1686 OPTICS LETTERS / Vol. 28, No. 18 / September 15, 2003

Broadband near-field interference spectroscopy of metalnanoparticles using a femtosecond white-light continuum

A. A. Mikhailovsky and M. A. Petruska

Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

M. I. Stockman

Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303

V. I. Klimov

Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received March 27, 2003

We demonstrate a new nanoscale spectroscopic technique that combines subwavelength near-field imaging withbroadband interference spectroscopy. We apply this technique to study phase spectra of surface plasmonsin individual gold nanoparticles and nanoparticle dimers. Collective plasmon oscillations in selected nanos-tructures are excited by a femtosecond white-light continuum transmitted through a subwavelength aperture.The interference spectra detected in the far field result from the coherent superposition of the aperture fieldand the secondary field re-emitted by the nanostructure. The analysis of these spectra allows us to accu-rately measure the positions and damping constants of single-nanostructure plasmon resonances. © 2003Optical Society of America

OCIS codes: 180.5810, 300.0300, 320.0320.

Metal nanoassemblies offer exciting opportuni-ties for manipulating light at the nanoscale viamorphology-controlled resonances associated withsurface-plasmon (SP) modes.1 –3 When a metalnanostructure is subjected to an external field, thedetected signal is determined by a superposition ofthe driving field with secondary (re-emitted) f ieldsassociated with induced SP oscillations.4 Because ofthe coherent nature of this superposition, the totalfield is strongly dependent on phases of plasmonoscillations. The phase manipulation can be used, inparticular, for controlling the spatial distribution ofSP modes.5

An initial step toward achieving phase control isunderstanding the phase responses of nanoscale metalsystems to applied fields. In this Letter we reporta new method for broadband studies of the phasespectra of SPs in individual nanoscale objects. Col-lective plasmon oscillations in selected nanostructuresare excited by a femtosecond white-light continuumtransmitted through a subwavelength aperture. As aresult of the coherent superposition of the aperturefield and the secondary f ield re-emitted by the nano-structure, the detected signals exhibit clear signa-tures of constructive and destructive interference andprovide direct information regarding the phase spec-trum of SPs. The analysis of the interference signalsallows us to determine the frequencies and damp-ing constants of plasmon resonances in single goldnanoparticles and two-particle assemblies (dimers).

In the case of an isolated plasmon resonance, thephase �f� of induced oscillations (i.e., the induced field)switches from 0 to p as the driving frequency �v� istuned across the resonant plasmon frequency �v0�, indirect analogy to the phase shift observed for a forced

0146-9592/03/181686-03$15.00/0

harmonic oscillator. Since the induced oscillations arein phase (out of phase) with the driving force below(above) the resonance, the total signal should show atransition from constructive (increased signal) to de-structive (decreased signal) interference exactly at theposition of the plasmon resonance, and in contrast tothe amplitude spectra, this position is not affected bydielectric losses in a metal. Therefore, interferencespectra can provide more-accurate information on plas-mon resonances than traditional studies of the ampli-tude responses.

The challenge in detecting the interference spectraof individual nanostructures is that the f ield emittedby a nanoscale object is many orders of magnitudelower than the applied f ield. To decouple the strongfield that excites a nanostructure from the weak(but phase-correlated) field that interferes with thenanostructure response, one can apply near-f ieldoptical excitation through a small ��100-nm� aper-ture.6 The subwavelength aperture produces a veryweak propagating f ield (i.e., a field measured byfar-field detectors), whereas it creates a much strongernear-zone f ield in the form of rapidly decaying, non-propagating, evanescent modes. By positioning thesample in close proximity �,10 nm� to the aperture,one can eff iciently drive plasmon oscillations via theevanescent-f ield component. The induced plasmonoscillations produce a secondary field with a largepropagating component (the nanostructure acts asa nanoantenna that efficiently converts evanescentmodes into the propagating radiation). After co-herent superposition with the far-zone component ofthe aperture field, the re-emitted field produces theinterference spectrum measured by a far-field detector(Fig. 1a).

© 2003 Optical Society of America

September 15, 2003 / Vol. 28, No. 18 / OPTICS LETTERS 1687

Fig. 1. a, Illustration that the signal measured by afar-field detector is due to the coherent superposition of anaperture driving field, EA

0 �v�exp�ivt�, and a phase-shiftedfield, E

p0 �v�exp�i�vt 1 f��, emitted by a nanoparticle.

b, Schematics of a near-f ield, broadband extinctionspectrometer–microscope. The femtosecond white-lightcontinuum generated in a sapphire plate is delivered toa sample through a near-field fiber probe. The sampleis mounted on an XYZ scanner. In the imaging mode,the light transmitted through the sample is collected witha photomultiplier tube (PMT); in the spectroscopic mode,the transmitted light is dispersed in a spectrometer andis detected with a CCD. c, Spectrum of the femtosecondwhite light at the output of a near-f ield fiber tip.

In the studies reported in Refs. 4 and 7, the ef-fect of the phase of SP oscillations on near-f ieldsignals was addressed experimentally with a single-wavelength excitation source. However, because ofthe relatively large width of plasmon resonances,broadband near-field illumination is required fordetection of the complete interference spectra of SPs.In our experiments such illumination is providedby a femtosecond white-light continuum coupledinto a fiber probe of a near-f ield scanning opticalmicroscope (NSOM; Fig. 1b). In addition to widespectral coverage (�1.8 to �2.8 eV; Fig. 1c) and highbrightness, the femtosecond continuum exhibits ahigh degree of spatial coherence, which results inlow, laser-beam-like divergence. The last-namedproperty allows us to couple the continuum into asingle-mode near-f ield f iber with efficiency greaterthan 40%, which is orders of magnitude higher thancoupling efficiencies achievable with incoherent lightsources.8

We used tapered fiber probes with a thin ��100-nm�Al coating and a 50–100-nm opening at the end (thesize of the opening determines the NSOM resolution).We tested all probes by scanning them across single�50-nm gold particles. Only probes that did not pro-duce imaging artifacts (e.g., side images, anisotropicshapes, or ringing structures) associated with theinteraction between the coating and the nanoparticle

were selected for the experiments. The samples ofrandom aggregates of sub-100-nm gold nanoparticleswere prepared on thin layers of poly-L-lysine bysettling from colloidal gold solutions. To measure theextinction spectra of individual particles–aggregates,we acquired pairs of transmission spectra by placingthe near-f ield tip either directly above the selectednanostructure or above the nominally transparent sub-strate region. The recorded spectra [I �v� and I0�v�,respectively] were used to calculate the near-f ieldextinction: Q�v� � 2ln�I �v��I0�v��.

To analyze the measured extinction spectra quan-titatively, we can present the total signal detectedby a far-field detector as a coherent sum of theaperture and the nanostructure f ields (Fig. 1a):I �v� ~ jEA

0 1 bP

j Epj �v�exp�ifj �v��j2, where EA

0 isthe amplitude of the aperture f ield (driving f ield),Ep

j �v� is the amplitude of the f ield associated witha SP resonance of a nanostructure at frequency v0j ,fj�v� is the phase shift of this f ield with respect tothe driving f ield, and b is the ratio of contributionsof aggregate and aperture f ields to the far-fieldsignal. Since Ep

j �v� ~ EA0 and I0 ~ jEA

0 j2, we can

describe the extinction spectra with the expressionQ�v� � 2lnj1 1 b

Pj uj �v�exp�ifj�v��j2, where uj �v�

is the line shape of the v0j resonance. We can

Fig. 2. a, Typical topographic (TOPO) and near-f ield(femtosecond white-light illumination) images of an iso-lated gold nanoparticle (the nominal size is 50 nm; thevisible size is larger because of resolution limitationsof the NSOM). b, Near-field extinction spectrum (solidred curve) of an individual �50-nm gold nanoparticlecompared with interference (dotted black curve) andphase (dashed blue curve) spectra (v0 � 2.245 eV andG � 0.18 eV) calculated with a forced harmonic oscillatormodel (inset). c, Position of the plasmon resonance de-rived from the near-f ield interference spectra as a functionof the nanoparticle diameter.

1688 OPTICS LETTERS / Vol. 28, No. 18 / September 15, 2003

Fig. 3. Near-field extinction spectrum (red curve) of ananoparticle dimer (insets); particle sizes are �50 nm.The dotted black and dashed blue curves are interferenceand phase spectra, respectively, calculated with a coupledharmonic oscillator model (v01 � 2.21 eV, v02 � 2.13 eV,G1 � G2 � 0.22 eV, and D12 � 0.16 eV; v01 and v02 aresingle-particle plasmon energies, and D12 is the couplingstrength).

simplify the expression for Q�v�, assuming that theoverlap between different resonances is weak andb ,, 1, which yields Q�v� � 22b

Pj uj �v�cosfj �v�.

In the case of an isolated spherical nanoparticle(a single plasmon resonance), the latter expressionreduces to Q�v� ~ 2u�v�cos f�v�, indicating thatthe near-f ield spectrally resolved extinction providesa direct measure of the phase spectrum of inducedplasmon oscillations. In terms of a forced harmonicoscillator, cos f � Dv���Dv�2 1 �G�2�2�1�2, whereDv � v 2 v0 is the detuning from the plasmon fre-quency and G is the damping constant (the resonancebroadening). The latter expression indicates that theinterference spectrum crosses over from negative topositive values exactly at the undamped resonancefrequency (for v � v0, cos f � 0, and Q � 0), whichis in contrast to the amplitude spectra, where theresonance occurs at v � �v2

0 2 G2�2�1�2.The spectra collected for individual particles im-

aged in Fig. 2a clearly exhibit the transition fromconstructive �Q , 0� to destructive �Q . 0� interfer-ence (solid red curve in Fig. 2b), as expected for anisolated plasmon resonance. For a particle of 50-nmdiameter, this transition occurs at 2.245 eV, whichprovides an accurate measure of the single-particleSP resonance energy. The same interference effect isobserved for nanoparticles of other sizes, which allowsus to derive the size dependence of SP energies. Asthe particle size is decreased, the plasmon energyincreases (Fig. 2c), consistent with the results ofprevious ensemble measurements.9

By using the forced harmonic oscillator model todescribe both the phase and the amplitude spectra ofSP oscillations, we are able to closely f it the spectrameasured for single particles (dotted black curve inFig. 2b). The calculated phase spectrum (dashedblue curve in Fig. 2b) indicates that the measuredextinction closely correlates with the phase shift thatoccurs at the resonant frequency. Our modeling also

allows us to derive the damping constant �G� thatdetermines the plasmon resonance broadening. Fora 50-nm particle, we obtain G � 0.18 eV, which isconsiderably smaller than linewidths observed in en-semble spectra.9

Figure 3 displays the near-f ield spectrum of ananoparticle dimer (solid red curve), which also ex-hibits a crossover from negative to positive extinction.However, in the range of positive extinction, thedimer spectrum shows a double-peak structure, whichindicates the existence of two plasmon modes that canbe assigned to longitudinal and transverse collectiveoscillations.1 We model this spectrum (dotted blackcurve in Fig. 3) assuming that the two plasmon modescorrespond to the two normal modes of a pair ofcoupled harmonic oscillators subjected to an externalforce. The forced oscillations in such a system arecharacterized by two phase shifts related to differentnormal modes, and these shifts are directly observablein the interference spectrum as two well-resolvedsteps that correlate with the phase change (dashedblue curve) in the dimer response.

In conclusion, we have demonstrated a newnanoscale spectroscopic technique that allows us tostudy interference spectra of plasmon oscillationsin individual gold nanoparticles and two-particleaggregates. Collective plasmon oscillations in se-lected nanostructures are driven by high-intensitybroadband near-field illumination with a femtosecondwhite-light continuum. By analyzing the interferencespectra resulting from the coherent superposition ofthe field emitted by a subwavelength apeture and thesecondary field emitted by a nanostructure, we areable to spectrally resolve the phase of plasmon oscil-lations in individual nanoparticles and nanoparticledimers and to determine the positions and dampingconstants of plasmon resonances.

This work was supported by Los Alamos LDRD andDevelopment Funds and the U.S. Department of En-ergy, Office of Science, Division of Chemical Sciences.V. I. Klimov’s e-mail address is klimov@lanl.gov.

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