The Optical Properties of One-, Two-, and Three-Dimensional Arrays of Plasmonic Nanostructures

Transcription

1 The Optical Properties of One-, Two-, and Three-Dimensional Arrays of Plasmonic Nanostructures Michael B. Ross 1, Chad A. Mirkin* 1,2, and George C. Schatz* 1,2 Department of Chemistry 1 and International Institute for Nanotechnology 2 Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA Correspondence: chadnano@northwestern.edu & g-schatz@northwestern.edu 1

2 a Experiment b Simulation Figure S1. Retarded dipole effects in two-dimensional plasmonic arrays. a. Experiment and b. simulation of two-dimensional arrays of 100 nm radius 35 nm height Ag cylindrical disks with changing spacing (depicted below each curve). Reprinted in part with permission from Ref 72 (main text) (Haynes, C. L.; McFarland, A. D.; Zhao, L.; Van Duyne, R. P.; Schatz, G. C.; Gunnarsson, L.; Prikulis, J.; Kasemo, B.; Käll, M., Nanoparticle Optics: The Importance of Radiative Dipole Coupling in Two-Dimensional Nanoparticle Arrays. J. Phys. Chem. B 2003, 107, ). Copyright 2003, American Chemical Society. S.1 Retarded dipole interactions in two-dimensional plasmonic arrays In the manuscript, we have focused primarily on the lattice plasmon mode as an example of how plasmonic arrays can be used to control collective optical properties with obvious device implications. However, plasmonic arrays can also be used as a platform to study the size and shape-dependent interparticle interactions in various nanoparticle arrangements, providing fundamental insights into the LSPR and how it interacts with photonic modes in the far-field. A powerful example of this was the identification of unusual narrowed and blue-shifted LSPRs in 2

3 2D arrays of cylindrical disks and triangular prisms (Figure S1). 1 In these systems, the scattering maximum of cylindrical arrays with a 500 nm interparticle spacing was ~750 nm; when the spacing was decreased to 260 nm the collective LSPR mode blue-shifted to ~650 nm. This pronounced spectral shift was unexpected because at these spacings one would expect the nanoparticles to be minimally interacting. This blue-shifted resonance was driven by strong radiative coupling between nanoparticles and retardation effects. Retardation effects, specifically radiative depolarization effects, are observed in large nanoparticles that are no longer quasistatic; these effects are the source of red-shifted LSPRs with increasing particle size. 2 Physically, retardation effects arise when the particle is of sufficient size that the diameter is a reasonable fraction of the wavelength of light. Due to this, a time-varying phase difference arises in the LSPR from one side of the particle to the other. This results in damped and broadened resonances (due to phase cancellation). 3-5 Typically, these are discussed within a single particle context. In the aggregate, these effects are easily explained by revisiting the coupled dipole framework; specifically, we can rewrite equation (7) from the main text in terms of the interparticle (i.e. inter-dipolar) spacing d: ( 1 ikd ij )( 3cos 2 θ ij )e ikd ij S= + k 2 ( sin 2 θ ij )e ikd ij 3 j i d ij d ij (10), Equation (10) describes the sum of dipolar interactions and is worth considering in detail. The first term scales as 1/d 3 and typically describes short-range electrostatic interactions between particles, such as the well known red-shifts that are observed when plasmonic nanostructures are brought closer together. A corollary of this is that once the particles are sufficiently far apart (usually several times their radius) the LSPR resembles that of the discrete particle; a result corroborated in a wide variety of plasmonic systems. The second term in Equation (10) describes 3

4 electrodynamic radiative dipolar interactions between particles, which scale with 1/d. The blueshifted resonances are a complex sum of the collective radiative lattice modes (1/d) and single particle retardation effects on (which scales the dipole term by e ikd ). When kd~π, these two effects change the signs of the real and imaginary parts of S, extensive analysis of these terms is provided in the two companion articles. 1, 6 We reiterate that the seemingly anomalous and highly complex plasmonic behavior in these arrays can be described in toto using a semi-analytical dipolar framework. S.2. Near field coupled plasmonic lattices It would be remiss if we did not discuss the immense effort that has been devoted to the properties of plasmonic nanoparticles and nanocrystals in much closer proximity than those discussed in the main text. These systems are more complex to simulate and understand due to the complex non-linear and orientation dependent plasmonic coupling that occurs between the nanoparticle building blocks. However, many of the design principles and examples we have outlined herein still apply. A striking observation by Collier 7, et. al. was an insulator-to-metal transition in Langmuir-Blodgett (LB) monolayers of small (2-5 nm) Ag quantum dots. Using a combination of optical second-harmonic generation (SHG) and reflectance spectroscopies, it was determined that below a critical separation (5 Å), the film began to exhibit metallic behavior where the reflectance was greatly increased and the SHG exhibited a sharp discontinuity. This proof-ofconcept inspired a great effort exploring the ability to tune the properties of LB materials in addition to characterizing and controlling their dielectric properties. Materials such as these require new simulation methodologies 8 and typically need highly monodisperse nanoparticles to form ordered nanoparticle networks. 4

5 More recently, the ability to assemble plasmonic nanoparticles (in addition to magnetic particles and quantum dots) into long-range crystalline films has led to precise control over the dielectric behavior of plasmonic superlattices. Typically, these materials use small (5-15 nm) building blocks where the dipolar nature, surface charge, and other entropic and enthalpic contributions dictate the crystal that is formed The optical response of these films is uniform over large regions, 12 while the thin film nature of these crystalline networks makes them amenable to ellipsometry measurements, which quantify the dielectric properties of a material. It has been observed that by changing the capping ligand between Au and Ag spherical particles can bring about a similar insulator-to-metal transition that is controlled by the length of the alkane chain By imprinting nanocrystalline arrays into large (100+ nm) cylindrical holes, a uniform optical response over a wide area is observed. Moreover, light transmission through these inverse hole arrays can be controlled by changing the capping ligand, which in turn changes the dielectric function of the plasmonic material. This work provides an exciting proof that robust tunable metamaterials are achievable over large areas. Much of the work so far has involved spherical particles, however anisotropic particles are often desirable due to their unique LSPRs and directional interactions. Tao, et. al. demonstrated that, by leveraging the inherent shape anisotropy of Ag nanoparticle building blocks, long-range highly ordered plasmonic films could be designed to exhibit tunable optical behavior throughout the visible range By changing the spacing between plasmonic constituents, long-range plasmonic arrays exhibit a complex combination of near-field coupling from higher-order resonances in addition to long-range diffractive photonic modes. 5

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