Plasmonic coupling in noble metal nanostructures

Chemical Physics Letters 487 (2010) 153–164

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FRONTIERS ARTICLE

Plasmonic coupling in noble metal nanostructures Prashant K. Jain a,b,*, Mostafa A. El-Sayed c,1 a

Department of Chemistry, University of California, Berkeley, CA 94720, United States Miller Institute for Basic Research in Science, University of California, Berkeley, CA 94720, United States c Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332, United States b

a r t i c l e

i n f o

Article history: Received 14 January 2010 In final form 26 January 2010 Available online 1 February 2010

a b s t r a c t Noble metal nanostructures display unique and strongly enhanced optical properties due to the phenomenon of localized surface plasmon resonance (LSPR). In assemblies or complex noble metal nanostructures, individual plasmon oscillations on proximal particles can couple via their near-field interaction, resulting in coupled plasmon resonance modes, quite akin to excitonic coupling in molecular aggregates or orbital hybridization in molecules. In this frontier Letter we discuss how the coupling of plasmon modes in certain nanostructure geometries (such as nanoparticle dimers and nanoshells) allows systematic tuning of the optical resonance, and also the confinement and enhancement of the near-field, making possible improved refractive-index sensing and field-enhanced spectroscopy and photochemistry. We discuss the polarization, orientation, and distance-dependence of this near-field coupling especially the universal size-scaling of the plasmon coupling interaction. In addition to radiative properties, we also discuss the effect of inter-particle coupling on the non-radiative electron relaxation in noble metal nanostructures. Ó 2010 Elsevier B.V. All rights reserved.

1. Localized surface plasmon resonances in metal nanoparticles Metal nanoparticles display strong and unique optical resonances in the visible and near-infrared (NIR) region of the electromagnetic spectrum due to the resonant response of their free electrons to the electric field of light [1–7]. This free electron response is described by the dielectric function of the metal as per the Drude model [8]:

eDrude ¼ 1

x2p x þ icx 2

ð1Þ

where x is the angular frequency of the light, c is the electron collision frequency in the bulk, and xp is the bulk plasma frequency of the free electrons, which is determined by the density of free electrons N in the metal and the effective mass me of the electrons as:

sffiffiffiffiffiffiffiffiffiffiffi Ne2 xp ¼ e0 me

ð2Þ

In the case of real metals, bound electrons contribute to the dielectric function, for instance due to inter-band transitions from the valence to conduction band, especially in the high frequency * Corresponding author. Address: Department of Chemistry, University of California, Berkeley, CA 94720, United States. Fax: +1 510 642 6911. E-mail addresses: [email protected] (P.K. Jain), [email protected] (M.A. El-Sayed). 1 Fax: +1 404 894 0294. 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.01.062

region of the spectrum. A high-frequency part e1 [9], therefore, has to be added to the Drude contribution for accurately describing the response of the metal electrons to the electromagnetic field:

e ¼ e1

x2p x þ icx 2

ð3Þ

When the metallic nanoparticle is subject to light excitation, the electric field of the light induces waves of collective electron oscillations confined to the surface of the nanoparticle, a phenomenon known as a localized surface plasmon resonance [1–5]. This wave motion is composed of different orders, from the lowest dipolar (Fig. 1a) to higher order multipoles [3], depending on the size of the nanoparticle relative to the wavelength of light. However, in the case of particles of size much smaller than the wavelength of light, (i.e., radius r k), the electron oscillation can be considered to be predominantly dipolar in nature. In this limit, the collective response of the electrons in a small metal nanoparticle to the electric field of the light (assumed to be uniform across the particle) is described by the dipolar polarizability a [10]:

a ¼ ð1 þ jÞe0 V

ðe em Þ ðe þ jem Þ

ð4Þ

where V is the volume of the particle and em is the medium dielectric constant. j is a shape factor that incorporates the dependence of the polarizability on the geometry of the surface that defines the electron oscillations. While j = 2 for a sphere, for more polarizable shapes such as particles with a high surface curvature along a

P.K. Jain, M.A. El-Sayed / Chemical Physics Letters 487 (2010) 153–164

Ó Copyright American Chemical Society 2008.

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Fig. 1. (a) Scheme showing the coherent collective oscillation of electrons of a metallic nanoparticle constituting a localized surface plasmon resonance (LSPR) mode. The LSPR results in an enhancement in the optical properties of the nanostructure, i.e., the electric field intensity near the particle, light scattering, light absorption, and surface enhanced scattering from adsorbed molecules are all enhanced at the LSPR frequency. (b) Extinction spectrum (from Mie theory) of a 20-nm silver nanosphere showing an LSPR around 380 nm and that of a 20-nm gold nanosphere with an LSPR at 520 nm. Reprinted figure (a) from Ref. [6].

given dimension (e.g., triangles, rod-shaped particles), the value of j can be much higher along that dimension [11]. The polarizability a becomes maximum (representing a strong resonance between the free electrons and the light field) at the frequency at which:

ReðeÞ ¼ jem

ð5Þ

Here Re denotes the real part. This frequency xsp corresponds to the localized surface plasmon resonance (LSPR) frequency of the particle. From Eqs. (3) and (5), we see that the LSPR frequency is determined by the bulk plasma frequency xp of the metal free electrons (however modulated by the presence of inter-band transitions) and further tuned by the geometry of the nanostructure (j) and the medium surrounding the particle (em).

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ne2 xsp ¼ me e0 ðe1 þ jem Þ

ð6Þ

While the real part of the metal dielectric function Re(e) governs the frequency position of the electron oscillation resonance, the imaginary part Im(e) incorporates the broadening and absorptive dissipation of the resonance due to damping and dephasing of the electron oscillations. For noble metals such as gold, silver, and copper this resonance lies in the visible region for small spherical nanoparticles. For instance, for a gold nanosphere in the 10–20 nm size range, the LSPR has a maximum around 520 nm in water, and around 380 nm for a

silver nanoparticle (Fig. 1b). Despite the fact that gold and silver have similar bulk plasma frequencies (in the UV) due to their similar electronic densities, (i.e., N = 5.90 1022 and 5.86 1022/cm3, respectively), the onset of d ? sp inter-band transitions is different in the two metals, resulting in their different LSPR positions. In the case of gold, the onset of inter-band transitions around 1.7 eV not only red-shifts the collective free electron resonance to its observed position at 2.4 eV (i.e., 520 nm) [9], but also strongly damps the plasmon resonance band, resulting in its increased broadening and absorptive dissipation, as compared to the plasmon resonance of a silver nanosphere (Fig. 1b). 2. The plasmonic near-field The surface plasmon oscillations induced by the field of the light result in a strong electric field confined to the surface of the nanoparticle. Due to the strong resonance, this near-field is greatly enhanced on the surface of the nanoparticle relative to the incident field E0 at frequencies corresponding to the LSPR. The electric field E at the surface of a metal nanoparticle is given in the dipolar limit by [8]:

Esurface ¼

ð1 þ jÞem E0 ðe þ jem Þ

ð7Þ

Thus, at resonance (Re(e) = jem), a strong near-field enhancement (|E|/|E0|)2 is expected. For instance, the resonant enhancement of the near-field intensity |E|2 on the surface of a 20-nm


silver nanoparticle has been calculated by electrodynamics simulations to be as high as 200 [12]. In case of nanorods of silver (of aspect ratio 2.8), the field intensity can be enhanced to as much as 3500 at the rod tips [12]. The near-field is damped by absorptive processes within the particle such as electron–phonon collisions and electron-surface scattering, as described by the imaginary part of the dielectric function. Alternatively, the near-field can couple with the incident field re-radiating energy, resulting in the scattering of light in the far-field, the cross-section of which is proportional to |a|2 [3]. This radiative decay of the field becomes dominant as the size of the particle increases and approaches the wavelength of light in the medium [13,14]. It must be noted that both the absorption and scattering by the particle are strongly enhanced at the LSPR frequency. As a result, the extinction/scattering spectra measured in the far-field (Fig. 1b) are closely representative of the spectrum of the plasmon oscillations and the associated near-field. For a small nanoparticle in an incident field E0, the near-field due to the particle can be approximated to be dipolar decaying with distance r away from the particle as 1/r3 [10]. However, for a finite-sized particle, the near-field at a distance r from the particle (along a direction parallel to the incident light polarization) is given by an expansion of all possible multipolar modes [15]:

€0 2aE0 3bE_ 0 4cE Enf ¼ þ þ þ 3 4 4pe0 r 4pe0 r 4pe0 r5

ð8Þ

where a, b, c, . . . are, respectively, the dipole, quadrupole, octupole, . . . polarizability tensors of the particle. The smaller the distance r (relative to the particle size) where the field needs to be estimated, the higher is the number of terms that need to be included in the near-field expansion. The strong plasmonic near-field greatly enhances the electronic transitions of optical absorbers and emitters (resonant with the LSPR frequency) placed in the vicinity of the nanoparticle. A canonical example of such a plasmonic near-field enhanced process is surface enhanced Raman scattering [16–18]. The cross-section of Raman scattering from molecular vibrations is known to be proportional to the square of the electric field intensity [19]. As a result, the Raman scattering is amplified several orders (typically five to six) due to the huge enhancement of |E|4 in the vicinity of the nanoparticle [19]. Other optical processes such as photoluminescence [20–24], second or higher harmonic generation (SHG) [25–27], magneto-optical phenomena [28], and photochemistry [29,27] have also been shown to be enhanced (in the spectral region around the LSPR frequency) in the presence of a plasmonic field. 3. Plasmon resonances in assemblies of metal nanoparticles When two metal nanoparticles are brought in proximity to each other, the near-field on one nanoparticle can interact with that on the other particle [30–34]. Thus, the electric field E felt by each particle is the sum of the incident light field E0 and the near-field Enf of the neighboring particle.

E ¼ E0 þ Enf

ð9Þ

As a result of this near-field interaction, plasmon oscillations of the two nanoparticles become coupled. This plasmon coupling modulates the LSPR frequency of the coupled-nanoparticle system. For instance, in spherical gold nanoparticles, assembly or aggregation into a close-packed structure results in a strong red-shift of the LSPR wavelength from the LSPR maximum of 520 nm of an isolated colloidal nanoparticle [35,36]. The red-shift is a manifestation of the favorable coupling of the plasmon oscillations of the proximal nanoparticles, i.e., a lower energy (or frequency) is re-

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quired to drive the coupled plasmon oscillation modes of the assembly. Mirkin coworkers [36] were the first to employ this assembly-induced shift for the sensing of trace amounts of sequence-specific DNA strands. The gold nanospheres were functionalized in a programmed scheme such that the presence of a DNA strand with the right DNA sequence would trigger via DNA hybridization the assembly of the gold nanoparticles. The resulting shift of the plasmon resonance absorption spectrum of the colloidal solution becomes useful for the highly sensitive optical detection of the target sequence. As shown by Schatz and coworkers, the extent of the plasmon resonance red-shift upon nanoparticle assembly depends on the number of particles in the assembly [35]. In a larger assembly (by particle number), each particle would be subject to the near-field of a large number of particles, resulting in a much stronger coupling and hence a larger red-shift. In addition, the distance between the nanoparticles in the assembly also determines the amount of plasmon red-shift, due to the rapid decay of a nanoparticle’s near-field with distance. The closer the particles in the assembly, the larger is the red-shift of the plasmon resonance [31,35,37]. The distance-dependence of plasmon coupling is described in significant detail later in this Letter.

4. Polarization and orientation dependence of plasmon coupling Solution-phase assembly of metal nanoparticles gives a simple qualitative picture of plasmon coupling. However, the most lucid characterization of the coupling has been obtained from dimers of metal nanodiscs fabricated in micron-sized arrays by electron beam lithography (Fig. 2a), which allows control over the interparticle distance and orientation of the interacting particles. Plasmon resonance absorption spectra of these arrays have shown that the plasmon coupling is polarization-dependent (Fig. 2) [31,33,37]. When the incident light polarization direction is parallel to the inter-particle axis (Fig. 2b), the plasmon resonance maximum of the nanodisc pair is red-shifted relative to the resonance of an individual nanodisc. The smaller the gap between the particles, the larger is the red-shift. On the other hand, when the light is polarized orthogonal to the inter-particle axis (Fig. 2c), the observed plasmon spectrum is blue-shifted with respect to the individual particle case; however the magnitude of the blue-shift is much smaller (almost undetectable) than the red-shift in the former case. Another elegant demonstration of the polarization dependence of plasmon coupling is seen in the plasmon resonance spectra of dimerized or assembled gold nanorods [10,38,39]. Nanorods, on account of their anisotropic shape, have two modes of plasmon resonance oscillation [40–42]. The plasmon oscillation along the short-axis of a gold nanorod (known as the transverse mode) has a maximum around 520 nm, similar to the resonance of a gold nanosphere. The plasmon oscillation along the long-axis mode gives rise to a plasmon band (known as the longitudinal mode) that is red-shifted with respect the short-axis mode. The resonance position of the long-axis mode depends on the aspect ratio of the nanorod – the higher the aspect ratio, the more red-shifted the band [43]. The longitudinal LSPR is also much stronger compared to the transverse mode due to the larger polarizability of the rod along the long-axis direction. Also, on account of their shape anisotropy, there are two orientations along which nanorods can be assembled/dimerized – either linked end-to-end or linked side-by-side. Thomas et al. [44] as well as Joseph et al. [45] used bifunctional thioalkyl carboxylic acid– based molecules to align gold nanorods in an end-to-end manner in colloidal solution. Plasmon absorption spectra of the colloid showed that the end-to-end linkage resulted in a strong red-shift of the longitudinal plasmon resonance band [44]. In experiments


Gap = 2 nm Gap = 7 nm Gap = 12 nm Gap = 17 nm Gap = 27 nm Gap = 212 nm

0.06

0.04

OD

OD

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Gap = 2 nm Gap = 7 nm Gap = 12 nm Gap = 17 nm Gap = 27 nm Gap = 212 nm

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Fig. 2. (a) Lithographically-fabricated array of 88-nm diameter gold nanodisc pairs with controlled inter-particle separation, in this case 12 nm (inset is a magnified SEM image clearly showing the inter-particle gap). Extinction spectra show that the LSPR of the particle pair (b) red-shifts with decreasing gap for polarization along the interparticle axis. (c) Blue-shifts very slightly with decreasing gap for polarization orthogonal to the inter-particle axis. Reprinted with permission from Ref. [31].

from our group, we were able to assemble gold nanorods in solution by the addition of negatively charged citrate linkers which bind the cationic surfactant bilayer on the sides of the rods, linking the nanorods together in a side-by-side orientation (Fig. 3a) [10]. In direct contrast to the red-shift observed in the former end-to-end linkage case, we showed that the side-by-side linkage resulted in a blue-shift of the longitudinal nanorod plasmon band. This observation is in line with the polarization dependence of plasmon coupling seen in lithographically fabricated dimers [31,33,37]. In the end-to-end linkage, the plasmon oscillations (longitudinal mode) are polarized along the inter-particle axis, giving rise to the redshift upon coupling (Fig. 3b). In the side-by-side case, the longitudinal plasmons are polarized orthogonal to the inter-particle axis, giving rise to the blue-shift upon coupling (Fig. 3c). The exact reverse shift is observed for the transverse plasmon mode of the nanorod, which is polarized 90° to the longitudinal mode, however the shift (coupling strength) is much smaller for the transverse mode due to the lower dipole moment of this mode. Thus, as a general rule, the plasmon oscillations couple ‘favorably’ (reduction in LSPR frequency) when they are polarized along the inter-particle axis, and ‘unfavorably’ (increase in LSPR frequency) when they are polarized orthogonal to the inter-particle axis.

Organic chromophores dimerized head-to-tail with respect to their transition dipole moment direction (known as J-dimers) show an absorption band that is red-shifted compared to that of the isolated chromophore, whereas parallel dimers (known as H-dimers) of organic chromophores show a blue-shifted absorption spectrum. The exciton-coupling model [46,47], which was developed to explain shifts in the spectra of dimerized organic molecules, therefore applies very well to the case of coupling between two plasmon resonant nanoparticles, as depicted in Fig. 4a and b. As per the exciton theory [47,48], the excited-state levels of the monomer split in two levels upon dimerization, a lower energy level and a higher energy level relative to the monomer excited state. These correspond to two possible arrangements of the transition dipoles of the chromophores in the dimer, i.e., in-phase or symmetric and out-of-phase or anti-symmetric. The energy splitting 2U is given by the interaction energy between the chromophores which is approximated by the Coulombic interaction between the transition dipole moments of the monomers [10]. The field E experienced by each dipole l is then the sum of the incident field E0 and the field due to the neighboring dipole:

5. Exciton-coupling model

The additional field experienced by each dipole depends not only on the distance r between the dipoles but also on their mutual orientation, as denoted by the parameter n given by:

The polarization/orientation dependence of the coupling described above is very similar to absorption spectra shifts observed in organic molecules upon their dimerization/aggregation [46,47].

E ¼ E0 þ

nl 4pe0 r 3

n ¼ 3 cos h1 cos h2 cos h12

ð10Þ

ð11Þ

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Absorbance (a.u.)

3.0

Au NRs + citrate

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Ó Copyright American Society 2006.

E

Extinction efficiency

Extinction efficiency

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Fig. 3. (a) Colloidal aggregation of gold nanorods by citrate linkers results in a side-by-side assembly (representative TEM shown in inset), resulting in a blue-shift of the longaxis LSPR mode. This is in contrast to the LSPR red-shift generally seen when nanoparticles are aggregated. Electrodynamic simulations verify that the long-axis LSPR mode of a nanorod dimer (b) blue-shifts with increasing coupling between nanorods for side-by-side assembly, in direct contrast to the (c) red-shift observed for end-to-end assembly of nanorods. Reprinted with permission from Ref. [10].

where h12 is the angle between the directions of the two dipoles, h1 is the angle between the direction of dipole 1 and the inter-dipole axis, and h2 is the angle between the direction of dipole 2 and the inter-dipole axis. From Eq. (10), the interaction energy U is therefore given by [48]:

U¼

njlj2 4pe0 r 3

ð12Þ

While this treatment strictly applies to molecular excitons, in the limit where the particle size is small compared to the inter-particle distance r, each of the interacting particles can be considered to be a dipolar exciton. It must be noted that in most cases of interparticle plasmon coupling, whether substrate-bound or solutionphase assembly, there is no relative rotation of the two interacting particles. While the direction of the dipole on each particle is determined by the incident polarization direction for isotropic particles, even in the case of anisotropic particles, the dipoles 1 and 2, in most cases, have fixed orientation with respect to each other. Hence, no orientation averaging is required in calculating the expressions in Eqs. (10)–(12). From Eq. (11), we see that for incident light polarization (and therefore both dipoles directed) along the inter-particle axis, n = 2. This implies a negative value of the interaction energy U, implying that the interaction is attractive for dipoles aligned symmetrically. As a result, we see a red-shift in the resonance frequency in the dimer. The configuration corresponding to the dipoles aligned anti-symmetrically is higher in energy, but is opti-

cally forbidden, since the dipoles, being equal and opposite, cancel out. This represents therefore a ‘dark mode’ in a dimer consisting of two identical particles (homodimer). For the case where the incident field polarization (and hence the direction of both dipoles) is orthogonal to the inter-particle axis, n = 1, resulting in a positive interaction energy, implying that the interaction is repulsive for a symmetric configuration of the dipoles. As a result, a blueshift of the resonance frequency is observed in this case, however the shift magnitude is smaller than the parallel polarization case, since the interaction energy is twofold smaller in magnitude in this case. The anti-symmetric configuration is lower in energy, but dark in the optical spectrum, due to the dipoles canceling out in a homodimer. In a heterodimer, where the two interacting particles are unidentical, for instance two nanorods of dissimilar aspect ratio, it has been theoretically shown that both the symmetric and anti-symmetric modes would be present in the optical spectrum. Of course, the anti-symmetric mode, otherwise dark in the homodimer, in the case of the heterodimer, is significantly weaker in intensity compared to the symmetric mode. Thus, all features of coupling between plasmonic nanoparticles are qualitatively explained by a dipolar exciton-coupling model; however there are important deviations from the model that need to be acknowledged. Since the particles have a finite size and cannot really be considered point dipoles, the retardation of the electromagnetic field has to be accounted for in the coupling interaction [10]. In fact, when the particle size becomes appreciable in relation to the wavelength of the light, resonance shifts that



158

Fig. 4. The energy level splitting resulting from the dipolar coupling of chromophores in a dimer, showing symmetric (w+) and anti-symmetric coupling (w) of excitons for (a) H-aggregate geometry or side-by-side dimer and (b) J-aggregate geometry or end-to-end dimer. (c) Analogy of plasmon coupling in nanorod dimers to hybridization of molecular orbitals. The end-to-end coupling of the nanorod long-axis LSPR is similar to the formation of a bonding r and anti-bonding r* mode. The side-by-side coupling of the nanorod long-axis LSPR is similar to the formation of a bonding p and anti-bonding p* mode. Note that the r*-like and p-like plasmon modes are optically dark due to their zero net dipole moment. Reprinted with permission from Ref. [10].

are anomalous to the exciton-coupling model are observed [49]. More importantly, the model neglects higher order multipole– multipole type interactions that become important when the interacting particles come very close (separation < 0.5 diameter) [31,34]. While the dipole–dipole treatment (Eq. (12)) suggests that the coupling strength increases with decreasing inter-particle distance as a function of 1/r3, in reality, the coupling strength increases much more steeply at shorter inter-particle distance (separation < 0.5 diameters). This will be elaborated upon in the section on the distance-dependence of plasmon coupling. Electrodynamic simulations based on the finite-difference-time-domain (FDTD) [50,51] and the discrete dipole approximation (DDA) methods [52] that include both electromagnetic retardation effects and multipolar interactions, come in handy when a quantitative characterization or comparison with experimental results is needed. However, at very close separations as the particles approach contact with each other, these methods are no longer reliable since the electric field between the particles becomes extremely large, possibly causing non-local perturbations in the dielectric function of the particles [53,54]. 6. Analogy of plasmon coupling to orbital hybridization The plasmon coupling interaction in nanoparticles assemblies can also be visualized as a hybridization of plasmon modes, anal-

ogous to the hybridization of atomic orbitals in molecules [10,34,55]. The plasmon hybridization model was developed by Prodan et al. [55] in order to explain plasmon resonances in metal nanoshells [56], which are discussed later in this Letter. When two metal nanostructures approach each other, the plasmon modes supported by the two surfaces hybridize, resulting in a lower energy (red-shifted) bonding plasmon mode and a higher energy (blue-shifted) anti-bonding plasmon mode [55]. The molecular hybridization analogy was extended further in our work on plasmon coupling between gold nanorods (Fig. 4c) [10]. The coupled longitudinal plasmon mode for the end-to-end nanorod dimer is bonding in nature analogous to the formation of a rbond from two pz orbitals. Consistent with the molecular analog of this bonding mode, the resulting electric field intensity for this mode peaks in the junction between the interacting nanorods [57]. On the other hand, the coupled longitudinal plasmon mode for the side-by-side dimer has an anti-bonding nature analogous to the formation of a p* bond from px/y orbitals, with the electric field concentrated on either side of the inter-particle junction. It must be noted that the r* mode in the end-to-end dimer and the p mode in the side-by-side dimer are ‘dark’ in the nanorod homodimers. The knowledge of the bonding or anti-bonding nature of the coupled/hybridized plasmon modes is quite useful in designing assembled/complex plasmonic nanostructures, where the near-field can be squeezed in a confined region of the


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7. Distance-dependence of plasmon coupling – plasmon ruler Since the strength of plasmon coupling (and the LSPR shift induced by it) is dependent on the distance between the particles, the LSPR spectrum of a pair of coupled (Ag or Au) nanoparticles can be used to report on the inter-particle distance, as first shown by Alivisatos and coworkers [58–60]. In a scheme in which a biomolecular structure is used to link the two particles together, dynamic distance changes (triggered by external biochemical stimuli/binding/signaling events) in the biomolecular structure can be probed by following the LSPR shift of the dimer. Since plasmonic nanoparticles scatter light very strongly, scattering spectra can be collected from single dimers using dark-field spectroscopy, allowing sensitive optical measurement of biomolecular distances and probing of distance changes at the nanoscale. Plasmonic nanoparticles do not suffer from the drawback of dye photobleaching, a major problem in the earlier method of biomolecular distance measurement – fluorescence resonance energy transfer (FRET). However, for the ‘plasmon ruler’ application, it is crucial to have a calibration of the LSPR shift as a function of inter-particle distance [60]. Besides, in order to design plasmon rulers with an appropriate dynamic distance range and distance sensitivity for the given biomolecular application, it helps to have a good working model of the distance-dependence of plasmon coupling [31]. In addition, the dependence of plasmon coupling strength on the inter-particle distance directly reflects the depth/decay of the nearfield in plasmonic nanostructures. 8. Distance-dependence of plasmon coupling – universal scaling The most definitive characterization of the distance-dependence of plasmon coupling has been obtained from metal nanoparticle pairs lithographically fabricated with systematically varying inter-particle separations. Extinction spectra of these metal nanoparticle pairs (with incident polarization along the inter-particle axis) have shown that the red-shift Dk in the plasmon resonance wavelength maximum increases almost exponentially with the reduction in the inter-particle gap s [31,32,37]. Su et al. followed by two other studies have shown an interesting size-scaling of this near-exponential distance dependence [31,32,37]. When the plasmon shift normalized by the LSPR wavelength maximum of the isolated particle (Dk/k0) is plotted against the inter-particle gap normalized by the particle size (s/D), the data points for different particle sizes fall on the same exponential trend (Fig. 5) [31]. We further showed from experimental spectra and electrodynamic simulations of gold nanodisc pairs (with inter-particle gaps down to 0.1 D) that this trend is represented by the approximate relationship [31]:

Dk k es=0:2D k0

ð13Þ

In other words, if Dk/k0 represents the near-field coupling strength, then regardless of the particle size, the coupling strength falls almost exponentially over a distance 0.2 times the particle diameter. Thus, for a larger particle the near-field coupling extends over a larger distance in proportion to its diameter. We further found that the size-scaling trend represented by Eq. (13) is quite universal, i.e., regardless of the type of the metal, the shape of the particle, or the surrounding medium, the near-field coupling depth is always 0.2 times the diameter, even though the preexponential factor k, which represents the maximum plasmon shift for the particle pair does change depending on the conditions [31].


nanostructure, for field-enhanced spectroscopy of absorbers/emitters placed in this region.

Fig. 5. The near-field coupling strength between two interacting gold nanodiscs (for polarization along inter-particle axis), as indicated by the fractional LSPR red-shift Dk/k0, falls almost exponentially with increasing inter-particle gap (normalized by the nanodisc diameter). The plasmon coupling shows an interesting size-scaling – the coupling strength falls with the same trend, decaying over a distance that is 0.2 times the particle diameter, a trend that is universal regardless of parameters such as the nanodisc diameter, shape, metal, or medium. Reprinted with permission from Ref. [31].

For instance, the experimental data of Gunnarsson et al. on silver nanodisc pairs shows a similar decay distance of 0.2D. The absolute LSPR shifts are however three times larger in the silver case [31,32], which can be attributed for by the well-known fact that the electromagnetic fields are stronger in silver. In gold, the plasmonic fields are damped relative to those in silver, on account of the spectral overlap of the LSPR with d ? sp inter-band transitions [9]. Regardless of the difference in the absolute strength of the near-field, the distance-decay of the field itself appears to be independent of the nature of the metal. Further universality is seen when we note that the trend represented by Eq. (13), while deduced from spectra of lithographic samples, applies equally well to pairs of colloidal gold nanospheres assembled by DNA linkers of varying number of base pairs [60]. We were able to estimate within fair agreement of the experimental values, the inter-particle separation in these nanosphere pairs from their observed plasmon shifts. Thus, Eq. (13) also serves as a ‘plasmon ruler’ calibration equation [31]. The origin of the universal size-scaling of plasmon coupling can be understood based on a simple dipolar coupling picture [31]. The fractional plasmon shift (Dk/k0) reflects the strength of the interparticle near-field coupling, which is directly determined by the combination of the polarizability of the particle, which is proportional to D3, and the decay of this field with distance r away from the particle as 1/r3. As a result, the coupling strength (and therefore Dk/k0) becomes a function of (r/D)3 irrespective of the other parameters of the system, thus resulting in the universal size-scaling that is observed. However, as discussed earlier, the dipolar model, while qualitatively satisfactory, does not take into account the multipolar interactions between the particles, which become important at small inter-particle gaps (smaller than 0.5D). The true distance-dependence of the plasmon coupling can be quantitatively reproduced only by a complete treatment that includes all modes of interaction (dipolar, quadrupolar, octupolar, etc.), as approximated well by computational electrodynamics methods such as DDA and FDTD. It must be noted that even in such a full treatment, the origin of the size-scaling discussed above would still be valid. For instance, the field due to a quadrupole decays as 1/r5, while the quadrupole polarizability is proportional to D5, and so on for higher order modes. Of course, when higher-order terms, e.g.,

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quadrupoles (1/r5), octupoles (1/r7), . . . enter into the interaction, the resulting distance-decay is significantly steeper than that predicted by the purely dipolar model, and is closely modeled by a single-exponential decay expressed by Eq. (13), rather than any inverse power law [31]. It must however be acknowledged that the exponential trend used to describe the distance-decay of the near-field coupling is not an analytic dependence but only an empirical fit best suited for comparing the near-field coupling depth for different systems. In fact between 0.5 and 1D, there are observable deviations of experimental and simulation data from the exponential fit. Besides, all these empirical analyses are limited to gaps larger than 0.1D and do not include the anomalously large shifts and new bands that emerge when particles almost touch [31,61,62].

9. Plasmon coupling in nanoshells and other complex nanostructures

10. Coupled particles for medium sensing Since the LSPR red-shift in a coupled-particle system is generally considered to be a measure of the attractive coupling between the particle plasmons, as per simple electrostatic arguments, the coupling-induced red-shift can be expected to decrease with an increase in the medium dielectric constant [65]. However, our


Metal nanoshells are nanostructures that consist of a dielectric or hollow core surrounded by a thin (10–20 nm) shell of metal, in most cases gold [56]. The Halas group developed this tunable nanostructure and showed that the LSPR of the metal shell nanostructure depends strongly on the relative dimensions of the metal shell and the dielectric core. As the gold shell thickness is decreased, there is red-shift in the nanoshell LSPR from the visible region (520 nm for a solid gold nanosphere) towards the nearinfrared region. When we plot the fractional red-shift (Dk/k0) of the nanoshells as a function of the shell thickness-to-core radius ratio (t/R), we find a universal trend for nanoshells of different size (Fig. 6) [62]. The decay length (fit by a single-exponential) for this trend is 0.2 in units of the core radius regardless of inner core material, the shell metal (gold or silver), and the surrounding medium. Thus, the nanoshell structure is quite analogous to the two-particle system – the nanoshell has two surfaces, the inner surface of shell and outer surface of the shell, each with its own plasmon mode. These two plasmon modes couple across the thickness of the shell. The strength of the coupling is therefore determined by the field decay across the thickness as 1/t3 and the core polarizability, which is proportional to R3, resulting in a similar size-scaling as in the two-particle system. Thus, the analogy of the nanoshell system to the two-particle system was shown earlier by Nordlander and Halas using the plasmon hybridization approach [34,55]. As an

additional feature over earlier models, the scaling model offers a quantitative empirical expression that incorporates the dependence of the nanoshell LSPR on both the shell-to-core ratio and the total nanoshell volume, while including associated size-dependent electromagnetic retardation effects [62]. There is, however, one major difference between the nanoshell structure and the two-particle system [62]. In the case of the twoparticle system, as discussed earlier, the dipole–dipole model under-estimates the steepness of the distance-decay of the near-field coupling. However, in the nanoshell case, a dipolar model gives the same trend as the full electrodynamic treatment. This is due to the spherical symmetry in the nanoshell system, which allows only modes of the same angular momentum to interact (i.e., l0 l = 0). This is the reason why the dipolar nanoshell resonance resulting from the coupling is describable by a purely dipolar interaction and does not involve higher-order interactions. We have also shown using electrodynamic simulations that the near-field coupling between two elongated nanoparticles assembled head-to-tail also decays as per the universal trend over a distance that is 0.2D [63]. In this case, however, D is the dimension of the elongated particle along the polarization direction. Tabor et al. recently verified this experimentally on lithographically fabricated nanorod dimers with varying inter-particle separation [64]. The absolute plasmon coupling strength (denoted by the pre-exponential factor k in Eq. (13)), however, depends on the particle shape (i.e., aspect ratio and curvature), without affecting the universal distance-decay. The higher the aspect ratio and sharper the endcurvature of the interacting particles, the larger is the absolute magnitude of the near-field coupling [63]. The universal distance-decay is also found to be valid in a system of three interacting nanospheres, a first step towards extending this model to chains/arrays/assemblies of metal nanoparticles [63]. In 3D assemblies, the volume fraction of the nanoparticles could be the scaling variable in lieu of the separation-to-size ratio used in the psuedo1D cases.

Fig. 6. The LSPR resonance of the gold nanoshell red-shifts as the thickness of the shell is decreased due to increasing coupling between the plasmon mode on the inner surface and that on the outer surface. The coupling strength represented by the fractional LSPR red-shift (Dk/k0) falls near-exponentially with increasing thickness, over a distance that is 0.2 in units of the nanoshell’s core radius, a trend that is universal regardless of other parameters such as total nanoshell size, metal, or medium. Reprinted with permission from Ref. [62].


electrodynamic simulations, which were recently verified by experiments of Acímovic´ et al. [66], showed that the coupling-induced red-shift increases linearly with an increase in the medium dielectric constant. The interaction energy U between the two plasmons decreases inversely with an increase in the medium dielectric constant em [10]. However, at the same time, the increase in em results, within each particle, in a reduction in the Coulombic restoring force acting on the polarized electrons, manifested as an increase in the electric dipole moment [10]. Since the interaction energy is proportional to the square of the dipole moment, a net increase in the plasmon coupling strength results from an increase in em. The dielectric constant of the medium surrounding a plasmonic nanostructure has a direct influence on its LSPR position as seen from the resonance condition in Eq. (5): ReðeÞ ¼ jem [67]. The sensitivity of the LSPR position to the medium refractive-index becomes useful in the optical detection of analytes programmed to bind in the local nano-environment of a plasmonic nanostructure [68,69]. For the most sensitive detection, it is desirable that the

LSPR λ max (nm)

630

600

570

Inter-particle gap 90 nm 65 nm 40 nm 25 nm 10 nm 6 nm 4 nm

540

1.0

1.2

1.4

1.6

Refractive index 180

140

120

100

80

0.5

1.0

1.5

s/D

2.0


160

Sensitivity (nm/RIU)

LSPR shift Dk be maximum for a given change in the medium refractive-index Dnm. It turns out from Eqs. (5) and (6) that the medium sensitivity (Dk/Dnm) is dependent on the shape factor j [11]. Shapes with a high j are most suited for plasmonic sensing. For instance, LSPR positions of polarizable shapes such as nanorods [70] and nanotriangles [68,69] are much more sensitive to the medium as compared to nanospherical particles [11]. We found that in the particle dimer system, as the inter-particle gap is decreased, there is an increase in sensitivity of the LSPR (mode polarized along the inter-particle axis) to the medium refractive-index (Fig. 7a) [65]. The shape factor j and hence the medium sensitivity of the dimer is found to increase near-exponentially with a decrease in the inter-particle gap (normalized by the particle diameter). The trend as seen in Fig. 7b closely matches the universal scaling decay. Thus, coupled particles are much better candidates for enhanced plasmon resonance nano-sensing as compared to colloids or arrays of non-interacting particles. Acímovic´ et al. recently experimentally verified this exponentiallyincreasing sensitivity enhancement in lithographically fabricated dimers of gold nanodiscs [66]. They were able to employ nanoparticle dimers with small gaps for highly enhanced detection of proteins, with sensitivity tending towards single-molecule detection. A similar effect has been theoretically [11,71] and experimentally [71] observed in gold nanoshells, where a reduction in the shell thickness/core radius ratio results in a near-exponential enhancement of the LSPR sensitivity. Thus, it can be physically visualized that the near-field interaction in the coupled-particle system results in a strong enhancement in the electric field within a confined nano-volume/junction of the nanostructure, resulting in an enhanced sensitivity of the optical resonance to the dielectric environment of this volume.

11. Plasmon coupling for field-enhanced spectroscopy

510

0.0

161

Fig. 7. (a) The LSPR maximum of a nanoparticle dimer (for polarization along dimer axis) increases linearly with increasing refractive-index, similar to an isolated nanoparticle, however the increase has a much higher slope for dimers with a smaller inter-particle gap. (b) The LSPR sensitivity to the medium increases almost exponentially with decreasing inter-particle gap s (normalized by the particle diameter D). Reprinted with permission from Ref. [65].

The near-field coupling between noble metal nanoparticles (for the bonding mode) is known to result in an enhanced field in the junction of the nanoparticles [12,18]. Intensity enhancements in the junction of up to 105 (depending on the shape/curvature of the interacting nanoparticles) have been theoretically predicted. These fields can be used to strongly enhance the Raman scattering of molecules lying in these junctions. In fact, the 13–14 order amplification of Raman scattering of single molecules on silver nanoparticles observed by Nie and Emory [17] has been shown by Brus and coworkers to be mostly from enhanced field hot-spots at the junction of two or more silver nanoparticles [18,72]. Typically, nanoparticles assembled together show a strong increase in the SERS enhancement compared to the isolated colloidal nanoparticles, with the SERS enhancement increasing rapidly with decreasing inter-particle gap between the particles [18,72–75]. However, recently Mahmoud et al. observed an anomalous trend in the SERS enhancement from aggregated assemblies of 80-nm gold nanoframes [76]. As, the aggregation of the hollow silver nanoframes was increased, the enhancement of SERS (normalized by the number of nanoframes in the aggregate) from adsorbed thiophenol molecules was found to decrease rather than result in an increase seen in a similar aggregation experiment [77] on solid silver nanocubes. This was despite the fact that the LSPR shift due to the aggregation of the nanoframes did not move their LSPR away from the spectral region of the Raman laser excitation and scattering frequencies. Electrodynamic simulations further showed that with decreasing inter-particle gap between the nanoframes, the field between the nanoframes was indeed enhanced, however this was at the expense of the field in the interior of the nanoframes. It is quite likely that the thiophenol molecules are predominantly adsorbed within the nanoframe cavities and therefore experience a reduced

162


field intensity as the nanoframes come closer, resulting in a lower SERS enhancement. This result reiterates that for obtaining most optimum SERS from complex plasmonic nanostructures, it is crucial to know the spatial profile and resonance spectrum of nearfields and hot-spots in the nanostructure relative to the electronic resonances/Raman scattering frequencies and adsorption sites of the Raman-active molecules.

12. Influence of coupling and near-field on electron relaxation In addition to the radiative properties of metal nanocrystals, non-radiative processes have also been very well studied. Ultrafast electron dynamics measurements using pump–probe techniques have shown that excited electrons in metal nanoparticles thermalize very fast (within 500 fs) to a hot Fermi distribution followed by electron cooling via electron–phonon collisions (1 ps) and slower cooling of the nanoparticle lattice via phonon–phonon coupling (100 ps) [2,41,78–81]. The hot-electron cooling rate in gold nanoparticles has been found to be 1 ps and is unaffected by changes in the size or shape of the nanoparticles [41]. However, the coupling between gold nanoparticles has been found to have a systematic effect on the non-radiative hot-electron cooling rate [82]. Ultrafast pump–probe experiments on gold nanoparticle aggre-

0.6

E Dotted line is experimental data

k

Solid line is theoretical fit Gap = 7 nm Period = 78.1 Gap = 12 nm Period = 68.3 Gap = 17 nm Period = 63.4 Gap = 27 nm Period = 57.6 Gap = 212 nm Period = 52.8

0.5 0.4

ΔA/A

gates (with nanoparticles almost touching each other) have shown that the electron cooling rate becomes faster (up to fourfold) with increased spatial coupling between nanoparticles in the aggregate. Increased spatial coupling between the nanoparticles possibly increases the phonon density of states resulting in enhanced electron–phonon coupling, and also causes delocalization of electrons across the aggregate, resulting in increased interfacial scattering. Both mechanisms would lead to faster electron cooling. Another interesting non-radiative process observed in metal nanoparticles is the excitation of coherent phonon oscillations (CPO) of the particle lattice due to the cooling of the hot electrons excited by an ultrafast laser [83,84]. These phonon oscillations have been detected optically to have a period of few tens of picoseconds (Fig. 8a). The CPO frequency has been generally thought to be characteristic of the elastic/acoustic properties of the metallic lattice [83]. However, it has been found in ultrafast measurements on nanodisc pairs (with incident light polarized along the interparticle axis) that the CPO frequency red-shifts as the gap between the interacting nanodiscs is decreased [84]. As shown in Fig. 8b, the red-shift of the CPO frequency mirrors very closely the near-exponential trend followed by the red-shift of the electron oscillation (LSPR) frequency (Fig. 8c) with decreasing gap. The origin of the CPO red-shift is therefore most likely the same as that of the LSPR shift, i.e., the near-field coupling between the nanoparticles.

ps ps ps ps ps

0.3 0.2 0.1

0

50

100 Delay Time (ps)

150

0.06

Δω

−Δω/ω0 (SPR)

ω0

0.2

0

−Δf/f (CPO)

⎛−s /D ⎛ = −0.51 . e xp ⎛ 0.17 ⎛

0.3

CPO

0.1

SPR

⎛−s /D ⎛ = −0.09 . e xp ⎛ 0.19 ⎛

Δf f0

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0.02

0.00

0.0 0.0

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1.5

s/D

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0.4

Fig. 8. (a) Optically-detected coherent phonon oscillations (CPO) in gold nanodisc pairs with different inter-particle gaps. The CPO frequency is seen to decrease as the interparticle gap decreases. (b) The fractional CPO red-shift increases almost exponentially with decreasing inter-particle gap (normalized by the particle diameter) with the same trend as the (c) fractional LSPR red-shift, as indicated by the similar decay rate of the curves. This implies that the CPO frequency modulation originates from the near-field coupling of the particles, which is known to systematically shift the LSPR. Reprinted with permission from Ref. [84].


Possibly, each nanoparticle due to the polarizing perturbation of the plasmonic field of the neighboring particle, has an effectively lowered free electron density and thus an effectively softened lattice with a lower CPO frequency [84]. Recently, Neretina et al. found that the plasmon near-field influences semiconductor excitonic relaxation in CdTe–Au core–shell nanorods [85,86]. It was found that the lifetime of the excitonic state of the CdTe was lowered in excitation regions (530–550 and 750–780 nm) that overlapped with the plasmon resonance modes of the Au nanoshells. Also, the enhancement in the exciton relaxation rate was found to be maximum when the transition dipole moment was parallel to the electric polarization of the plasmon excitation, indicating a plasmonic near-field enhancement of the exciton relaxation in CdTe [86]. The transition dipole moment of the CdTe exciton couples with the near-field of the Au nanoshells, possibly enhancing excitonic relaxation via radiative processes such as Auger or multiphoton ionization. Alternatively, the excitonic energy of CdTe could be transferred into plasmon excitations in the Au nanoshell. These experiments really demonstrate the ability to use plasmonic fields to tune the rates of electronic relaxation and associated photochemical and photophysical processes. 13. Summary In this Letter, we have reviewed recent findings regarding the near-field coupling between noble metal nanoparticles – its theoretical basis, its distance-decay, dependence on other parameters such as geometry and medium of the nanostructure, analogy to exciton-coupling in molecular aggregates and orbital hybridization in molecules, and its effect on radiative (scattering and absorption spectra) properties, near-field enhancement, and electron relaxation properties of the nanostructure. The findings and the models resulting from them hold promise for designing complex/assembled nanostructures with plasmon resonance modes tuned specifically for highly improved refractive-index based nano-sensing [11,65,66], field-enhanced spectroscopy [18,72,87], plasmon-enhanced photochemistry [29], and plasmonic waveguiding [88]. Acknowledgements We thank Wenyu Huang, Susie Eustis, Mahmoud A. Mahmoud, Svetlana Neretina, and Wei Qian and for their collaborative contributions to some of the work discussed here. P.J. would like to thank the Miller Institute for Basic Research in Science at UC Berkeley for funding. M.A.E. thanks the Materials Research Division of the National Science Foundation (No. 0527297) for funding. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

G. Mie, Ann. Phys. 25 (1908) 377. S. Link, M.A. El-Sayed, Int. Rev. Phys. Chem. 19 (2000) 409. K.L. Kelly, E. Coronado, L.L. Zhao, G.C. Schatz, J. Phys. Chem. B 107 (2003) 668. L.M. Liz-Marzan, Langmuir 22 (2006) 32. M.A. El-Sayed, Acc. Chem. Res. 37 (2004) 326. P.K. Jain, X. Huang, I.H. El-Sayed, M.A. El-Sayed, Acc. Chem. Res. 41 (2008) 1578. P. Mulvaney, Langmuir 12 (1996) 788. U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995. M.M. Alvarez, J.T. Khoury, G. Schaaff, M.N. Shafigullin, I. Vezmar, R.L. Whetten, J. Phys. Chem. B 101 (1997) 3706. P.K. Jain, S. Eustis, M.A. El-Sayed, J. Phys. Chem. B 110 (2006) 18243. P.K. Jain, M.A. El-Sayed, J. Phys. Chem. C 111 (2007) 17451. E. Hao, George C. Schatz, J. Chem. Phys. 120 (2004) 357. P.K. Jain, K.S. Lee, I.H. El-Sayed, M.A. El-Sayed, J. Phys. Chem. B 110 (2006) 7238. C. Sonnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, et al., Phys. Rev. Lett. 88 (2002) 077402.

163

[15] D.J. Griffiths, Introduction to Electrodynamics, third edn., Prentice-Hall, Inc., New Jersey, 1999. [16] J.A. Dieringer, A.D. McFarland, N.C. Shah, D.A. Stuart, A.V. Whitney, C.R. Yonzon, et al., Faraday Disc. 132 (2006) 9. [17] S. Nie, S.R. Emory, Science 275 (1997) 1102. [18] J. Jiang, K. Bosnick, M. Maillard, L. Brus, J. Phys. Chem. B 107 (2003) 9964. [19] G.C. Schatz, Acc. Chem. Res. 17 (1984) 370. [20] J.R. Lakowicz et al., Proc. SPIE 6099 (2006) 609909/1. [21] G. Ritchie, E. Burstein, Phys. Rev. B 24 (1981) 4843. [22] F. Tam, G.P. Goodrich, B.R. Johnson, N.J. Halas, Nano Lett. 7 (2007) 496. [23] G.T. Boyd, Z.H. Yu, Y.R. Shen, Phys. Rev. B 33 (1986) 7923. [24] M.B. Mohamed, V. Volkov, S. Link, M.A. El-Sayed, Chem. Phys. Lett. 317 (2000) 517. [25] C.K. Chen, T.F. Heinz, D. Ricard, Y.R. Shen, Phys. Rev. B 27 (1983) 1965. [26] G.T. Boyd, T. Rasing, J.R.R. Leite, Y.R. Shen, Phys. Rev. B 30 (1984) 519. [27] S. Kim, J. Jin, Y. Kim, I. Park, Y. Kim, S. Kim, Nature 453 (2008) 757. [28] P.K. Jain, Y. Xiao, R. Walsworth, A.E. Cohen, Nano Lett. 9 (2009) 1644. [29] A. Sundaramurthy, P.J. Schuck, N.R. Conley, D.P. Fromm, G.S. Kino, W.E. Moerner, Nano Lett. 6 (2006) 355. [30] P.K. Jain, X. Huang, I.H. El-Sayed, M.A. El-Sayed, Plasmonics 2 (2007) 107. [31] P.K. Jain, W. Huang, M.A. El-Sayed, Nano Lett. 7 (2007) 2080. [32] L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, et al., J. Phys. Chem. B 109 (2005) 1079. [33] W. Rechberger, A. Hohenau, A. Leitner, J.R. Krenn, B. Lamprecht, F.R. Aussenegg, Opt. Commun. 220 (2003) 137. [34] P. Nordlander, C. Oubre, E. Prodan, K. Li, M.I. Stockman, Nano Lett. 4 (2004) 899. [35] J.J. Storhoff, A.A. Lazarides, R.C. Mucic, C.A. Mirkin, R.L. Letsinger, G.C. Schatz, J. Am. Chem. Soc. 122 (2000) 4640. [36] R. Elghanian, J.J. Storhoff, R.C. Mucic, R.L. Letsinger, C.A. Mirkin, Science 277 (1997) 1078. [37] K.H. Su, Q. Wei, X. Zhang, J.J. Mock, D.R. Smith, S. Schultz, Nano Lett. 3 (2003) 1087. [38] M.B. Cortie, X. Xu, M.J. Ford, Phys. Chem. Chem. Phys. 8 (2006) 3520. [39] M. Gluodenis, F.C.A. Jr, J. Phys. Chem. B 106 (2002) 9484. [40] R. Gans, Ann. Phys. 37 (1912) 881. [41] S. Link, M.A. El-Sayed, J. Phys. Chem. B 103 (1999) 8410. [42] C.J. Murphy, T.K. Sau, A.M. Gole, C.J. Orendorff, J. Gao, L. Gou, et al., J. Phys. Chem. B 109 (2005) 13857. [43] S. Link, M.B. Mohamed, M.A. El-Sayed, J. Phys. Chem. B 103 (1999) 3073. [44] K.G. Thomas, S. Barazzouk, B.I. Ipe, S.T.S. Joseph, P.V. Kamat, J. Phys. Chem. B 108 (2004) 13066. [45] S.T.S. Joseph, B.I. Ipe, P. Pramod, K.G. Thomas, J. Phys. Chem. B 110 (2006) 150. [46] M. Kasha, Radiat. Res. 20 (1963) 55. [47] M. Kasha, H.R. Rawls, M.A. El-Bayoumi, Pure Appl. Chem. 11 (1965) 371. [48] B.Z. Packard, D.D. Toptygin, A. Komoriya, L. Brand, J. Phys. Chem. B 102 (1998) 752. [49] J.P. Kottmann, O.J.F. Martin, Opt. Lett. 26 (2001) 1096. [50] D.W. Brandl, N.A. Mirin, P. Nordlander, J. Phys. Chem. B 110 (2006) 12302. [51] L.A. Sweatlock, S.A. Maier, H.A. Atwater, J.J. Penninkhof, A. Polman, Phys. Rev. B 71 (2005) 235408/1. [52] B.T. Draine, P.J. Flatau, J. Opt. Soc. Am. A 11 (1994) 1491. [53] J. Zuloaga, E. Prodan, P. Nordlander, Nano Lett. 9 (2009) 887. [54] F.J. García de Abajo, J. Phys. Chem. C 112 (2008) 17983. [55] E. Prodan, C. Radloff, N.J. Halas, P. Nordlander, Science 302 (2003) 419. [56] S.J. Oldenburg, R.D. Averitt, S.L. Westcott, N.J. Halas, Chem. Phys. Lett. 28 (1998) 243. [57] J. Aizpurua, G.W. Bryant, L.J. Richter, F.J. García de Abajo, B.K. Kelley, T. Mallouk, Phys. Rev. B 71 (2005) 235420/1. [58] C. Sonnichsen, B.M. Reinhard, J. Liphardt, A.P. Alivisatos, Nat. Biotechnol. 23 (2005) 741. [59] B. Reinhard, S. Sheikholeslami, A. Mastroianni, A.P. Alivisatos, J. Liphardt, Proc. Natl. Acad. Sci. USA 104 (2007) 2667. [60] B.M. Reinhard, M. Siu, H. Agarwal, A.P. Alivisatos, J. Liphardt, Nano Lett. 5 (2005) 2246. [61] A.M. Funston, C. Novo, T.J. Davis, P. Mulvaney, Nano Lett. 9 (2009) 1651. [62] P.K. Jain, M.A. El-Sayed, Nano Lett. (2007) 2854. [63] P.K. Jain, M.A. El-Sayed, J. Phys. Chem. C 112 (2008) 4954. [64] C. Tabor, D. Van Haute, M.A. El-Sayed, ACS Nano 3 (2009) 3670. [65] P.K. Jain, M.A. El-Sayed, Nano Lett (2008). [66] S.S. Acímovic´, M.P. Kreuzer, M.U. Gonzalez, R. Quidant, ACS Nano 3 (2009) 1231. [67] S. Underwood, P. Mulvaney, Langmuir 10 (1994) 3427. [68] A.J. Haes, R.P. Van Duyne, J. Am. Chem. Soc. 124 (2002) 10596. [69] M.D. Malinsky, K.L. Kelly, G.C. Schatz, R.P. Van Duyne, J. Am. Chem. Soc. 123 (2001) 1471. [70] C. Yu, J. Irudayaraj, Anal. Chem. 79 (2007) 572. [71] Y. Sun, Y. Xia, Anal. Chem. 74 (2002) 5297. [72] A.M. Michaels, J. Jiang, L. Brus, J. Phys. Chem. B 104 (2000) 11965. [73] B. Nikoobakht, M.A. El-Sayed, J. Phys. Chem. A 107 (2003) 3372. [74] X. Huang, I.H. El-Sayed, W. Qian, M.A. El-Sayed, Nano Lett. 7 (2007) 1591. [75] A. Pal, T. Pal, J. Raman Spectrosc. 30 (1999) 199. [76] M.A. Mahmoud, M.A. El-Sayed, Nano Lett. 9 (2009) 3025. [77] M.A. Mahmoud, C.E. Tabor, M.A. El-Sayed, J. Phys. Chem. C 113 (2009) 5493. [78] S. Link, M.A. El-Sayed, Ann. Rev. Phys. Chem. 54 (2003) 331. [79] S. Link, C. Burda, Z.L. Wang, M.A. El-Sayed, J. Chem. Phys. 111 (1999) 1255.

164


[80] [81] [82] [83] [84] [85]

P.K. Jain, W. Qian, M.A. El-Sayed, J. Am. Chem. Soc. 128 (2006) 2426. J.H. Hodak, A. Henglein, G.V. Hartland, Pure Appl. Chem. 72 (2000) 189. P.K. Jain, W. Qian, M.A. El-Sayed, J. Phys. Chem. B 110 (2006) 136. W. Huang, W. Qian, M.A. El-Sayed, J. Phys. Chem. B 109 (2005) 18881. W. Huang, W. Qian, P.K. Jain, M.A. El-Sayed, Nano Lett. 7 (2007) 3227. S. Neretina, W. Qian, E. Dreaden, M. El-Sayed, R.A. Hughes, J.S. Preston, et al., Nano Lett. 8 (2008) 2410. [86] S. Neretina, E.C. Dreaden, W. Qian, M. El-Sayed, R.A. Hughes, J.S. Preston, et al., Nano Lett. 9 (2009) 3772. [87] J.B. Jackson, N.J. Halas, Proc. Natl. Acad. Sci. USA 101 (2004) 17930. [88] S.A. Maier, P.G. Kik, H.A. Atwater, S. Meltzer, E. Harel, B.E. Koel, et al., Nat. Mater. 2 (2003) 229.

Prashant K. Jain is a Miller Fellow at the University of California-Berkeley. He received his PhD at Georgia Tech and performed postdoctoral work at Harvard University on the optical properties of plasmonic nanostructures. He has published 18 peer-reviewed papers and given several contributed and invited talks on this topic. He has been a recipient of the ACS Physical Chemistry Outstanding Research Poster Award (2006), Best Chemistry PhD student Award from Georgia Tech (2006), MRS Gold Award (2007), and the Atlanta Area Chemical Physics Award (2008). He is a nominated full member of Sigma Xi and the Royal Society of Chemistry, UK.

Mostafa A. El-Sayed, Julius Brown Chair, Regents Professor, and Director, Laser Dynamics Lab at Georgia Tech, received his PhD at FSU and was on the faculty at UCLA (1961–1994). He has published over 500 papers, given over 45 special lectures, and 200 invited talks in areas of photochemistry, photobiology, laser spectroscopy, metal and semiconductor nanostructures, and nanomedicine. He is a US National Academy of Science member, an elected Fellow of AAAS, APS, ACS, and the American Academy of Arts and Sciences. His notable awards include the 2007 National Medal of Science, King Faisal International Prize, and the First Class Medal of the Egyptian Republic.