On the Use of Plasmonic Nanoparticle Pairs As a Plasmon Ruler: The Dependence of the Near-Field Dipole Plasmon Coupling on Nanoparticle Size and Shape † Christopher Tabor, ‡ Raghunath Murali, § Mahmoud Mahmoud, ‡ and Mostafa A. El-Sayed* ,‡ Laser Dynamics Laboratory and Microelectronics Research Center, Georgia Institute of Technology, Atlanta, Georgia 30332 ReceiVed: September 5, 2008; ReVised Manuscript ReceiVed: October 29, 2008 The localized surface plasmon resonance (LSPR) spectral band of a gold or silver nanoparticle is observed to shift as a result of the near-field plasmonic field of another nanoparticle. The dependence of the observed shift on the interparticle distance is used as a ruler in biological systems and gave rise to a plasmonic ruler equation in which the fractional shift in the dipole resonance is found to decrease near exponentially with the interparticle separation in units of the particle size. The exponential decay length constant was observed to be consistent among a small range of nanoparticle sizes, shapes, and types of metal. The equation was derived from the observed results on disks and spherical nanoparticles and confirmed using results on a DNA conjugated nanosphere system. The aim of the present paper is to use electron beam lithography and DDA calculations to examine the constancy of the exponential decay length value in the plasmonic ruler equation on particle size and shape of a number of particles including nanoparticles of different symmetry and orientations. The results suggest that the exponent is almost independent of the size of the nanoparticle but very sensitive to the shape. A discussion of the nanoparticles most suitable for different applications in biological systems and a comparison of the plasmonic ruler with Forster resonance energy transfer (FRET) is mentioned. Introduction Metallic nanoparticles are of great interest due to their optical and radiative properties. The interaction of a noble metal nanoparticle with incident light of a specific energy induces intense localized fields at the surface of the particle. These fields are induced when conduction band electrons of the noble metal nanoparticle couple with the electric field of incident light at a resonant frequency, generating a plasmonic oscillation localized on the surface of the nanoparticle, known as the localized surface plasmon resonance (LSPR). 1-4 This plasmonic oscillation occurs at a specific resonance wavelength that is dependent on the particle’s properties (dielectric function, size, and shape) and the dielectric constant of the host medium. By changing these parameters, one can tune the optical properties of the noble metal nanoparticles to optimize them for different applications. The intense localized field at the nanoparticle surface and the tunability of the LSPR in noble metal nanoparticles gives them enormous potential in medical, 5-7 optical, 8-11 and sensor 12-16 applications. When two nanoparticles come into close contact (separations of less than 2 particle diameters), the near-field dipole plasmonic fields couple with one another, reducing the overall resonance energy of the particle pair. 17-19 Colloidal studies have provided initial qualitative data on the near-field coupling between plasmonic nanoparticles, and many groups 12,20,21 have reported on the effect of aggregation on the optical extinction of nanoparticles in solution. To achieve quantitative measurements of the coupling of two plasmonic metal nanoparticles, it is necessary to use lithographic techniques to fabricate nanopar- ticles of homogeneous size, shape, and interparticle separation. However, only recently has it been technologically possible to fabricate nanoparticles of high homogeneity and low feature size thanks to advancements in electron beam lithography (EBL). Quantitative studies on the near field dipole plasmon coupling between two nanoparticles as a function of interparticle separa- tion were independently first reported by Su et al. 22 and Rechberger et al. 17 in a spheroidal gold nanoparticle. They concluded that “when the [LSPR] peak shift is scaled by the peak wavelength and the gap is scaled by the particle... length, all data points fall on a common curVe.” The common curve was an exponential decay of the coupling, measured by the fractional shift in the plasmon resonance (Δλ/λ), as a function of the interparticle separation (s) scaled by the particle size (D). It was later shown that while the true dependence of the dipole coupling on the scaled interparticle separation goes as (s/D) -3 , a single exponential of the form (Δλ/λ) ) A × e (-s/D/τ) very nearly approximates the dependence. 23 This exponential ap- proximation is also useful for quantifying the relative strength of the dipole field by the magnitude of the pre-exponential factor A and the decay length of the field away from the particle surface by the magnitude of τ. Using discrete dipole approximation (DDA) calculations, our group has examined the plasmonic decay law for nanospheres, 23,24 nanoshells, 25,26 nanoellipses, 24 and nanodisks, 23 and using elec- tron beam lithography (EBL) the gold nanodisk was studied and the exponential decay length value was found to agree with the DDA results and with the results of silver nanodisks. 27 From these studies it was concluded that this common coupling trend has a scaled decay length that is largely independent of the particle material, dielectric environment, size, and shape. 23-26 We have also loosely shown mathematically why this decay of the scaled quantities should be largely independent of the nanoparticle properties. 23 By using this common coupling behavior a plasmon ruler equation was developed. Work from * Corresponding author. E-mail: melsayed@gatech.edu. † Part of the “Max Wolfsberg Festschrift”. ‡ Laser Dynamics Laboratory, Georgia Institute of Technology. § Microelectronics Research Center, Georgia Institute of Technology. J. Phys. Chem. A 2009, 113, 1946–1953 1946 10.1021/jp807904s CCC: $40.75  2009 American Chemical Society Published on Web 12/17/2008