Modeling optical energy transfer along passive and active chains of metal nanoparticles

Abstract

Controlling light in the nanoscale has significant uses for the ultracompact and ultrafast communication interconnects required for on-chip data networks. Of the many routes pursued to achieve this goal, employing surface plasmon polaritons (SPPs) sustained by chains of closely spaced metal nanoparticles appears to offer sound potential. The present research was undertaken with the aims of (i) studying the SPP guiding properties of metal nanoparticle chains (MNCs) through detailed theoretical modeling and analysis; and (ii) establishing practical design rules that can aid the construction of efficient MNC-based SPP guiding structures. Modeling SPP guidance along chains of linearly arranged nanoparticles allows a number of fundamentally important issues to be addressed related to their theoretical treatment. The propagation characteristics (dispersion and attenuation) of SPPs guided along a linear chain are governed by SPPs' dispersion relation, whose solutions yield the dependency between the frequency and wave number of the guided modes. These solutions can generally be expressed by taking either frequency or wave number as complex numbers. In contrast to previous studies, which have focused solely on the solutions with complex frequency, the present study reveals that complex wave number solutions are the appropriate choice for the accurate description of SPP features. The mathematical relationship between the two solutions is established and the complex frequency solution is shown to be applicable only when SPPs experience little or no attenuation. Substantial simplifications to the method of obtaining solutions are also achieved through the derivation of approximate analytical solutions in the small-attenuation limit. A notable assumption in past studies has been to neglect the effect of the finite size of nanoparticles in the mathematical model of an MNC. It is demonstrated here that the finite-size effects play a significant role in governing SPP characteristics and must be accounted for when treating MNCs found in practical situations. Analysis of SPPs' properties through solutions to the dispersion relation reveal several novel features regarding their dependency on various material and structural parameters of MNCs. For example, the reduction of the effective cross-section of guided modes by compressing nanoparticle size increases SPPs' attenuation and causes their spectra to blue-shift. When optical gain is supplied to a nanoparticle chain by either embedding the chain in an active medium or by introducing active materials into the nanoparticles, significant reduction of SPP attenuation is achievable with practically available gain levels (e.g., gains of the order of 10 3 cm −1 enable SPP propagation length to be increased from about 1 μm to more than 50 μm). Comparison of the two gain supplying methods suggests that embedding the chain in an active medium is the most efficient approach to suppress SPP attenuation. Employing the dispersion relation to model SPP propagation is not possible when an MNC has irregularities, such as imperfect nanoparticle sizes or bends in the guided path. To address such scenarios, a formulation capable of treating an arbitrarily-arranged chain of nanospheres is derived. The typical excitation source of a nanoparticle chain&#8210a localized source, such as a nanotip of a tapered fiber or metal probe&#8210is incorporated into the formulation. The dependence of SPP properties on the imperfections of nanoparticles is examined and a number of important features of SPP routing through MNC-bends are identified. SPP guidance through a power splitter formed by a Y-shaped nanoparticle chain is also analyzed. An additional outcome of the research is the development of a novel formulation for the finite-difference time-domain (FDTD) method. When computationally modeling optical devices/structures that involve metals or, generally, any linear dispersive material, conventional FDTD formulations have the drawback of being unable to accommodate arbitrary dispersion models. This is compounded by the fact that when the dimensions of the modeled structures exceed a computationally manageable grid, the perfectly-matched-layers (PMLs) that must be employed to absorb spurious reflections from the grid boundaries need to be tailored for the different models. The proposed FDTD formulation eliminates these deficiencies by incorporating a generic dispersion model to the FDTD algorithm and a unified PML applicable to all practically useful media.