Investigation of the Validity of the Universal Scaling Law on Linear Chains of Silver Nanoparticles

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 platformfor 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 coupledmode 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 medium (n(m)). The decay constant of the LMis linearly proportional to n(m) while the corresponding constant of the TM decays exponentially with n(m). Upon changing the nanoparticle size, the change in the peak position of the LMdecreases 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.