Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis

Abstract

We demonstrate an efficient eigen-decomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of showing the dispersion relation and mode quality simultaneously. It can also separate the material and geometrical properties, so its efficiency does not depend on the complexity of the material polarizability.The method is applied to analyze the guided modes of a single and a pair of metal chains. The more accurate dynamic dipole polarizability typically gives a red-shift compared with the results obtained with the broadly used quasistatic dipole polarizability with radiation correction.There are recent interests of using metal nanoparticle (MNP) chains to function as a designable subwavelength waveguide to transport optical signals. 1,2Wave propagation along MNP chains is mediated by coupled plasmonic resonances. Such plasmonic waveguides may serve as the building blocks for making nanoscale optical devices. 3 , 4 However, energy loss due to radiation and absorption in MNPs can be serious, and thus the design of low loss MNP waveguides become a priority concern. 5-11To investigate the waveguide modes of periodic MNP chains, some authors calculated the dispersion relations. 2,[12][13][14][15][16][17] In the presence of dissipation, the guided modes have a finite life-time, and cannot be described completely by a simple dispersion relation between the real ω and real k . It is customary to allow either one of ω and k to be a complex number. Operationally, this requires root searching of a complex function in the complex number plane. Such kind of root searching is time consuming, especially when full dynamic effect is considered. Some authors, therefore, only calculate the dispersion relation within quasistatic approximation. 2,14To include the retardation effect associated with radiation, other authors use the quasistatic dipole approximation (DA) with radiation correction. 12,13,15,16 However, such an approximation is not accurate for particle size greater than 50 nm when absorption loss is not negligible. 18Here, we demonstrate an eigen decomposition (ED) method 19,20 with a more accurate dynamic DA 21,22 to account for material properties. Such method does not require a root searching in the complex plane. The method consider both ω and k on the real line and, at the same time, shows effectively the qualities of the guided modes.We begin by considering an infinite periodic chain of MNPs along the z -direction, with particle diameter d = 50 nm and center-to-center distance of adjacent particles a = 75 nm.

Localization characteristics of two-dimensional quasicrystals consisting of metal nanoparticles

“…11,12 For those modes that have Bloch k vectors with magnitudes less than c h , the mode can couple with free photons and the lifetime will be finite due to radiation loss. If k Ͼ c h , the mode becomes a guided mode ͑confined in the 2D plane͒ that has no radiation loss.…”

“…We first note that the characteristics of electromagnetic ͑EM͒ states of two-dimensional ͑2D͒ arrays of MNPs have already received some attentions in the literature. 11,12,[17][18][19][20] In previous studies on the wave transport in electronic and photonic systems, the spatial localization of eigenmodes have been the main focus of theoretical analysis. [21][22][23] The electronic system has true eigenmodes that are derived from bound states.…”

Analytical study of the plasmonic modes of a metal nanoparticle circular array

“…We note that the only approximation that we use in this paper is the dynamic dipole approximation. 23,24 Retardation effects are included via the dynamic Green's function and material polarizability.…”

Formation of nonreciprocal bands in magnetized diatomic plasmonic chains

“…We denote the dipole moment of nanoparticle in the nth unit cell as p n;σ where σ = A or B for type A and B particles, respectively. These dipole moments satisfy a set of self-consistent equations, known as the coupled dipole equations [14][15][16]:…”