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Low absorption losses of strongly coupled surfaceplasmons in nanoparticle assembliesWei-Shun Changa, Britain A. Willinghama, Liane S. Slaughtera, Bishnu P. Khanala, Leonid Vigdermana,Eugene R. Zubareva, and Stephan Linka,b,1

aDepartment of Chemistry, and bDepartment of Electrical and Computer Engineering, Laboratory for Nanophotonics, Rice University, Houston, TX 77005

Edited by Federico Capasso, Harvard University, Cambridge, MA, and approved September 26, 2011 (received for review August 20, 2011)

Coupled surface plasmons in one-dimensional assemblies of metal

nanoparticles have attracted significant attention because strong

interparticle interactions lead to large electromagnetic field

enhancements that can be exploited for localizing and amplifying

electromagnetic radiation in nanoscale structures. Ohmic loss (i.e.,

absorption by the metal), however, limits the performance of any

application due to nonradiative surface plasmon relaxation. While

absorption losses have been studied theoretically, they have not

been quantified experimentally for strongly coupled surface plas-

mons. Here, we report on the ohmic loss in one-dimensional assem-

blies of gold nanoparticles with small interparticle separations of

only a few nanometers and hence strong plasmon coupling. Both

the absorption and scattering cross-sections of coupled surfaceplasmons were determined and compared to electrodynamic simu-

lations. A lower absorption and higher scattering cross-section for

coupled surface plasmons compared to surface plasmons of iso-

lated nanoparticles suggest that coupled surface plasmons suffer

smaller ohmic losses and therefore act as better antennas. These

experimental results provide important insight for the design of

plasmonic devices.

nanoparticle self-assembly ∣ photothermal heterodyne imaging ∣

surface plasmon resonance ∣ single particle spectroscopy ∣

dark-field imaging

P

lasmonic antennas can convert optical radiation into intense

local field distributions or enable coupling to guided modesthat are confined to subwavelength dimensions (1–4). Strong sur-face plasmon (SP) coupling between neighboring nanoparticles(NPs) also leads to large enhancements of electromagnetic fields,

which benefit various applications such as waveguides (5, 6),nano-antennas (7–9), field enhanced spectroscopies (10–12), andbiological sensors (4, 13, 14). The interparticle coupling resultingfrom near-field interactions between closely spaced NPs is inver-sely proportional to d3 where d is the distance between the NPs(6). The largest local field enhancements are indeed found forthe smallest interparticle distances (11, 15). Extremely small in-terparticle gaps of a few nanometers can be achieved in self-assembled nanostructures (16–19), opening up new paths for thedesign of plasmonic devices. With bottom-up assembly, preciseperiodic positioning of the NPs is more difficult and hence struc-

tures with a distribution of NP gaps are created. However, highthroughput patterning for large area fabrication at reduced costsmake NP assemblies attractive alternatives to structures made by conventional top-down approaches (20). For the system studiedhere, SI Appendix, Fig. S1 shows an example of a periodic array of rings assembled from a chloroform solution of 40 nm goldNPs. In addition, the recent use of correlated electron and opticalmicroscopy on individual NP assemblies is making it possible todecipher the effects of local NP ordering and symmetry breakingon the collective optical response (21).

Independent of the plasmonic nanostructure, absorption by the metal is thought to be the main mechanism for plasmonenergy dissipation due to nonradiative relaxation processes (3,22–24). Substantial attenuation of electromagnetic waves due toohmic loss is therefore the major issue for applications such as

subwavelength plasmonic circuits (4, 5, 22–28). For example,the propagation distances of SP polaritons are significantly re-duced because of absorption losses, limiting the effectivenessof plasmonic waveguides (22–28). Although a few theoreticalstudies have reported on absorption losses of SPs (22–24, 28),quantitative experimental studies are urgently needed. In parti-cular, a deeper understanding of the field enhancements andabsorption losses for coupled SPs in NP assemblies is required forthe rational design of improved plasmonic NP devices.

The strength of near-field interactions between NPs is directly related to the red-shift of the coupled SP resonance as generally probed by scattering spectroscopy for small NP assemblies such

as dimers and trimers (15, 29, 30). Higher order SP modeshave also been observed for larger assemblies of closely spacedNPs (31). In addition, it has been shown that the spectral depen-dence of the electromagnetic field enhancement in these NPstructures follows the collective scattering response (15, 32, 33).Because significantly larger electromagnetic field enhancementsare encountered for coupled SPs (9, 11, 15, 33), more efficientplasmonic antennas can be realized for excitation at wavelengthscorresponding to coupled SPs rather than the single NP SP reso-nance, unless the magnitude of ohmic loss also increases andabsorption losses become prohibitive. Therefore, measuring bothabsorption (σ ABS) and scattering cross-sections (σ SCA ) for coupledSPs in closely spaced NP assemblies is necessary to understandthe interplay between electromagentic field enhancement and

ohmic loss. While SP absorption of a single NP has been measuredby photothermal heterodyne imaging (34–37), absorption of red-shifted coupled SPs has not been explored in detail.

In this work, we separately measured absorption and scatteringof coupled SPs in individual self-assembled nanostructures.Micrometer large rings composed of polystyrene-functionalizedgold NPs (31) served as quasi one-dimensional (1D) NP chains,

whose structures were analyzed using electron microscopy (Fig. 1 A and SI Appendix, Fig. S1). Experiments were comple-mented by detailed electrodynamic simulations. We found that,

whereas σ SCA increases for coupled SPs compared to isolatedNPs, σ ABS decreases for coupled SPs compared to the SP of theindividual gold NPs.

Results and Discussion

Rings of polystyrene-coated 40-nm gold NPs were fabricated onglass slides as described previously (31). Polyvinyl alcohol films with a refractive index of 1.5 were spin-cast on top of the ringsto provide a homogenous surrounding medium. Fig. 1 A shows ascanning electron microscopy (SEM) image of an NP ring with a

Author contributions: W.-S.C. and S.L. designed research; W.-S.C., B.A.W., and L.S.S.

performed research; B.P.K., L.V., and E.R.Z. synthesized polystyrene-functionalized gold

nanoparticles and assembled them into ring-like superstructures; W.-S.C. and B.A.W.

analyzed data; and W.-S.C. and S.L. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/

doi:10.1073/pnas.1113563108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1113563108 PNAS ∣ December 13, 2011 ∣ vol. 108 ∣ no. 50 ∣ 19879–19884

http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1113563108/-/DCSupplemental/Appendix.pdf




http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1113563108/-/DCSupplemental














diameter of 4.6 μm. Due to the large ring diameter compared tothe NP size and hence small local curvature, a segment of the ringmimics a 1D NP chain.

The emergence of strongly coupled SP modes was visualizedby acquiring scattering spectra for approximately 500-nm-longsegments along the NP ring circumference. The length of the ringsegment was determined by the size of a pinhole placed in theimaging plane of a home-built single particle microscope. Fig. 1 Bshows a scattering spectrum with multiple, broad peaks for thering segment (cyan) that is marked by the cyan rectangle inFig. 1 A. The additional resonances at lower energies comparedto the response of a single 40-nm gold NP (orange) result fromstrong near-field coupling between the NPs (19, 31).

Wavelength resolved imaging was used to investigate theabsorption and scattering of coupled SPs for the NP ring.Fig. 1 C– E display the absorption images for the ring in Fig. 1 Arecorded by photothermal heterodyne imaging, which selectively measures only the absorption through heat-induced refractiveindex changes of the surrounding medium (34–39). Excitation was

performed with lasers operating at 785, 675, and 514 nm as indi-cated by the dashed colored lines in Fig. 1 B. Heating powers werekept below the threshold for laser mediated melting of the NPsas confirmed by the absence of a change in the scattering spectrumfor the same local ring segment before and after photothermalimaging (SI Appendix, Fig. S2). Dark-field scattering images(Fig. 1 F – H ) at corresponding wavelengths were obtained by pla-cing 40-nm band pass filters centered at 800, 700, and 550 nm infront of the avalanche photodiode.

Excitations with 514 and 550 nm for absorption and scattering,respectively, are also resonant with the SP mode of the constitu-ent 40-nm gold NPs (Fig. 1 B) in addition to higher order coupledSP modes. On the other hand, at the two longer wavelengthsonly coupled SPs of the NP ring were excited as confirmed by measuring absorption images of single NPs with 785 and 675 nm

(SI Appendix, Fig. S3). The coupled SP modes are more sensitiveto the local arrangement of the NPs and several hot spots withlarge intensities that do not scale with the number of NPs perarea are present in both absorption (Fig. 1 C and D) and scatter-ing (Fig. 1 F and G) images. This result is characteristic of non-uniform electromagnetic field enhancements in strongly coupledNP clusters (40). Interestingly, at these longer wavelengths theabsorption and scattering intensity distribution along the ring(i.e., the number and location of hot spots) do not correlate with

each other. In contrast, at 514 nm the absorption intensity of the ring approximately scales with the number of NPs per area(SI Appendix, Figs. S4 and S5).

The coupled SP absorption modes for the NP ring were furtherinvestigated by polarization sensitive imaging. For wavelengthsred-shifted from the single NP SP resonance, the absorption in-tensities were highly polarized along the direction of the local NPalignment. Fig. 2 presents wavelength resolved and polarizationsensitive absorption (left) and scattering (right) images of the NPring for two orthogonal polarizations. At the longest wavelength(785 nm for absorption and 800 nm for scattering), both absorp-tion and scattering intensities increased when the polarization

was parallel to the local ring segment. Minimum intensities wereobserved for polarization directions perpendicular to the local NPalignment. A similar trend, although with less contrast, was alsoobserved for absorption at 675 nm and scattering at 700 nm. Onthe other hand, the absorption and scattering images taken at theshortest wavelength did not depend on the polarization.

With increasing wavelength, the polarization dependence of coupled SP modes increases for both absorption and scattering.This was quantified by recording images as a function of polar-ization angle θ in 30° increments (SI Appendix, Figs. S6 and S7).Fig. 3 A and B show the polarization dependence of the absorp-tion intensities for 785 nm (purple), 675 nm (red), and 514 nm(green) excitation analyzed at the ring locations marked by the

yellow and cyan rectangles in Fig. 1 A, respectively. The corre-sponding data for SP scattering at 800, 700, and 550 nm is givenin Fig. 3 C and D. The polarization dependence was examined by fitting the intensities I to I ð θÞ ¼ N ð1 þ M cos 2ð θ − ϕÞÞ where N

is a normalization constant (36). The modulation depth M repre-sents the average in plane projection of a collection of dipolesdescribing the system. M ¼ 1 for a single dipole or if all dipoles

Fig. 1. Absorption and scattering of coupled SPs in a self-assembled NP ring.

( A) SEM image of a ring composed of 40-nm gold NPs. The diameter of this

ring was 4.6 μm. (B) Scattering spectra of the ring segment (cyan) marked by

the cyan rectangle in A and a single NP (orange). The purple, red, and green

dashed lines represent the excitation wavelengths of 785, 675, and 514 nm

that were used for photothermal heterodyne imaging. The purple, red, andgreen bars illustrate the spectral bandwidths of 800 Æ 20, 700 Æ 20, and

550 Æ 20 nm that were used for wavelength selective scattering imaging.

C , D, and E show the photothermal images of the NP ring with circularly

polarized excitation at wavelengths of 785, 675, and 514 nm, respectively.

F , G, and H are the unpolarized scattering images of the ring recorded at

800 Æ 20, 700 Æ 20, and 550 Æ 20 nm, respectively. Note that the images

are not scaled to each other as they were acquired adjusting the intensity

of the incident or detected light so that the signal covered the full dynamic

range for each experiment.

Fig. 2. Polarization sensitive and wavelength dependent photothermal and

scattering images of an NP ring. Photothermal images of the same ring as

shown in Fig. 1 A excited with horizontal (first column) and vertical (second

column) polarizations, and scattering images detected with horizontal (third

column) and vertical (forth column) polarizations. The excitation and detec-

tion wavelengths for absorption and scattering are displayed next to the

corresponding images.

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are aligned in parallel, while M ¼ 0 if the dipoles are randomly distributed (SI Appendix, Fig. S8). The phase angle ϕ gives theorientation of the average dipole moment in the sample plane

with respect to a reference axis. Consistent with a parallel orien-tation of the coupled SP oscillations and the local NP alignment,the polarization traces for the two highlighted ring locations are90 ° out of phase.

Oscillation of coupled SPs parallel to the local NP alignmentdirection was furthermore found to be independent of the spe-cific ring location and mostly uniform around the entire ring. Theabsorption and scattering images were divided into 40 and 24areas, respectively, which was based on the resolution of the twoimaging techniques. Modulation depths M and angles ϕ for eachof these areas were then determined. The distributions of M va-lues for absorption and scattering are summarized in Fig. 3 E and F . The mean modulation depths are of comparable magnitude forabsorption and scattering: h M 785i ¼ 0.75 Æ 0.21 and h M 800i ¼0.66 Æ 0.11; h M 675i ¼ 0.45 Æ 0.22 and h M 700i ¼ 0.45 Æ 0.14;h M 514i ¼ 0.11 Æ 0.06 and h M 550i ¼ 0.12 Æ 0.07. The error repre-sents the standard deviation of M . The difference for the longest

wavelength is most likely due to the larger wavelength interval of 40 nm probed by scattering in combination with the wavelengthdependence of M . These results demonstrate how near-field in-teractions between isotropically shaped NPs lead to polarizedcollective nonradiative modes in addition to radiative modes.

Electrodynamic simulations of local ring segments were car-ried out to validate and further interpret the experimental results.

Because the scattering spectrum in Fig. 1 A was cut off at lowenergies due to the limited spectral range of the Si CCD camera,

we measured broadband extinction spectra covering a range of 500–1,800 nm in order to access the entire SP response of theNP ring. The SEM image in Fig. 4 A shows the NP arrangementof a local ring segment. Extinction spectra recorded with linearpolarization parallel and perpendicular to the local alignment of the NPs, as indicated by the blue and red arrows in Fig. 4 A, aregiven in Fig. 4 B and display a strong SP peak at 1,400 nm as well

as multiple peaks between 500 and 1,000 nm. The longest wave-length SP modes are all highly polarized along the quasi 1D NPalignment. Although the relative intensities of these SP modes

varied slightly from one ring area to another and for different NPrings having different diameters, all extinction spectra recordedshared similar spectral profiles (SI Appendix, Fig. S9).

Using the experimental NP arrangement, we calculated polar-ized extinction spectra using code developed based on general-ized Mie theory (GMT) (41, 42). Fig. 4C shows the arrange-ment of 26 NPs that were all assumed to be 40-nm spheres andspaced at least 1 nm apart. Although this presents a simplificationof the actual system where the NPs are highly faceted, GMT hasthe advantage of being able to compute the collective optical re-sponse of a large number of NPs while including many multipoles

(42). The calculated polarized extinction spectra (Fig. 4 D) showmultiple SP resonances for wavelengths shorter than 1,000 nm,qualitatively reproducing the experimental results except forthe SP resonance at 1,400 nm, which is absent in the GMT simu-lations. Increasing the number of NPs in the simulation did notpush the longest wavelength SP resonance beyond 1,000 nm, con-sistent with previous results showing that the infinite chain limit isreached for about 10 NPs (42, 43).

Fig. 3. Polarization of NP ring SPs for absorption and scattering intensities

along an NP ring. ( A and B) Polarization dependence of the photothermal

intensityof thelocalringsegmentsmarked by theyellow andcyanrectangles

in Fig. 1 A, respectively. Purple, red, and green symbols represent excitation

wavelengths of 785, 675, and 514 nm. The lines are fits and yield modulation

depths of M 785 ¼ 0.93 and 0.76; M 675 ¼ 0.47 and 0.55; M 514 ¼ 0.06 and 0.12.

(C and D) Polarization dependence of the corresponding scattering intensity

for the same local ring segments. Purple, red, and green symbols represent

the spectral windows of 800 Æ 20, 700 Æ 20, and 550 Æ 20 nm. The lines are

fits and yield modulation depths of M 800 ¼ 0.82 and 0.65; M 700 ¼ 0.47 and

0.31; M 550 ¼ 0.11 and 0.05. (E and F ) Histograms of the modulation depth

obtained from the photothermal and scattering polarization traces, respec-

tively. For this analysis, the ring was divided into 40 and 24 segments for

the photothermal and scattering measurements, respectively. Note that the

colors of the bars correspond to those of the polarization traces.

Fig. 4. Experimental and simulated extinction spectra for a segment of an

NP ring. ( A) SEM image of a ring segment composed of 40-nm gold NPs.

(B) Extinction spectra of the ring segment in A recorded with excitation

polarization parallel (blue) and perpendicular (red) to the 1D NP alignment

direction. (C and D) GMT calculations for the ring segment marked by the

magenta square in A. The modeled NP arrangement in C was taken from the

SEM image keeping the minimum surface-to-surface separation between

neighboring NPs greater than 1 nm. (E and F ) FEM calculations for the ring

segment marked by the yellow square in A. For the FEM calculations, the NPs

labeled 1–8 a n d 9–11 were allowed to touch and hence coupled conductively.

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The longest wavelength SP resonance can be explained by conductive plasmon coupling for touching NPs. Because GMTcan only solve the optical response for nontouching NPs, we usedthe finite element method (FEM) to simulate the NP assembly shown in Fig. 4 E containing only the first 13 NPs as these FEMcalculations required significantly more computer resources. Thecalculated extinction spectrum with longitudinal polarization inFig. 4 F shows a strong SP resonance at 1,600 nm as well as severalmultipolar peaks with lower intensities. For this NP arrangement

conductive contact for NPs 1–

8 and 9–

11 was assumed. However,because of the limited resolution of SEM it was not clear whichNPs were actually touching. Therefore, different NP arrange-ments with varying numbers of touching NPs were simulated. Thegeometry in Fig. 4 E resulted in the best qualitative agreementbetween the experimental (Fig. 4 B) and calculated spectra(Fig. 4 F ). The simulation results for other NP arrangements aregiven in SI Appendix, Fig. S10. Further optimization of the NPshape and assembly geometry could in principle lead to betteragreement between experiment and theory, butthe main conclusionhere is that it is necessary to consider touching NPs to explain thelongest wavelength SP mode in these NP rings, which we assign to acharge transfer plasmon resonance (44–46). Because GMT matchesthe experimental results well for wavelengths below 1,000 nm thecollective SP response in this wavelength range is assigned to mostly

capacitive plasmon coupling between nontouching NPs. As all scattering and absorption measurements discussed

earlier were also limited to the spectral range of 500–1,000 nm, we have chosen to use GMT to interpret the experimental results. Although this approach ignores the contribution from touchingNPs, important physical insight can be gained. Fig. 5 A showsunpolarized absorption (magenta) and scattering (blue) spectrasimulated by GMT for the ring segment marked by the cyan rec-tangle in Fig. 1 A. The experimental scattering spectrum (cyan) re-corded with unpolarized excitation is also included. The excellentagreement between the experimental and calculated spectra con-firms the validity of the GMTcalculationand justifies our approach.

Based on the calculated spectra, the difference in modulationdepths can now be explained more quantitatively. At 785∕800 nm,because a combination of the SP dipole mode and the first higher-order mode was excited, the modulation depth was smaller than 1.

At 675∕700 nm, only higher-order SP modes were excited, whichresulted in a smaller modulation depth. At 514∕550 nm, bothhigher-order longitudinal as well as transverse SP modes were ex-cited yielding the smallest modulation depth because of the ortho-gonal nature of these modes. Unpolarized interband transitionsfurthermore contributed to the reduced modulation depth at this

wavelength.Strongly coupled SPs at wavelengths red-shifted from the

single NP SP response have smaller σ ABS but larger σ SCA . Thiscan be directly seen from the simulated absorption and scatteringspectra in Fig. 5 A but can also be further quantified experimen-tally. We determined σ ABS and σ SCA of the NP ring by comparingthe absorption and scattering intensities for the ring and indivi-

dual NPs. We measured wavelength resolved photothermal anddark-field images for the NP ring and individual gold NPs underthe same conditions. To cover the three wavelength regions of interest and yield strong scattering signals, we selected NP sam-ples with mean sizes of 96 nm, 33 × 63 nm, and 22 × 70 nm as

verified separately by TEM (SI Appendix, Fig. S11). FEM calcu-lations of σ ABS and σ SCA for these NPs were performed assuminga homogenous surrounding medium with a refractive index of 1.5(SI Appendix, Fig. S12). Experimentally, only NPs with a peak

wavelength within Æ10 nm of the calculated value were selectedbased on their scattering spectra (SI Appendix, Fig. S13). The ab-sorption and scattering intensity ratios between the individualNPs and areas along the ring were obtained and then multipliedby the calculated σ ABS and σ SCA of the single NPs. This procedure

yields σ ABS;ring and σ SCA ;ring for ring areas having a size that

was limited by the optical resolution. To allow for comparisonsindependent of the detection area σ ABS;ring and σ SCA ;ring weredivided by the number of NPs per integration area to giveσ ABS and σ SCA , which also include normalization constants thattake the different spectral observation windows into considera-tion. Further details regarding the calculation of σ ABS andσ SCA are discussed in the supporting information (SI Appendix,Figs. S14—S16 and Tables S1–S4).

Fig. 5 B– D shows histograms of σ ABS for the NP ring excitedat 785, 675, and 514 nm, respectively. The median σ ABS is signif-icantly lower for the SPs at 785 and 675 nm compared to the SPat514 nm. We determined values of σ ABS ¼ 736 nm2 at 785 nm and

Fig. 5. Absorption and scattering cross-sections of SPs in an NP ring.

( A) Simulated absorption (magenta) and scattering (blue) spectra of the ring

segment marked by the cyan rectangle in Fig. 1 A. The experimental scatter-

ing spectrum (cyan) from Fig. 1 A is also included for comparison. (B–D)

Histograms of σ ABS obtained from 40 ring segments of the photothermal

images for 785, 675, and 514 nm excitation, respectively. (E –G) Histograms

of σ SCA obtained from 24 ring segments of the scattering images measured

with band pass filters of 800 Æ 20, 700 Æ 20, and 550 Æ 20 nm, respectively.

(H and I ) Electromagnetic-field enhancements of the same NP ring segmentat 785 and 514 nm, respectively.



























σ ABS ¼ 163 nm2 at 675 nm compared to σ ABS ¼ 1;048 nm2 at514 nm. The median is used here to exclude the effect of a fewhot spots that are more dominant at longer wavelengths. On theother hand, the median σ SCA calculated from the histograms gi-

ven in Fig. 5 E–G increases slightly for 800 nm (σ SCA ¼576 nm2) and 700 nm (σ SCA ¼ 560 nm2) relative to 550 nm(σ SCA ¼ 521 nm2). The accuracy of this cross section analysis was

verified by comparing the wavelength dependence of σ SCA ;ring forthe area marked by the yellow rectangle in Fig. 1 A with the

scattering spectrum taken at the same location (SI Appendix,Fig. S17). The very good agreement between σ SCA ;ring and thescattering spectrum validates the procedure for the cross-sectionanalysis. The observed trend for σ ABS and σ SCA in Fig. 5 B–Galso agrees well with the simulated absorption and scatteringspectra in Fig. 5 A. These results lead us to conclude that in NPassemblies with small interparticle distances, smaller absorption,but larger scattering occurs for strongly coupled SP resonancesat lower energies compared to the single NP SP. Because thescattering intensity is directly related to the electromagnetic fieldenhancement (15, 32, 33), the larger σ SCA at red-shifted wave-lengths should make coupled SPs better antennas. A larger elec-tromagentic field enhancement at 785 nm compared to 514 nm

was furthermore confirmed by calculating the field distributions(Fig. 5 H and I ) using GMT for the local ring segment corre-sponding to the spectra in Fig. 5 A.

Small interparticle distances in assemblies of many NPs asinvestigated here in self-assembled NP rings are important to

observe lower σ ABS than σ SCA for strongly coupled SPs. This isillustrated by GMT simulations of a simpler system of orderedlinear chains with varying number of NPs. Fig. 6 shows scattering(blue) and absorption (magenta) efficiencies of NP chains withinterparticle gaps of 1 nm (solid line) and 20 nm (dash line), com-posed of 2 ( A) , 3 ( B) , 6 (C), and 10 ( D) NPs. For gaps of g ¼ 1 nm, the dipole SP resonance red-shifted from 685 nmfor a dimer to 862 nm for 10 NPs, while for 20 nm gaps becauseof reduced plasmon coupling the spectral shift was only 20 nm,

which is further illustrated in the inset of Fig. 6 A

for chain lengthof up to N ¼ 15. For both interparticle distances, the scatteringefficiency of at the dipole SP resonance (superradiant mode)furthermore increases relative to the absorption efficiency withincreasing number of NPs. This is shown in the inset of Fig. 6 B

where the ration of QSCA ∕Q ABS is plotted vs. N . However, only for g ¼ 1 nm scattering becomes more dominant than absorptionfor the ordered linear chains in Fig. 6. The stronger scatteringresults from an increased dipole of the collective SP response asmore NPs contribute. The interparticle distances have to be smallthough to allow for strong coupling. Consistent with our results,calculations of NP dimers and heptamers have shown that radia-tion dominates the competition between scattering and absorp-tion at the superradiant mode (47, 48). Interband absorptionnear the single NP resonance also contributed to the higher

absorption cross section at 514 nm.

ConclusionsIn summary, we have measured σ ABS and σ SCA of coupled SPsin self-assembled quasi 1D structures composed of 40-nm goldNPs. Coupled absorption modes excited at longer wavelengthscompared to the SP of the constituent single NPs were identifiedby polarization sensitive imaging and verified by electromagneticcalculations. Similar to scattering, the collective nonradiative SPmodes are sensitive to the overall morphology of the NP assembly as the absorption intensities were enhanced when the polariza-tion was parallel to the local ring segments. In addition, we founda lower σ ABS in combination with a higher σ SCA for the coupledSPs in these chemically prepared NP assemblies, implying smallerohmic losses and larger local fields at red-shifted wavelengths,

allowing one to minimize absorptive losses while maximizing elec-tromagnetic field enhancements with coupled SPs for the designof efficient plasmonic nano-antennas.

Materials and MethodsSample Preparation. Polystyrene-functionalized gold NPs (MWPS ¼ 10 ;000 g∕

mol)were synthesized followingthe procedure described elsewhere (18). The

diameter of the gold NPs was 40 Æ 5 nm as confirmed by TEM (JEOL 1230 HC-

TEM operated at 80 kV). By allowing a drop of the functionalized gold NPs

solution to dry on a glass slide, rings were formed at the interface between

the organic solvent and water droplets that condensed from the air due to

evaporative cooling of chloroform. A goldpattern was evaporated onto glass

slides using an indexed copper TEM grid (Ted Pella) that had no support layer,

allowing us to locate the same structures in scanning electron and optical

microscopy.

Dark-Field Spectroscopy. Dark-field excitation was performed in a reflected

light geometry using an inverted microscope (Zeiss) with a halogen lamp as

the excitation source. Scattered light was collected using a Zeiss EC Epiplan-

Neofluar objective (50×, N:A: ¼ 0.8). After passing through a 50-μm pinhole,

the signal was focused onto an avalanche photodiode (Perkin Elmer). A

polarizer and a band pass filter were placed in the detection path after the

pinhole to measure the polarization and wavelength dependence of the

scattered light. The images were created by scanning the sample using a

piezo scanning stage (Physik Instrumente) connected to a surface probe

microscope controller (RHK Technology). Scattering spectra were acquired

with a spectrometer and a Si CCD camera (Princeton Instruments).

Broadband Extinction Spectroscopy. Extinction spectra were acquired using

the same microscope setup. Light from a tungsten halogen lamp (Newport)

was incident from above the sample to allow for excitation at normal inci-

dence. The transmitted light was collected by a Zeiss EC Epiplan-Neofluar

Fig. 6. Absorption and scattering efficiency of ordered NP chains. ( A–D)

Scattering (QSCA, blue) and absorption (QABS, magenta) efficiencies of linear

chains composed of 2 ( A), 3 (B), 6 (C ), and 10 (D) 40-nm gold NPs. The effi-

ciency Q is defined as the optical cross section normalized by the geometric

cross-section of the total number of NPs. Spectra were calculated for gaps

of g ¼ 1 nm (solid line) and g ¼ 20 nm (dashed line) between neighboring

NPs. The insets in A and B show the resonance maximum and the ratio of

scattering and absorption efficiencies at the dipole SP mode for gaps of 1

and 20 nm as a function of NP number, respectively. The dotted horizontal

line in the inset in B, QSCA∕QABS ¼ 1, is given as a reference to illustrate when

scattering becomes more dominant than absorption.

Chang et al. PNAS ∣ December 13, 2011 ∣ vol. 108 ∣ no. 50 ∣ 19883









objective and directed either through the same 50-μm pinhole toward the Si

CCD camera or focused into a 100-μm diameter fiber that was connected to a

spectrometer (Andor Technology SR-163) equipped with an InGaAs array de-

tector (Andor Technology DU491A-2.2). Broadband extinction spectra were

then created by combining spectra from the Si CCD camera (500–1,000 nm)

and the InGaAs array detector (900–1,800 nm).

Photothermal Heterodyne Imaging. Photothermal heterodyne imaging was

performed in transmission geometry (39) using the same microscope setup.

A 514-nm Arþ laser (Modu-Laser) and 675-nm or 785-nm diode lasers (Power

Technology) were used as the heating beams. The polarization of the heating

beams was controlled using half and quarter waveplates. A 633-nm He-Ne

laser (JSD Uniphase) was employed as the probe beam. Each laser was fo-

cused independently to ensure best overlap at the focus between heating

and probe beams for optimum resolution. The intensity of the heating beam

was modulated at 400 kHz with an acousto-optic modulator (IntraAction).

The laser beams were focused on the sample with a Zeiss Fluar objective

(100×, N:A: ¼ 1.3). The transmitted probe beam was collected by a Zeiss EC

Epiplan-Neofluar objective (50×, N:A: ¼ 0.8). The heating beam was rejected

by a 633-nm band pass filter (Thorlabs). The photothermal signal was

detected by an avalanche photodiode module (Hamamatsu) and fed into

a lock-in amplifier (Princeton Applied Research), which was connected to

the same surface probe microscope controller. Photothermal images were

acquired by scanning the sample.

Electrodynamics Simulations. GMT calculations were performed using a code

that we have developed for modeling individual and multiple spherical metal

NPs(42). Fora singlesphere,the electrodynamic solution forthe optical cross-

sections is thewell-known Mietheory (49) in which thescattered andincident

fields are represented as a complete expansion of vector spherical harmonics

with appropriate weighting coefficients. By extending this solution to N

NPs, whereby the incoming scattered fields from neighboring NPs act as

further excitations, the scattering coefficients for each of the N NPs are

solved, yielding analytical solutions for the electrodynamic fields and optical

cross-sections. FEM calculations were carried out using the commercially

available software COMSOL Multiphysics, which can simulate arbitrary NPgeometries including overlapping spheres that mimic the conductive overlap

of neighboring NPs. All calculations were carried using tabulated values

for the complex dielectric response of gold (50) and an effective dielectric

medium of 1.5.

ACKNOWLEDGMENTS. S.L. acknowledges financial support by the Robert A.Welch Foundation (Grant C-1664), National Science Foundation (NSF)(CHE-0955286), Office of Naval Research (N00014-10-1-0989), and 3M for aNontenured Faculty Grant. E.R.Z. acknowledges financial support by NSF(DMR-0547399, DMR-1105878) and the Robert A. Welch Foundation(C-1703).W.S.C. thanks the Richard E. Smalley Institute for a Peter and Ruth Nicholasfellowship and L.S.S. thanks the NSF Integrated Graduate Education andResearch Traineeship Nanophotonics fellowship program.

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1

Supplementary Information

Low absorption losses of strongly coupled surface plasmons in

nanoparticle assemblies

Wei-Shun Changa, Britain A. Willingham

a,,,, Liane S. Slaughter

a, Bishnu P. Khanal

a,

Leonid Vigdermana, Eugene R. Zubarev

a, and Stephan Link

a,b,1

aDepartment of Chemistry,

bDepartment of Electrical and Computer Engineering

Laboratory for Nanophotonics, Rice University, Houston, TX, 77005

1To whom correspondence should be addressed. E-mail: [email protected]



2

CONTENTS: Page

Figure S1 4

Figure S2 5

Figure S3 5

Comparison of photothermal intensities of isolated NPs and NP ring at 514 nm 6

Figure S4 7

Figure S5 7

Figure S6 8

Figure S7 9

Figure S8 9

Figure S9 10

Figure S10 11

Calculation of σSCA for the NP ring 11

Figure S11 12

Figure S12 13

Figure S13 14

Figure S14 15

Table S1 15

Table S2 16

Figure S15 17



3

Calculation of σABS for the NP ring 17

Figure S16 18

Table S3 18

Table S4 19

Figure S17 20

References 20



4

Fig. S1 SEM (left) and scattering (right) images of an array of NP rings. The optical image was

taken for a smaller area in order to clearly show the structure of the rings given the lowerresolution. Arrays of NP rings were fabricated by first patterning arrays of circular hydrophilicareas with a hydrophobic background through the use of microcontact printing (1). A silicon

wafer master was coated with photoresist and patterned on a Heidelberg DWL66 Laser Writer. A

polydimethylsiloxane (PDMS) stamp was then cast from this master by pouring over it a mixture(10:1 by mass) of PDMS pre-polymer (Sylgard 184, Dow Corning) and curing agent, degassing

the mixture, and heating at 70 °C for 1 hour. Hydrophilic regions were then patterned onto a

gold-coated glass slide by stamping of a 2 mM solution of 16-mercaptohexadecanoic acid inethanol, followed by dipping into a 2 mM solution of hexadecanethiol in ethanol to form the

hydrophobic background, and then rinsing with ethanol. The substrate was cooled to 5-10oC and

briefly exposed to moist air. The condensation of water occurred almost exclusively on the

hydrophilic sites and created a periodic array of near monodisperse water droplets. Finally, amethylene chloride solution of polystyrene-functionalized nanoparticles was cast onto the

substrate leading to the formation of a periodic array of NP rings after drying.



5

Fig. S2 Scattering spectra of the ring segment before (cyan) and after (orange) photothermal

imaging to show that the heating and probe laser beams did not melt the NPs and alter the NP

ring structure.

Figure S3. Wavelength dependent absorption of single gold NPs and a NP trimer. Because of the

high sensitivity of photothermal heterodyne imaging, excitation of the long wavelength tail of thesingle NP resonance at 785 and 675 nm can be ruled out. Correlated SEM (A) and photothermal

images recorded with 514 (B), 675 (C), and 785 (D) nm excitation were collected for single NPs

and a trimer. At 514 nm both the trimer and the single NPs were visible, while at 675 nm and785 nm only the trimer was observed. The white circles in (C) and (D) indicate the position of

the single NPs. If the absorption intensities at 675 and 785 nm scaled linearly with number of

NPs, then based on the signal to noise ratio and background levels in (C) and (D) , the individualNPs would be visible as well. This is furthermore consistent with the observation that thescattering intensity of 40 nm NPs at 785 and 675 nm is zero (Fig. 1B) and that calculations

predict very similar spectral profiles for absorption and scattering of NPs in this size range.

Therefore, these results indicate that the absorption images of the ring for excitation at 785 and675 nm are due to coupled SPs.



6

Comparison of photothermal intensities of isolated NPs and NP ring at 514 nm

The photothermal intensities of single isolated NPs and NPs in the ring were compared to

show that at 514 nm the absorption intensity of the ring approximately scales with the number of

NPs per area. The same 40 nm NPs that were used to assemble the NP ring were drop-casted on

a glass slide followed by spin-casting a polyvinyl alcohol (PVA) film to ensure a homogenous

sounding medium. Single NPs were identified by SEM. The heating and probe wavelengths for

the photothermal measurements were 514 and 633 nm, respectively. For single NPs, the

excitation power was 500 µW. The excitation power for the NP ring was 50 µW to avoid

saturating the signal. The probe power was 800 µW for both measurements. Fig. S4A shows a

photothermal image of 40 nm NPs with 514 nm excitation. The intensities were integrated for

390 x 390 nm2 areas indicated by the white boxes, which was based on the optical resolution of

the photothermal images. Fig. S4B shows a photothermal image of the NP ring with 514 nm

excitation. The intensities were integrated for the same areas of 390 x 390 nm2

as shown again

by the white boxes. To compare the intensity per particle of single isolated NPs and individual

NPs in the ring assembly, the intensities of the different ring segments were normalized by the

number of NPs contained in each of the white boxes and then scaled to an excitation power of

500 µW. The number of NPs was obtained by overlaying the photothermal and SEM images.

Fig. S5 displays the power dependence of the photothermal intensity for 40 nm NPs with

514 nm excitation. The red line is a linear regression. The photothermal intensity scales linearly

with the excitation power which is consistent with previous results(2) and therefore justifies the

linear scaling factor used for the intensity comparison.



7

Fig. S4 Photothermal intensity of NPs with 514 nm excitation. (A), (B) photothermal images (6.7

x 6.7 µm2) of 40 nm NPs and the NP ring for 514 nm excitation, respectively. (C) histogram of

photothermal intensity of single isolated 40 nm NPs with excitation power of 500 µW. (D)

histogram of photothermal intensity of 40 nm NPs in the ring with excitation power of 50 µW.The intensities were normalized by the number of NPs per excitation volume and scaled to the

excitation power of 500 µW.

Fig. S5 Power dependence of the photothermal intensity for 40 nm NPs with 514 nm excitation. The error bar represents the standard deviation of the intensity from several NPs. The red line is

a linear regression.

Figs S4C and S4D show the photothermal intensity histograms of single isolated NPs and

single NPs in the ring assembly, respectively. The intensity distributions are comparable. The

distribution of isolated NPs is slightly narrower than that of the NPs in the ring. However,

several isolated NPs show higher intensities due to size inhomogeneity because larger triangular



8

NPs were also present as verified by correlated SEM imaging. The intensity histogram of single

NPs in the ring assembly is broader, but the maximum intensity is not as large as those of the

larger triangular NPs. Because the intensity of the NPs in the ring was normalized by the number

of NPs for each integration area, the contribution from larger triangular NPs is averaged with the

intensities of spherical NPs. This effect appears to lead to an apparent higher intensity per NP for

some areas and hence results in the broader intensity histogram observed for the NPs in the ring

assembly. Therefore, the intensities of single isolated NPs and NPs in the ring are comparable for

514 nm excitation.

Dark-field scattering is significantly less sensitive, making the same comparison to

individual 40 nm NPs more difficult. However, based on the similar intensity distributions for

absorption and scattering, as shown in Figs. 1E and 1H, the same conclusion should also apply

for scattering.

Fig. S6 Polarized photothermal images of the NP ring for 785 nm excitation. The arrows

represent the direction of excitation polarization.



9

Fig. S7 Polarized scattering images of the NP ring recorded for a spectral window of 800 ± 20nm. The arrows represent the direction of detection polarization.

Fig. S8 Polarization dependence of the photothermal intensity for a single spherical NP (40 nm)with 514 nm excitation (black circle), a single nanorod (22 x 70 nm) with 785 nm excitation

(purple), and a single nanorod (25 x 75 nm) with 675 nm excitation (blue). The lines show fits of

the data points to ))(2cos1()( φ θ θ −+= M N I . The recovered modulation depth M was 0.08 for

the almost spherical NP consistent with an isotropic SP oscillation. In contrast, the modulation

depths M for the 22 x 70 nm and 25 x 75 nm nanorods were 0.96 and 1.02, respectively. This

confirms our ability to measure by polarization sensitive photothermal imaging a maximum

modulation depth of unity as expected for the longitudinal dipole mode of a nanorod.



10

Fig S9 Unpolarized extinction spectra of local segments for different NP rings. The diameters of

the rings were 4.1(top), 4.6 (middle) and 5.6 (bottom) µm. The fact that the maxima of the

different SP modes did not change significantly for different ring diameters confirms that the

observed optical response originated from local NP segments and were not due to modes

delocalized over the entire ring. In addition, independent of the ring and the local segment all

spectra show SP resonances beyond 1000 nm that were assigned to SP coupling between

touching NPs.



11

Fig. S10 FEM calculations of a local ring segment considering conductive coupling between

neighboring NPs. The NP geometry is given in (A) and (C) and the corresponding extinction

spectra are shown in (B) and (D). The excitation polarization was parallel to the long axis of the

NP arragment. In (A), two groups of NPs were touching (NPs #1, 2, and NPs #6, 7). In (C), three

groups of NPs were touching (NPs #1, 2, NPs #3, 4, 5, and NPs #6, 7).

Calculation of σσσσSCA for the NP ring

The scattering cross section σSCA for a ring of NPs was calculated by obtaining the ratio

of the scattering intensities from the NP ring (ISCA,Ring) and a single NP (ISCA,NP) and then

multiplying this ratio by the theoretical σSCA,NP of a single NP, as given in eq. S1.

NPSCA

ringSCA

NPSCAringSCA I

I

,

,

,, ×=σ σ (S1)

σSCA,NP was calculated by solving Maxwell’s equations for a known size of the NP and

the dielectric constants of the metal and surrounding medium. To obtain efficient scattering

intensities for single NPs at 800, 700, and 550 nm, we selected NPs with average sizes of 22 x 70

nm, 33 x 63 nm, and 96 nm which were first characterized by TEM (Fig. S11A-C). The size

distributions of each sample were 22 ± 4 x 70 ± 11 nm, 33 ± 5 x 63 ± 12 nm and 96 ± 7 nm (Fig.

11D), respectively. The error corresponds to the standard deviation of the NP size. The scattering



12

spectra of the NPs were calculated by FEM using the software COMSOL Multiphysics assuming

the average size for each NP sample and a homogenous embedding medium with a refractive

index of 1.5 (Fig. S12A).

Fig. S11 TEM images of 96 nm (A), 33 x 63 nm (B), and 22 x 70 nm (C) NPs. The scale bars

represent 100 nm for all images. (D) size distribution of the three NP samples.



13

Fig. S12 Calculated scattering and absorption cross sections of NPs. Calculated scattering (A)

and absorption (B) spectra of 96 nm (green), 33 x 63 nm (red) and 22 x 70 nm (purple) NPs

using the software COMSOL Multiphysics. The refractive index of the medium was chosen to be

1.5. The green, red, and purple bars in (A) mark the detection wavelengths of 550 ± 20, 700 ±

20, and 800 ± 20 nm, respectively. The green, red, and purple lines in (B) mark the excitation

wavelengths of 514, 675, and 785 nm, respectively.

In order to measure the scattering intensities of the single NPs, we drop-cast the NP

solution on a pre-cleaned glass slide, which was followed by spin-casting a thin layer of PVA

film to ensure a homogeneous surrounding medium with a refractive index of 1.5. The scattering

spectra of the single NPs were measured by dark-field microscopy and fit to a Lorentzian

function as expected for single NPs (Fig. S13). Only NPs with a peak wavelength within ± 10

nm of the predicted value based on the mean size of the experimental distribution (Fig. S12A)

were selected. About 20 NPs of each sample were chosen following this procedure. The

scattering intensities of the three NP samples with average sizes of 22 x 70, 33 x 63, and 96 nm

were then measured by dark-field microscopy using bandpass filters of 800 ± 20, 700 ± 20, and

550 ± 20 nm. Fig. S14A shows a scattering image of 96 nm NPs recorded with a bandpass filter



14

of 550 ± 20 nm. The intensities of the selected NPs were integrated over a 850 x 850 nm2

area,

which was the resolution for the scattering image and is represented by the white boxes in Fig.

S14A. The 96 nm NPs were chosen because the scattering intensity of individual 40 nm NPs was

too low to yield reliable results. The same procedure was performed for the 22 x70 and 33 x 63

nm NPs using bandpass filters of 800 ± 20 and 700 ± 20 nm, respectively. In this way, we

determined the measured scattering intensities (ISCA,NP) for each sample.

Fig. S13 Scattering spectra of single NPs. Representative spectra are shown for NPs taken from

the samples with average sizes of 22 x 70 (A), 33 x 63 (B), and 96 nm (C). The black lines are

fits to a Lorentzian function, which is the expected line shape for single NPs.



15

Fig. S14 Calculation of σSCA for a NP ring. (A), (B) Scattering images (6.7 x 6.7 µm2) of 96 nm

NPs and the NP ring recorded with a 550 ± 20 nm bandpass filter, respectively. The white boxes

(850 x 850 nm2 each) represent the integration areas used for calculating the scattering intensity.

(C) Histogram of integrated scattering intensities for the NP ring, where the integrated area

corresponds to the size of the white boxes in (B). (D) Histogram of σSCA,ring for the NP ring

calculated using eq. S1.

The calculated σSCA,NP of the 22 x 70, 33 x 63 and 96 nm NPs were obtained by

integrating the simulated scattering spectra for the spectral windows of 800 ± 20, 700 ± 20, and

550 ± 20 nm and then normalized by the band width of the filter (40 nm), respectively. In Table

S1 the scattering intensities and σSCA,NP for each NP sample are given.

Table S1: Summary of the scattering intensity and σSCA for individual NPs (error is the standard

deviation)

Sample (detection window) ISCA,NP (MHz) σSCA,NP (nm2)

96 nm (550 ± 20 nm) 7.4 ± 0.7 2.1 x 104

33 x 63 nm (700 ± 20 nm) 1.7 ± 0.9 1.5 x 103

22 x 70 nm (800 ± 20 nm) 2.6 ± 1.5 4.6 x 103

The scattering intensities of the NP ring were acquired with bandpass filters of 800 ± 20,

700 ± 20, and 550 ± 20 nm. Note that the scattering images of the NPs and the NP ring were

measured side-by-side for each wavelength to ensure the same experimental conditions. The



16

intensities of the ring segments (ISCA,ring) were also acquired by integrating areas of 850 x 850

nm2

along the ring to compare to the single NPs. Fig. S14B shows the scattering image of the NP

ring taken with a bandpass filter for 550 ± 20 nm. Each white box represents the integration area

used for the intensity calculation. The ring was divided into 24 segments according to the

experimental resolution. Fig. S14C shows the histogram of the scattering intensities of these 24

segments. Values for σSCA,ring of the ring were calculated using eq. S1. Table S2 shows the mean

scattering intensity and σSCA,ring of the24 ring segments for wavelengths of 800 ± 20, 700 ± 20,

and 550 ± 20 nm.

Table S2: Summary of the mean scattering intensity, σSCA,ring, and σSCA for the 24 ring segments(error is the standard deviation)

Detection window ISCA,ring (MHz) σSCA,ring (nm2) σSCA (nm

2)

550 ± 20 nm 7.9 ± 2.0 (2.2 ± 0.6) x 104

560 ± 128

700 ± 20 nm 29.0 ± 8.3 (2.5 ± 0.7) x 104

656 ± 177

800 ± 20 nm 12.8 ± 4.8 (2.3 ± 0.8)x 104 608 ± 247

Fig. S14D displays the σSCA,ringt histogram of the NP ring. The numbers of NPs for each

ring segment were also acquired by overlaying Fig. S14B with the SEM image and counting the

number of NPs for each white box (Fig. S15A). The normalized σSCA, which represents σSCA,ring

per NP, was calculated by σSCA,ring / N where N is the number of NPs for each ring segment. σSCA

at 800 ± 20, 700 ± 20, and 550 ± 20 nm are also listed in Table S2.



17

Fig. S15 Scattering (A) and absorption (B) images overlaid with the SEM image allowing the

determination of the average number of NPs per integration area.

Calculation of σσσσABS for the NP ring

The calculation of σABS for the NP ring was similar to that of σSCA. Photothermal images

were acquired from the same NPs analyzed in the scattering experiments using circularly

polarized excitation. The excitation wavelengths for the 22 x 70, 33 x 63, and 96 nm NPs were

785, 675, and 514 nm, respectively. The excitation and probe powers ranged between 8 - 54 and

99 -127 kW/cm2

for the different samples to avoid signal saturation. Fig. S16A shows a

photothermal image of 96 nm NPs excited at 514 nm. Each white box corresponds to the area

used to calculate the intensity, which was chosen to be 390 x 390 nm2

based on the optical

resolution of the photothermal images. Photothermal images for 22 x70 and 33 x 63 nm NPs

were also measured, using 785 and 675 nm excitation. The measured absorption intensities

(IABS,NP) of each sample are given in Table S3. The calculated σABS,NP for these samples at 785,

675, and 514 nm using the simulated spectra in Fig. S13B are also listed in Table S3.



18

Fig. S16 Calculation of σABS for a NP ring. (A), (B) Photothermal images (6.7 x 6.7 µm2) of 96

nm NPs and the NP ring for 514 nm excitation, respectively. The white boxes (390 x 390 nm2)

present the integration areas used for the intensity calculation. (C) Histogram of integrated

absorption intensities for the NP ring, where the integrated area corresponds to the size of the

white boxes in (B). (D) Histogram of σABS,ring for the NP ring calculated using eq. S2.

Table S3: Summary of the absorption intensity and σABS for individual NPs (error is standard the

deviation)

Sample (excitation wavelength) IABS,NP (V) σABS.NP (nm2)

96 nm (514 nm) 9.6 ± 4.8 1.5 x 10

4

33 x 63 nm (675 nm) 14.1 ± 6.0 4.5 x 103

22 x 70 nm (785 nm) 3.2 ± 1.2 9.6 x 103

The photothermal images of the NP ring were also measured with 785, 675, and 514 nm

excitation and circular polarization. The photothermal images of the NP ring and NPs were again

measured side-by-side for each wavelength to ensure the same experimental conditions. Fig.

S16B shows the photothermal image of the NP ring with 514 nm excitation. The white boxes

represent the same integration areas for calculating the experimental absorption intensity as was

used for the single NPs (390 x 390 nm2). The ring was therefore divided into 40 segments. Fig.



19

S16C displays a histogram of absorption intensities (IABS,ring) for 40 ring segments. Values

for σABS,ring of the NP ring were calculated using eq. S2.

NP ABS

ring ABS

NP ABSring ABS

I

I

,

,

,, ×=σ σ (S2)

Table S4 shows the mean absorption intensity and σABS,ring of the 40 ring segments for 514, 675,

and 514 nm excitation.

Table S4: Summary of the mean absorption intensity, σABS,ring, and σABS for the 40 ring segments

(error is the standard deviation)

Excitation wavelength IABS,ring (V) σABS,ring (nm2) σABS (nm2)

514 nm 11.0 ± 5.3 (1.7 ± 0.8) x 104

1205 ± 570

675 nm 13.4 ± 16.8 (4.3 ± 5.3) x 103

335 ± 544

785 nm 4.6 ± 3.4 (1.4 ± 1.0) x 104

988 ± 830

Fig. S16D shows a histogram of σABS,ring obtained from the 40 ring segments. The

number of NPs within each segment was again acquired by overlaying Fig. S16B with the SEM

image and counting the number of NPs for each white box (Fig. S15B). The normalized σABS,

which represents σABS,ring per NP, was calculated by σABS,ring / N where N is the number of NPs for

each ring segment. The mean values of σABS for the 40 rings segments at 785, 675, and 514 nm

are listed in Table S4.

Although the excitation volume contained ~ 15 NPs in the case of the NP ring, the

photothermal signal is dominated by changes in the refractive index of the medium and not the

NPs themselves as shown by photothermal imaging of single NPs in different media(3),

justifying the analysis chosen here. In addition, the good agreement between the measured

photothermal intensities and calculated values for various NP sizes further verifies the accuracy



of photothermal imaging in determining SP absorption regardless of the volume of the NPs

probed in the excitation area(4).

Fig. S17 σSCA,ring (blue) at 550, 700 and 800 nm of the ring segment marked by the yellow

rectangle in Fig. 1A. The yellow line shows the scattering spectrum of the same ring segment.

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wei-shun chang et al- low absorption losses of strongly coupled surface plasmons in nanoparticle...

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