dθ. (19) θ The results of fitting re shown in Supplementry Figure S11. The corresponding distribution of dipole orienttions (Supplementry Figure S1) shows tht most Ru dipoles embedded in the PAH/PSS polymer film re oriented t 75 reltive to the surfce norml with stndrd devition for the Gussin distribution of 10. This distribution ws utilized in the clcultion of the spontneous emission rtes in the min text. The ner prllel orienttion of the dipoles is consistent with other mesurements of the orienttion of plnr orgnic dyes on surfces We find tht other distribution functions, such s n isotropic distribution, show Mcmilln Publishers Limited. All rights reserved.

16 very poor mtch to the mesured ngle resolved fluorescence. This shows tht n isotropic distribution is poor ssumption in this plsmonic system nd likely in mny other systems. Supplementry Figure S11. Angle resolved p polrized emission under p polrized excittion under four different incidence ngles long with p polrized emission under vrying incidence ngles for two fixed observtion ngles. Circles re mesured vlues nd solid lines re clculted vlues bsed on n optiml distribution function C θ ). ( Supplementry Figure S1. Distribution of Ru dipole orienttions on the polymer film bsed on the fits to the dt in Supplementry Figure S Mcmilln Publishers Limited. All rights reserved.

17 7. Experimentl setup for mesuring single NPAs Supplementry Figure S13. Experimentl setup for mesuring single NPAs. TL indictes Thorlbs, NF indictes New Focus, nd PQ indictes PicoQunt Mcmilln Publishers Limited. All rights reserved.

18 8. Power dependence of single cubes Supplementry Figure S14. Fluorescence emission from single cube s function of power incident on the smple surfce for four different gp thicknesses, showing tht the power used ws in the liner excittion regime. The dt re fitted to power lw function with the exponent, α, indicted in the legend. 9. References 1 Plik, E. D. Hndbook of opticl constnts of solids. (Acdemic Press, 1985). Lssiter, J. B. et l. Plsmonic Wveguide Modes of Film-Coupled Metllic Nnocubes. Nno Lett. 13, (013). 3 Moreu, A. et l. Controlled-reflectnce surfces with film-coupled colloidl nnontenns. Nture 49, (01). 4 Rose, A. et l. Control of Rditive Processes Using Tunble Plsmonic Nnoptch Antenns. Nno Lett. 14, (014). 5 Berbern-Sntos, M. N., Bodunov, E. N. & Vleur, B. Mthemticl functions for the nlysis of luminescence decys with underlying distributions 1. Kohlrusch decy function (stretched exponentil). Chem. Phys. 315, (005). 6 Berbern-Sntos, M. N., Bodunov, E. N. & Vleur, B. Mthemticl functions for the nlysis of luminescence decys with underlying distributions:. Becquerel (compressed hyperbol) nd relted decy functions. Chem. Phys. 317, 57-6 (005). 7 Berbern-Sntos, M. N. & Vleur, B. Luminescence decys with underlying distributions: Generl properties nd nlysis with mthemticl functions. J. Lumin. 16, 63-7 (007) Mcmilln Publishers Limited. All rights reserved.

19 8 Fogrty, A. C., Jones, A. C. & Cmp, P. J. Extrction of lifetime distributions from fluorescence decys with ppliction to DNA-bse nlogues. Phys. Chem. Chem. Phys. 13, (011). 9 Enderlein, J., Ruckstuhl, T. & Seeger, S. Highly efficient opticl detection of surfcegenerted fluorescence. Appl. Opt. 38, (1999). 10 Brritult, P., Getin, S., Chton, P., Vinet, F. & Fouque, B. Determintion of surfcebound-fluorophore orienttion by goniometric fluorescence polriztion: ppliction to quntifiction of DNA-chip redouts. Appl. Opt. 41, (00). 11 Huston, A. L. & Reimnn, C. T. Photochemicl Bleching of Adsorbed Rhodmine 6g s Probe of Binding Geometries on Fused-Silic Surfce. Chem. Phys. 149, (1991) Mcmilln Publishers Limited. All rights reserved.