The Extinction Spectra of Silver Nanoparticle Arrays:  Influence of Array Structure on Plasmon Resonance Wavelength and Width

Abstract

We use high-quality electrodynamics methods to study the extinction spectra of one-dimensional linear chains and two-dimensional planar arrays of spherical silver nanoparticles, placing emphasis on the variation of the plasmon resonance wavelength and width with array structure (spacing, symmetry), particle size, and polarization direction. Two levels of theory have been considered, coupled dipoles with fully retarded interactions and T-matrix theory that includes a converged multipole expansion on each particle. We find that the most important array effects for particles having a radius of 30 nm or smaller are captured by the couple dipole approach. Our calculations demonstrate several surprising effects that run counter to conventional wisdom in which the particle interactions are assumed to be governed by electrostatic dipolar interactions. In particular, we find that for planar arrays of particles with polarization parallel to the plane the plasmon resonance blue shifts as array spacing D decreases for D larger than about 75 nm and then it red shifts for smaller spacings. In addition, we find that the plasmon narrows for D > 180 nm but broadens for smaller spacings. The results can be rationalized using a simple analytical model, which demonstrates that the plasmon wavelength shift is determined by the real part of the retarded dipole sum while the width is determined by the imaginary part of this sum. The optimal blue shifts and narrowing are found when the particle spacing is slightly smaller than the plasmon wavelength, while red shifts and broadening can be found for spacings much smaller than the plasmon wavelength at which electrostatic interactions are dominant. We also find that the array spectrum does not change significantly with array symmetry (square or hexagonal) or irradiated spot size (i.e., constant array size or constant particle number).

Plasmonic polymers unraveled through single particle spectroscopy

“…14 Theoretical analysis revealed that for both double and single column chains, the superradiant mode not only reaches an infinite chain limit for N L = 5 -10, consistent with earlier studies, 27,50,52 but also redshifts due to plasmonic interactions as well as phase retardation as L Tot increases. 50,51 As the latter effect also depends on the width of the significantly beyond what has been reported before for single particle studies. 25,27,40,52 Our direct observation of the infinite chain limit eliminates the need to establish it through simulations.…”

“…To summarize a body of literature, as long as 2.0 < D/r ≤ 2.5, where D is the center-to-center distance between the NPs and r is the NP radius, the energy of the lowest energy peak plateaus for a number of repeat units, N L , between 5 and 10, even though a range of r (5 -55 nm) and interparticle gaps (0.5 -30 nm) has been investigated. 21,23,25,47,48,[50][51][52] The interaction strength between surface plasmons is significantly reduced though when D/r increases from 2.01 to 2.1, as investigated in detail both experimentally and through simulations for the smallest chain lengths of dimers and trimers. 32,[53][54][55] Due to this decrease in coupling, saturation of the redshifting for the lowest energy longitudinal chain mode is predicted to occur at chain lengths as short as 7 NPs and at shorter wavelengths as the interparticle gap increases.…”

Vivid, full-color aluminum plasmonic pixels

“…3A shows the theoretical spectrum of a pixel with identical physical parameters as the experimental system (solid line), calculated using a coupled dipole method where the nanorods are described as point dipoles with a polarizability obtained from finite element method modeling (COMSOL) (45,46). For a more complete description of the theory, see SI Appendix, Fig.…”

O efeito SERS na análise de traços: o papel das superfícies nanoestruturadas

“…Vários trabalhos teóricos de Schatz et al apresentam os espectros de extinção, calculados a partir da teoria de Mie, acrescida dos termos envolvendo o acoplamento dos dipolos (DDA -"discrete dipole approximation"), para diferentes nanopartículas de Ag ou Au, como agregados lineares de nanoesferas 45 , esferóides e prismas 46 , ou ainda, estruturas ordenadas bidimensionais de nanoesferas metálicas 47 . Mais recentemente eles obtiveram experimentalmente o espectro do plasmon de superfícies de pares isolados de nanodiscos de Ag, utilizando um microscópio óptico no modo "dark field", e mostraram que, quando a polarização da radiação incidente é paralela ao eixo interpartículas, é possível observarem-se efeitos de confinamento de plasmon e desvio da banda para o vermelho 48 .…”