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Collective plasmon modes in a compositionally asymmetric nanoparticledimerFuyi Chen, Negash Alemu, and Roy L. JohnstonCitation:AIP Advances 1, 032134 (2011); doi: 10.1063/1.3628346View online: http://dx.doi.org/10.1063/1.3628346View Table of Contents: http://aipadvances.aip.org/resource/1/AAIDBI/v1/i3Published by theAIP Publishing LLC.Additional information on AIP AdvancesJournal Homepage: http://aipadvances.aip.orgJournal Information: http://aipadvances.aip.org/about/journalTop downloads: http://aipadvances.aip.org/features/most_downloaded

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AIP ADVANCES 1, 032134 (2011)

Collective plasmon modes in a compositionally asymmetricnanoparticle dimer

Fuyi Chen,1,a Negash Alemu,1 and Roy L. Johnston2,b1State Key Laboratory of Solidification Processing, Northwestern Polytechnic University,

Xian, 710072, P. R. China2School of Chemistry, University of Birmingham, Birmingham, B15 2TT, U. K.

(Received 26 May 2011; accepted 28 July 2011; published online 11 August 2011)

The plasmon coupling phenomenon of heterodimers composed of silver, gold and

coppernanoparticles of 60 nm in size andspherical in shape were studied theoretically

within the scattered field formulation framework. In-phase dipole coupled -modes

were observed for the Ag-Au and Ag-Cu heterodimers, and an antiphase dipole

coupled -mode was observed for the Ag-Au heterodimer. These observations agree

well with the plasmon hybridization theory. However, quadrupole coupled modes

dominate the high energy wavelength range from 357-443 nm in the scattering

cross section of the D=60 nm Ag-Au and Ag-Cu heterodimer. We demonstrate

for the first time that collective plasmon modes in a compositionally asymmetricnanoparticle dimer have to be predicted from the dipole-dipole approximation of

plasmon hybridization theory together with the interband transition effect of the

constitutive metals and the retardation effect of the nanoparticle size. Copyright

2011 Author(s). This article is distributed under a Creative Commons Attribution 3.0

Unported License. [doi:10.1063/1.3628346]

I. INTRODUCTION

The optical properties of individual metal nanoparticles are dominated by their localized sur-

face plasmon resonances (LSPR), which are associated with the collective coherent oscillation of

conduction electrons in metallic nanostructures.1 The electromagnetic field surrounding a metal-

lic nanoparticle that has been excited near the plasmon resonance can extend for a considerable

distance, and a compelling analogy therefore exists between the plasmon resonance of individual

nanoparticles and the wave functions of simple atoms. Similar to the roles of atoms in molecules and

solids, metal nanoparticles can assemble to create a diverse range of new plasmonic nanoclusters, 2

including dimers,3 trimers,4 quadrumers5 and tetramers,6 etc.7 Each type of plasmonic nanocluster

exhibits its own unique set of collective plasmon modes.

The simplest description of collective plasmon modes is the dipoledipole interaction during

the coupling of two nearby oscillators. For two adjacent metallic spheres a lower-energy resonance

corresponds to two longitudinally aligned dipoles giving rise to a strong red-shifted absorption

peak in the optical spectrum. For the higher energy resonance the coupled dipoles cancel each other,

resulting in a resonance with essentially a zero net dipole moment that does not interact with incident

light and does not appear in the optical absorption spectrum of the particle pair. Depending on the

nanoparticle size and interparticle distance, higher-order multipoles can also play an important rolein collective plasmon modes.8

It is striking that the simplest description of collective plasmon modes, the dipoledipole

interaction has resulted in a substantial understanding of a rich array of new electromagnetic

aEmail: [email protected]: [email protected]

2158-3226/2011/1(3)/032134/16 C Author(s) 20111, 032134-1

http://dx.doi.org/10.1063/1.3628346http://dx.doi.org/10.1063/1.3628346http://dx.doi.org/10.1063/1.3628346http://dx.doi.org/10.1063/1.3628346mailto:%[email protected]:%[email protected]:%[email protected]:%[email protected]://dx.doi.org/10.1063/1.3628346http://dx.doi.org/10.1063/1.3628346http://dx.doi.org/10.1063/1.3628346

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032134-2 Chen, Alemu, and Johnston AIP Advances 1, 032134 (2011)

properties, such as subradiant (dark) plasmonic modes,9 Fano resonances,10 optical nanodiodes,11

electromagnetically induced transparency12 and, in particular, the magnetic response,13 which is

excited by the antisymmetric plasmonic resonance in various arrays of nanoparticle pairs such as in

metal nanostrip dimers,14, 15 nanodisk dimers,16, 17 and metal plate pairs.18, 19

Symmetry breaking in collective plasmon modes can introduce effects that are not present

in the symmetrical configurations. Recently, these effects that come from the coupling betweenthe otherwise uncoupled plasmon modes of the system were investigated using compositionally

asymmetric nanoparticle dimers.2023 For example, Fano-type absorption line profiles were ob-

served in the absorption spectra of the gold nanoparticles because of an interaction between the

discrete local plasmon resonance of silver and the interband transition of gold in a D=10 nm

Au-Ag heterodimer with an interparticle distance of 3 nm.20 The two plasmonic resonances ex-

hibit a simultaneous shift for the D=30 nm Au-Ag heterodimer, and this is in contrast to the

homodimer.21 Anomalous red-shifts of the antibonding modes were observed with respect to the

silver local plasmon resonance mode in the scattering spectra of the heterodimer composed of a

30 nm silver and a 40 nm gold nanoparticle, and this was induced by the coupling of silver

particle plasmon resonance to the continuum of the interband transitions in gold.22 The Fano

resonance has only been induced by the longitudinal component of the heterodimer surface plas-

mon resonance in a heterodimer composed of a 10 nm silver and a 30 nm gold nanoparticle. 23

Despite this intense research, neither the dipolar eigenmodes nor the induced charge configura-

tion of plasmonic resonance have been addressed in these recent heterodimers,2023 which indi-

cates that the interaction between the strongly coupled heterodimer is not as completely under-

stood as in the homodimer. Therefore, a systematic study of the collective plasmon modes in

the heterodimer is required, as it may result in a new theoretical paradigm and a host of novel

applications.

We studied a D=60nm Ag-Auand a D=60 nm Ag-Cu nanoparticle heterodimer under different

interparticle separations (1-15 nm) and variable polarizer angles (0-90) as prototype systems. We

found that the longitudinal coupling between the nanoparticles shows a strong dependence on the

size of the dimer gap in the Ag-Au and Ag-Cu heterodimers. We demonstrate for the first time that a

quadrupole-coupled mode emerges in the Ag-Au heterodimers and dominates the scattering spectra

of the Ag-Cu heterodimers. An antiphase dipole-coupled mode was observed with low intensity

in the Ag-Au heterodimer; this configuration of two stacked antiphased nanoparticles is known as

magnetic resonance, and is essential for the development of negative refractive index materials in

the visible region of the spectrum.

II. METHODOLOGY

The extinction spectra and electromagnetic field distribution of the nanoparticle dimers were cal-

culated using the finite difference time domain (FDTD) method. Three-dimensional vector Maxwell

equations in the different nanostructures were solved within the scattered field formulation frame-

work. The FDTD calculations with a finer grid for the elected distances revealed the plasmon

hybridization mode in almost perfect agreement with Mie theory for spheres. The surface charge

distributions that were induced on the nanoparticle profiles were evaluated using the calculated elec-tromagnetic fields. The dimer was formed by identical spherical nanoparticles whose surfaces are

separated by a distances gap, ranging from one half of sphere radius a down to conductive touching

with gap=-3 nm. Here, we consider spheres with a diameter of 60 nm. The dielectric functions

were described using the tabulated empirical data of Johnson and Christy with a linear interpolation

for pure copper, silver and gold.24 The dimer without a substrate was embedded in an air medium

surrounded by a perfectly matched layer. The distance was a full wavelength from the nanoparticles

to avoid spurious reflections and to avoid absorbing the energy of evanescent fields. A total-field

scattered-field plane wave, which was used for excitation, was inserted on the inside of the perfectly

matched layers near the air medium interface. The studied model was discretized by a conformal

mesh method with a side length of 0.1 nm in the dimers.


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III. RESULTS AND DISCUSSION

A. Ag-Ag nanoparticle homodimer

We start with a simple homodimer and show the calculated scattering spectra of a

D=60 nm silver nanoparticle homodimer in vacuum as a function of the polarization angle in

Fig. 1(a), including parallel (black curve) and perpendicular (red curve) incident polarization withrespect to the dimer axis in Fig. 1(b). These results clearly illustrate that only the longitudinal

resonance mode (L) is present in the scattering spectrum when the polarizer is oriented along the

interparticle axis and the L-mode results from the longitudinal LSPR coupling of the particle plas-

mons and displays two distinct peaks. The lower energy peak is present at 464 nm and the higher

energy peak is at 357 nm. When the polarizer is oriented perpendicular to the interparticle axis

only the transverse resonance mode (T) contribution is observed at 364 nm, because of transverse

LSPR coupling. At all the intermediate angular orientations the scattering spectra show L- and T-

orthogonal modes and a clear isosbestic point is present near 412 nm in the spectrum. In Fig. 1(b),

a 60 nm isolated silver nanoparticle shows dipole resonance () at 378 nm. By comparison with

the single particle resonance () the lower energy L-mode has a longer wavelength and a stronger

intensity and the T-mode is slightly blue shifted and lower in intensity.

Figure 1(c) shows the calculated scattering spectra of a D=60 nm silver nanoparticle homod-

imer in vacuum as a function of interparticle separations under longitudinal polarization. For an

interparticle separation larger than 9 nm, only lower energy L-modes are present and observed to

red-shift significantly from 411 nm at a 15 nm gap to 505 nm at a 1 nm gap. For an interparticle

separation smaller than 9 nm the scattering peak splits into two well-defined peaks and the higher

energy L-mode (at 357 nm in Fig. 1(b)) is spectrally separated from the lower energy L-mode by

a pronounced dip. This phenomenon is the result of strong longitudinal SPR coupling, and indi-

cates that the electromagnetic interaction between the nanoparticles is far more significant for an

interparticle separation smaller than 9 nm. These higher energy L-modes have been observed to

red-shift slightly with a decrease in the interparticle separation, which agrees with previous studies

on nanoparticle dimer arrays.25, 26

Figure 2 shows the electric-field intensity and the surface charge distribution profile for the L-

mode and the T-mode in a D=60 nm silver nanoparticle homodimer. As expected, the electric field

intensity is enhanced at the junction of the Ag-Ag homodimer for both the lower energy and the high

energy L-mode; however, the local charges exhibit a dipole-dipole (DD) pattern for the lower energy

L-mode (464 nm) and a quadrupole-quadrupole (QQ) pattern for the high energy L-mode (357 nm).

For the T-mode at 364 nm the electric field intensity is localized around the silver nanoparticle,

i.e., the nonjunction ends of the Ag-Ag homodimer and the local charges exhibit a dipole-dipole

(DD) pattern. For the dipole-dipole L-mode and the dipole-dipole T-mode the charges confined to the

same edge of the nanoparticle have the same sign, which indicates that these dipole-dipole modes are

in-phase collective plasmon modes. Therefore, the bonding-mode () and antibonding-mode (*)

can be assigned as for the dipole-dipole L-mode and the dipole-dipole T-mode, respectively, from

the classification frame of the plasmon hybridization model.27 The quadrupole-quadrupole L-mode

is associated with the spectral superposition of higher order longitudinal resonance modes, and its

main contribution comes from the quadrupole plasmon resonance of an individual silver particle.25, 26

The collective plasmon modes can also be classified as bright and dark modes for the complex

nanostructures that consist of multiple closely spaced nanoparticles or patterned nanoholes. Asshown in Fig. 2, the quadrupole-quadrupole L-mode, the dipole-dipole L-mode and the dipole-

dipole T-mode possess finite net dipole moments, and these plasmonic modes are bright plasmonic

modes, which are efficiently excited by incident light and are clearly visible in the optical spectrum.

The quadrupole-quadrupole L-mode is not bright for an interparticle separation bigger than 9 nm in

the homodimer.

B. Ag-Au nanoparticle heterodimer

Dark plasmonic modes possess a zero net dipole moment and do not couple to light, and are

therefore not very prominent in optical spectra. To enhance the manifestation of dark plasmonic


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FIG. 1. Scattering spectra for the D=60 nm silver nanoparticle homodimer as a function of the polarization angle with

interparticle separations of 3 nm (a). Scattering spectra under longitudinal and transverse polarization with respect to a

60 nm isolated silver nanoparticle (b), and as a function of interparticle separations under a polarizer angle of 0 degrees (c).

modes we introduced compositional asymmetry in the collective plasmon modes, and can therefore

discuss the optical properties of a D=60 nm silver and gold nanoparticle heterodimer. In Fig. 3(a)

and 3(b) we show the calculated scattering spectra of the Ag-Au nanoparticle heterodimer as a

function of the polarization angle (0-90) and the two extreme cases for orthogonal polarization,

respectively. Following the identification of the L- and T- plasmon modes in homodimers similar

mode can be assigned as the Ag-Au heterodimer. Figure 3(a) and 3(b) shows that the Ag-Au

heterodimer supports the higher energy L-mode at 410 nm, the lower energy L-mode at 545 nm

under longitudinal polarization (0), the higher energy T-modes at 373 nm and the lower energy

T-mode at 527 nm under transverse polarization (90). The primitive or unhybridized mode of


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FIG. 2. Electric near-field profiles and surface charge distributions in a D=60 nm silver nanoparticle homodimer for

longitudinal and transverse resonance modes.

the isolated 60 nm silver nanoparticle (1) and the isolated 60 nm gold nanoparticle (2) are

at 379 and 531 nm, respectively. This result is quite different from the D=60 nm Ag-Ag homodimer,

where only two or three bright modes exist. The scattering spectra in Fig. 3(a) and 3(b) show four

bright modes at 410 nm (L-mode), 545 nm (L-mode), 373 nm (T-mode) and 527 nm (T-mode).

Figure 3(c) shows calculated scattering spectra as a function of interparticle separation under

longitudinal polarization for a D=60 nm silver and gold nanoparticle heterodimer. Both the lower

energy L-mode at 545 nm and the high energy L-mode at 410 nm were observed to red-shift

significantly with a decrease in the interparticle separation although the high energy L-mode changes

from a peak to a flat shoulder in the scattering spectra for interparticle separations smaller than 9 nm.

The L-mode is a bonding-mode where a large portion of the electric field experiences a modified

dielectric environment and increases with a decrease in interparticle separation.

In Figure 4, we calculated the surface charge distribution for four bright modes in a D=60 nm

silver and gold nanoparticle heterodimer. The high energy L-mode at 410 nm and the lower energy

L-mode at 545 nm, similar to that of the D=60 nm Ag-Ag homodimer, gave an enhanced electric

field intensity at the junction of the dimer and revealed a quadrupole-quadrupole (QQ) mode and a

dipole-dipole (DD) mode in the surface charge pattern, respectively. The dipole-dipole L-mode at

545 nm is a bonding-mode () in the plasmon hybridization model like that in the D=60 nm Ag-Ag

homodimer.

The high energy T-mode at 373 nm and the lower energy T-mode at 527 nm are new collectiveplasmonic modes for the Au-Ag heterodimer, which exhibits a dipole-quadrupole (DQ) mode and

a dipole-dipole (DD) mode in the surface charge pattern. Judging from the signs of the charges

confined to the nanoparticle edge the dipole-dipole T-mode at 527 nm is an out-of-phase collective

plasmon mode of the individual silver plasmons (1) and the gold plasmons (2). It is important to

note that the lower energy T-mode at 527 nm, which is an otherwise dark mode in the symmetric

dimer, is clearly visible in the optical spectrum in the Au-Ag heterodimer, and can be assigned as a

bonding-mode () from the classification frame of the plasmon hybridization model.

For the higher energy T-mode at 373 nm the electric field intensity is localized around the silver

nanoparticle of the D=60 nm Ag-Au heterodimer and the surface charge in the Ag nanoparticle

exhibits a dipolar pattern while the surface charge in the Au nanoparticle exhibits a quadrupolar


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FIG. 3. Scattering spectra for a heterodimer of a D=60 nm silver and gold nanoparticle heterodimer as a function of the

polarization angle with interparticle separations of 3 nm (a). Scattering spectra under longitudinal and transverse polarization

with respect to the normalized scattering spectra for a 60 nm isolated silver and gold nanoparticle (b), and as a function of

interparticle separations at a polarizer angle of 0 degrees (c).

pattern. The charges confined to the Au nanoparticle have a + sign in the left half-sphere and this

is opposite to the Ag neighbor nanoparticle and the - sign in the right half-sphere indicating that

the quadrupolar charge pattern in the Au nanoparticle is induced by the electric field from the nearby

Ag nanoparticle.

As shown in Figure 4, the quadrupole-quadrupole (QQ) L-mode at 410 nm, the dipole-dipole

(DD) L-mode at 545 nm, the dipole-quadrupole (DQ) T-mode at 373 nm and the dipole-dipole (DD)

T-mode at 527 nm have a nonzero electric dipole moment and can be excited by an incident plane


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FIG. 4. Electric near-field profiles and surface charge distributions in a D=60 nm sliver and gold nanoparticle heterodimer

for longitudinal and transverse resonance modes.

wave. The dipole-dipole (DD) T-mode or the -mode at 527 nm dipole are active, because of the

incomplete cancellation of the dipoles of the silver and gold particles in the Au-Ag heterodimer.

C. Ag-Cu nanoparticle heterodimer

As another example of a nanoparticle heterodimer, we obtained the optical properties of a D=

60 nm silver and copper nanoparticle heterodimer. The calculated scattering spectra of the het-

erodimer are shown in Fig. 5(a) as a function of the polarization angle. The extreme cases for the

longitudinal and transverse polarization are plotted in Fig. 5(b). Similar to the 60 nm silver particle

homodimer, scattering from the longitudinal polarization has a higher energy L-mode at 443 nm and

a lower energy L-mode at 575 nm. Scattering from transverse polarization has a T-mode at 373 nm.

Figure 5(c) shows the calculated scattering spectra as a function of interparticle separation

under longitudinal polarization for a D=60 nm silver and copper nanoparticle heterodimer. The

higher energy L-mode gave a significant red-shift with a decrease in interparticle separation and it

splits into two well-defined scattering peaks for interparticle separations smaller than 2 nm. Lower

energy L-modes were clearly observed for interparticle separations smaller than 5 nm and these red-

shift slightly with a decrease in interparticle separation and they have a lower scattering intensity

compared to the higher energy L-mode.

Figure 6 shows the electric field intensity and the surface charge distribution profile for the

higher energy L-mode at 443 nm, the lower energy L-mode at 575 nm and the T-mode at 373 nm

in a D=60 nm silver and copper nanoparticle heterodimer. As expected, the electric field intensity

is enhanced at the junction of the Ag-Cu heterodimer for the higher energy L-mode and the lower

energy L-mode. The surface charge configurations exhibit a dipole-dipole (DD) pattern for thelower energy L-mode and a quadrupole-quadrupole (QQ) pattern for the higher energy L-mode.

The charges confined to the same edge of the nanoparticle show the same sign for the lower energy

L-mode and the opposite sign for the higher energy L-mode. This indicates that the lower energy

L-mode is an in-phase collective plasmonic mode and the higher energy L-mode is an out-of-phase

collective plasmonic mode. The lower energy dipole-dipole L-mode for these modes at 575 nm is a

bonding-mode () in the classification frame of the plasmon hybridization model.

Compared to collective plasmonic modes in the Ag-Au heterodimer the higher energy

quadrupole-quadrupole (QQ) L-mode is more prominent in the scattering spectra of the Ag-Cu

heterodimer. The Ag-Cu heterodimer supports only one T-mode at 373 nm, which is almost the

same as the T-mode at 373 nm in the Ag-Au heterodimer, which is a dipole-quadrupole (DQ)


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FIG. 5. Scattering spectra for a D=60 nm sliver and copper nanoparticle heterodimer as a function of the polarization angle

with interparticle separations of 3 nm (a). Scattering spectra under longitudinal and transverse polarization with respect to

the normalized scattering spectra for a 60 nm isolated copper nanoparticle (b), and as a function of interparticle separations

from 1 nm to 15 nm under a polarizer angle of 0 degrees (c).

collective plasmonic mode. The quadrupole charge pattern in the copper nanoparticle is due to phase

retardation effects of the Ag nanoparticles and not from the LSPR coupling of the gold particle

plasmons.

D. The dipole-dipole approximation of the plasmon hybridization model

According to the well-established model of plasmon hybridization introduced by Nordlander and

Halas,27, 28 it is sufficient to consider a longitudinal or transverse interaction for simple geometries.


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FIG. 6. Electric near-field profiles and surface charge distributions in a D=60 nm silver and copper nanoparticle heterodimer

for longitudinal and transverse resonance modes.

FIG. 7. Dipole-dipole interaction model from the first approximation of the hybridization model. A level scheme of two

coupled dipoles are shown where the bright mode is red and the dark mode is black (middle) while the surface charge

distributions in the dimer under longitudinal coupling (left) and transverse coupling (right) are also shown.

We set up a dipoledipole interaction model as a first approximation of the plasmon hybridization

model, as shown in Fig. 7, and the collective plasmon modes can be viewed as bonding and antibond-

ing linear combinations of primitive plasmons in molecular orbital theory. The individual nanosphere

plasmon modes (1 and 2) of two interacting metal nanoparticles hybridize either in-phase (1 +

2) or out-of-phase (1 2). Under longitudinal polarization the in-phase combination reflects

a bonding mode and the out-of-phase mode represents an antibonding configuration, respectively

denoted and *.29 When the polarization is transverse the in-phase combination is an antibonding

mode (*) and the out-of-phase mode is a bond mode ().29


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1. D=60 nm Ag-Ag homodimer

I n a D=60 nm Ag-Ag homodimer (Figs. 1 and 2) the low-energy L-mode at 464 nm is a -mode

with its electric field strongly localized at the junction of the dimer and the only T-mode at 364 nm is

a *-mode. Both of these modes are bright in-phase modes. However, the antiphase mode was not

observed in the Ag-Ag homodimer. These results agree with the dipole-dipole approximation of theplasmon hybridization model wherethe antiphasemode is spectrally dark, because of the cancellation

of the equal but oppositely oriented dipoles on the two particles. Therefore, the homodimer structure

under longitudinal polarization supports only a bonding plasmon mode () and the homodimer

under transverse polarization supports only an antibonding *-mode. It is important to note that the

high-energy L-mode at 357 nm, as observed in the D=60 nm Ag-Ag homodimer, is a quadrupole-

quadrupole (QQ) mode.

2. D=60 nm Ag-Au heterodimer

In the D=60 nm Ag-Au heterodimer (Figs. 3 and 4), the lower energy L-mode at 545 nm is a

bonding -mode and a bright in-phase mode, while the lower energy T-mode at 527 nm is a bonding

-mode and an otherwise dark antiphase mode. The high energy L-mode at 410 nm is a bonding

quadrupole-quadrupole (QQ) mode and the high energy T-mode at 373 nm is a dipole-quadrupole

(DQ) mode. The Ag-Au heterodimer does not support the antibonding *-mode and the *-mode.

These are not the expected results, because the heterodimer is expected to support all the bonding

and antibonding modes at the same time because of its broken symmetry. This is in striking contrast

to previous work on a D=40 nm Ag-Au heterodimer, which show that it is possible to excite all four

bonding and antibonding modes through the preparation of compositionally asymmetric dimers. 22

While the in-phase *-mode is a bright mode as observed in the D=60 nm Ag-Ag homodimer,

the absence of* i n t h e D=60 nm Ag-Au heterodimer is not just due to its antibonding property. The

magnitude of the coupling of the anti-bonding mode to external light will depend on the net dimer

dipole. The anti-bonding mode has zero dipole moment in homodimer, which does not give rise to

a sufficiently large cross section to be seen in the extinction spectra. By reducing the symmetry, the

anti-bonding mode for a heterodimer has a non-zero dipole moment because of the asymmetry in

composition, as in this study. Though it interacts more weakly with light than the bonding dimer

mode, the anti-bonding heterodimer mode gains intensity and eventually is seen in the extinction

spectra. In this sense, both antiphase * and modes have similar magnitudes of coupling to light.

The * and *-modes are absence in the D=60 nm Ag-Au heterodimer. The proposed reason

is that the high-energy antibonding *-mode and the *-mode are blue-shifted with respect to the

LSPR of the isolated gold nanoparticles (2), and then they are typically located near the ultraviolet

(UV) region, are damped by the interband transitions of the gold nanoparticles, and appear as dark

modes in the heterodimer.

Theoretically, noble metal nanoparticles (Cu, Ag & Au) attract significant attention because

they can support localized surface plasmon resonances in the ultraviolet, visible, and near-infrared

regions of the spectrum depending on internal and external effects. The optical properties of these

metal nanoparticles originate not only from the coherent oscillation of conduction electrons but also

from optical excitation of an electron from an occupied state in the valence band to an unoccupied

state in the conduction band, which is known as an interband transition. In view of this electronicstructure theory,1 it is very important to consider the interaction of electronic interband transitions

with individual plasmon resonances or coupled plasmon modes.

According to the model of plasmon hybridization, there are two plasmon modes under longi-

tudinal polarization, namely a low energy in-phase bonding mode and a high energy out of phase

anti-bonding mode. Generally, the low energy bonding mode is located at visible or near infrared

wavelengths, while the higher energy anti-bonding mode is positioned near the ultraviolet region.

Since the anti-bonding mode shows small net dipole moment, the strength of its interaction with

light is also weak and it may be obscured by the interband transitions in the metal.

The antiphase -mode in a D=60 nm Ag-Au heterodimer is an important result in this study,

because its antisymmetric plasmonic resonance may be used to excite the magnetic response 13


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in various arrays of nanoparticle pairs. We confirm that this antiphase mode occurs in Ag-Au

heterodimers for a diameter range of 40-60 nm and a separation range of 1-3 nm.

3. D=60 nm Ag-Cu heterodimer

In the D=60 nm Ag-Cu heterodimer (Figs. 5 and 6) the lower energy L-mode at 575 nm is

a bonding -mode and a bright in-phase mode, the high energy L-mode at 443 nm is a bonding

quadrupole-quadrupole (QQ) mode and the high energy T-mode at 373 nm is a dipole-quadrupole

(DQ) mode. The Ag-Cu heterodimer does not support a *-mode, a *-mode or even a -mode

as this is not expected for the heterodimer. Similar to the Ag-Au heterodimer, a possible reason is

that both the high energy */*-mode and the low energy -mode are diminished by the interband

transitions of copper nanoparticles and appear as dark modes in the heterodimer. The electronic

interband transitions of the metals are electronic transitions from the energetically deeper valence

band into the conduction band, which forms a steep absorption edge starting at the threshold

frequency, where all plasmon resonance diminishes dramatically. The threshold energies are 3.8 eV

(326 nm), 2.5 eV (500 nm) and 2.1 eV (590 nm) for pure Ag, pure Au and pure Cu, respectively. By

comparing the collective plasmon modes of the 60 nm Ag-Au heterodimer with that of the 60 nm

Ag-Cu heterodimer there is tendency that the low interband transition energies of the constitutivemetals causes the low energy -mode and the two high energy antibonding modes to be diminished

by the interband transitions of the copper nanoparticles, and this causes the lowest energy -mode

to be visible in the Ag-Cu heterodimers.

Compared to previous studies into theD=40 nm Ag-Auheterodimer,22 the high energy collective

plasmon modes are governed by the quadrupole moment in the two 60 nm Ag-Au (Cu) heterodimers

from 357-443 nm. Although resonant excitation of larger spherical particles gives rise to broad

extinction spectra with significant contributions from high-order multipole modes, for the silver

particle of size D=60 nm in this study the quadrupole absorption components were not able to be

isolated form the dipole scattering for Ag-Au (Cu) heterodimers.

The proposed reason is a retardation (finite size) effect, which is also found in the larger

homodimer, as shown in the quadrupole-quadrupole L-mode in the D=60 nm Ag-Ag homodimer.

The retardation effect becomes more apparent in larger nanostructures with respect to the spatial

wavelengthof thelight at theplasmonresonance andthe onset of higherordered multipolar resonance

modes strongly influences and even shadows the position of the anti-bonding resonance. In this

study, a quadrupole-coupled mode emerges for the D=60 nm Ag-Au nanoparticle heterodimer at

interparticle separations smaller than 9 nm, and it is prominent in the D=60 nm Ag-Cu nanoparticle

heterodimer while it has the highest scattering intensity for all the investigated interparticle gap

separations and polarizer angles.

In general, the optical properties of coupled plasmonic particles can be systematically modeled

and studied in to two regimes depending on the overall size of the system. When the size of the

hybridized system is smaller than the plasmon wavelength, the coupled plasmonic system can be

modeled under the quasi-static (dipole) limit, thus retardation effect can be neglected. However,

when the dimension of the coupled system is greater than the incident wavelength the quasi-

static approximation is no longer applicable (results in significant error) because of retardation

effects. Therefore, it is desirable to consider retardation, which is the effect of the phase differencebetween the fields propagating from two different regions of the nanoparticle, during the study

of large size coupled plasmons to obtain reasonable and accurate optical properties for the given

system.

In the quasi-static regime, we get a constant resonant frequency independent of particle dimen-

sions or retardation effects, if the bulk dielectric is used the size effect in the quasi-static regime

comes from the dependence of the permittivity on the nanoparticle size because of quantum con-

finement. For nanoparticles which are large in size, as in our case, the quantum confinement or size

dependence of dielectric coefficients becomes negligible and the role of retardation effect comes to

play and higher order multipolar resonance modes begin to be observed. Therefore, the appearance

of higher order multipolar modes is due to retardation or finite size effect.


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FIG. 8. Scattering spectra calculated for varying dimer separation and conductive overlap for the silver-gold heterodimer.

E. Effects of conductive contact on the collective plasmon modes

In real experiments, a molecular layer of surfactant molecules used in the self-assemble may

actually wet the particle surface. The gap between the heterodimers Au-Ag and Ag-Cu is probably

governed by the size of the molecular species and is expected to keep the nanoparticles 2-3 nm apart,

however, conductive contact can still occur at localized points, especially if the coating is uneven and

considering that the molecules on the nanoparticle surface can rearrange. These issues are especially

significant for correlating simulations with experiments while even high resolution TEM only yields

a 2-D projection of 3-D objects, thereby obscuring important topographical and structural details.

Figure 8 shows the scattering spectra calculated for varying dimer separation and conductive

overlap for the silver-gold heterodimer. The accompanying near-field plots and surface charge

distributions corresponding to selected separation and wavelength points are shown in Figure 9. As

the gap decreases from 3 to 0 nm, the spherical nanoparticles begin to make conductive contact at

a single point: the 545 nm peak corresponding to the dipole-dipole (DD) coupled plasmon mode

splits into two modes, i.e., a DD coupled mode at 554 nm and a new infrared dipole-dipole (DD)

coupled mode at the 1128 nm peak, respectively. The 410 nm peak corresponding to the quadrupole-

quadrupole (QQ) coupled plasmon mode splits into two modes, one red shifts from 410 nm toa quadrupole-quadrupole (QQ) coupled mode at 414 nm, the other blue shifts from 410 nm to a

quadrupole-dipole (QD) coupled mode at 384 nm. With increasing conductive overlap from 0 to

-3 nm, the infrared dipole-dipole (DD) coupled mode at 1128 nm blue shifts to a dipole nanorod

mode at 772 nm and a new coupled mode appears at 364 nm due to retardation effects. However, the

dipole-dipole (DD) coupled mode at 554 nm, the high-order multipolar quadrupole -dipole (QD) at

384 nm and quadrupole-quadrupole (QQ) at 414 nm coupled modes disappear in the new scattering

spectrum with gap=-3 nm, in part, due to mode decoupling.

Figure 9 shows the electric near-field profiles and surface charge distributions in a D=

60 nm sliver-gold nanoparticle heterodimer at selected wavelengths with gap = 3nm, 0 nm and

-3 nm. Obviously, oscillations driven by external light in electrically separated particles must respect


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FIG. 9. Electric near-field profiles and the surface charge distributions for neighboring silver and gold spheres with their

separation gap=-3 nm, 0 nm and 3 nm, the wavelength corresponding to selected points of Fig. 8. For the dimer with gap=

3 nm, the near-field maps at = 1288 nm is also calculated before the single point contact to check conductive effects, the

near-field maps at = 410 nm is not plotted here and it is same to the profile in Fig. 4.

charge neutrality within each particle. In the near-field maps of the dipole-dipole (DD) coupled mode

of the Ag-Au dimer with gap= 3 nm at = 1288 nm, the charge pileup in each particle near the gap

region has a spatial width along the sphere surface that is compensated by a smooth distribution of

the opposite charge along the rest of the sphere surface.

Because intraparticle charge neutrality is no longer required when the two particles overlap (i.e.each half of the overlapping dimer can have a net charge), it is expected that the charge buildup at the

physical gap of separated particles would neutralize as soon as the gap is diminished. Surprisingly,

the charge remains on the edges of the narrow conductive neck, as shown in the Ag-Au dimer with

gap= 0 nm at = 1288 nm. The large pileup of induced charge in the interparticle gap gives rise to

a physical mode that corresponds to the infrared peak that emerges right after the particles touch at

a single point in Fig. 8. For the infrared dipole-dipole (DD) coupled mode at 1128 nm, there is a net

electrical charge in each half of thedimer, that is, eithersilver or gold particle is charged, as illustrated

in the lower inset of Fig. 9. This shows that the dominant low-energy modes of non-touching and

touching dimers are distinctly different. For non-touching spheres, the lowest-energy dipole-dipole

(DD) mode, which arises from coupling between dipole modes of each sphere, is charge neutral in


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FIG. 10. Scattering spectra calculated for varying dimer separation and conductive overlap for the silver-copper heterodimer.

each sphere. For touching spheres, the lowest-energy mode is a true dipolar mode with a net charge

on each particle.

As shown in the Ag-Au dimer at = 772 nm, when the overlap grows to gap= - 3 nm, the

charge in each particle has a smooth distribution along the sphere surface, the charge pileup effect at

the narrow conductive neck eventually disappears, and the response again becomes that expected for

a single particle. The 1128 nm lowest-energy mode of the single-point-touching dimer transitions

into the 772 nm higher energy mode of the overlapping dimer. The charge density plot shows the

conductive 772 nm mode resembles the dipole mode of a continuous nanorod having twice the

length of the constituent nanospheres, and the near-field map and charge distribution of the 364 nm

mode resembles the dipole mode of an individual silver nanosphere.30

Figure 10 shows the scattering spectra calculated for varying dimer separation and conductive

overlap in the silver-copper heterodimer, and their accompanying near-field maps and the surface

charge distributions are similar to the corresponding modes in the silver-gold heterodimer. As the

spherical nanoparticles begin to make conductive contact at a single point with gap=0 nm, the

575 nm peak corresponding to the dipole-dipole (DD) coupled plasmon mode splits into two modes,

i.e., a dipole-dipole (DD) coupled mode at 438 nm and a new infrared dipole-dipole (DD) coupled

mode at the 1123 nm. The 443 nm peak corresponding to the quadrupole-quadrupole (QQ) coupledplasmon mode disappears in thenew scattering spectrum with gap=0 nm. With increasing conductive

overlap from 0 to -3 nm, the infrared dipole-dipole (DD) coupled mode at 1123 nm blue shifts to a

dipolenanorod mode at 762nm anda new coupled mode emerges at 365nm dueto retardation effects,

and the dipole-dipole (DD) coupled mode at 438 nm disappears in the new scattering spectrum with

gap=-3 nm.

The presence of new plasmon modes due to the conductive contact has been observed in both

silver-gold and silver-copper systems approaching toward a single point of contact and the plas-

mon resonance mode has a similar wavelength around 1223 -1228 nm. As the particles approach

closer with gap = -3 nm, the dominant dipolar feature in both metallic system becomes simi-

lar with the plasmon resonance around 762-772 nm. However, at a single point of contact, with


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gap = 0 nm, the silver-gold heterodimer exhibits a richer structure of higher-energy modes than

the silver-copper heterodimer. The silver-gold heterodimer exhibits three resonance peaks and the

silver-copper heterodimer exhibits one resonance peak with two shoulders in the wavelength range

300-650 nm of the scattering spectra.

IV. CONCLUSIONS

In summary, the plasmon-coupling phenomenon of heterodimers composed of silver, gold and

copper nanoparticles with a size of 60 nm were studied theoretically using the finite difference

time domain method within the outline of the scattered field formulation. The energies and the

line widths of the collective plasmon modes strongly depend on interparticle gap separations and

polarization angles. In-phase bonding-modes were observed forthe Ag-Au andAg-Cu heterodimer

and an antiphase bonding -mode was observed for the Ag-Au heterodimer, and these are in good

agreement with that expected from plasmon hybridization theory. However, the quadrupole-coupled

mode dominates the high energy wavelength range from 357-443 nm in the scattering cross section

of the D=60 nm Ag-Au and Ag-Cu heterodimer. We demonstrate for the first time that collective

plasmon modes in a compositionally asymmetric nanoparticle dimer like the D=60 nm Ag-Au and

Ag-Cu heterodimer cannot simply be predicted using plasmon hybridization theory. The interband

transition energies of the constitutive metals and nanoparticle size retardation can overlap spectrally

with the antibonding mode from plasmon hybridization, which results in new collective plasmon

modes, such as a bonding quadrupole-quadrupole (QQ) mode and a dipole-quadrupole (DQ) mode

in the Ag-Au heterodimer. This is a unique phenomenon and has not previously been observed in a

compositionally asymmetric nanoparticle dimer.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Nos. 50971100

and 50671082), the Research Fund of State Key Laboratory of Solidification Processing (NWPU),

China (Grant No. 30-TP-2009), the NPU Foundation for Fundamental Research (No. NPU-FFR-

ZC200931), and the Graduate Starting Seed Fund of Northwestern Polytechnical University (Nos.

Z2011002, Z2010011, and Z200915).

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