The discrete dipole approximation (DDA) is used to model the absorption efficiency of isolated gold (Au) and silver (Ag) ellipsoidal nanoparticles. The characteristics of the plasmonic bands of those nanostructures depend strongly on the size and orientation of the particles in both the lab and target frames. At specific rotation and incident angles, the desired plasmonic mode can be excited. The result of the simulation shows the possibility of excitation of three plasmonic modes—one longitudinal mode (LM) and two transverse modes (TM)—corresponding to the redistribution of the polarization charges along each principal axis. At oblique incidence of the incoming light, both the Au LM and a hybrid Au TM are observed whereas three more distinct plasmonic modes can be found in the case of the Ag particle. The effect of length distribution on the characteristics of the plasmonic bands is also examined for the three principal axes. The band position of the plasmonic bands associated with the electronic oscillation along each principal axis is found to vary linearly with the axis length. The linear variation of the band position of the LM is steeper as compared with the one found for the other modes.

The absorption spectra for a gold nanocube and for a gold nanobar are calculated by using the Discrete Dipole Approximation (DDA). The results show the excitation of a single albeit broad surface plasmon (SP) band of the gold nanocube. The extinction cross section of the gold nanocube is dominated by the absorption cross section that gains importance as the width increases. Further increasing the nanocube size beyond 80 nm will result in an optical response mainly characterized by scattering properties. The absorption spectrum of the nanobar shows the excitation of both the longitudinal mode (LM) and the transverse mode (TM). The nanobar is also compared to a cylinder, a spherically capped cylinder, and a spheroid of the same aspect ratio. The band position of the TM of the nanobar is red-shifted as compared to the ones calculated for other morphologies, while the LM is either blue-shifted or red-shifted depending on the morphologies considered.

Due to the wide range of variation in the plasmonic characteristics of the metallic nanoparticles arranged in linear arrays, the optical spectra of these arrays provide a powerful platform for spectroscopic studies and biosensing applications. Due to the coupling effect between the interacting nanoparticles, the excited resonance mode is shifted with the interparticle separation. The change in the resonance energy of the coupled mode is expressed by the fractional plasmon shift which would normally follow a universal scaling behavior. Such a universal law has been successfully applied on a system of dimers under parallel polarization. It has been found that the plasmon shift decays exponentially over interparticle spacing. The decay length is independent of both the nanoparticle and dielectric properties of the surrounding medium. In this paper, the discrete dipole approximation (DDA) is used to examine the validity of extending the universal scaling law to linear chains of several interacting nanoparticles embedded in various host media for both parallel and perpendicular polarizations. Our calculations reveal that the decay length of both the coupled longitudinal mode (LM) and transverse modes (TM) is strongly dependent on the refractive index of the surrounding mediumnm. The decay constant of the LM is linearly proportional tonmwhile the corresponding constant of the TM decays exponentially withnm. Upon changing the nanoparticle size, the change in the peak position of the LM decreases exponentially with the interparticle separation and hence, it obeys the universal law. The sensitivity of coupled LM to the nanoparticle size is more pronounced at both smaller nanoparticle sizes and separations. The sensitivity of the coupled TM to the nanoparticle size on the other hand changes linearly with the separation and therefore, the universal law does not apply in the case of the excited TM.

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