412 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 8, NO. 3, MAY 2009 An Equivalent Circuit Modeling of an Equispaced Metallic Nanoparticles (MNPs) Plasmon Wire Kyungjun Song and Pinaki Mazumder, Fellow, IEEE Abstract—Based on the electric dipole moment (EDM) model of free oscillating electrons inside a single metallic nanoparticle (MNP), a comprehensive methodology is presented in the paper for calculating the equivalent circuit elements associated with an MNP. To find out the passive circuit elements for the MNP, the electromagnetic (EM) power flows are calculated by deriving the relaxation damping, radiation outflow, host matrix EM coupling, and applied signal interaction. The law of conservation of energy is then used to compute the extended oscillatory equation motion of a spherical MNP. The resonant behavior of a single MNP is represented by a lumped resonant circuit model, where the circuit parameters RLC are derived from the equation of motion of the EDM and EM near-field energy outside the MNP. Finally, equiva- lent circuit of a linearly equispaced MNPs plasmon wire is modeled as a voltage-controlled voltage source by using the nearest surface plasmon interactions. Index Terms—Full-width at half-maximum (FWHM), lumped resonant circuit model, optical interconnect, radiation damping, relaxation damping, surface plasmon (SP), surrounding matrix damping, voltage-controlled voltage source (VCVS). I. INTRODUCTION T HE FEASIBILITY of silicon lasing, photodetection, and cointegration of on-chip optical interconnect has sparked enormous optimism in CMOS very large-scale integration (VLSI) industry because intrachip high-speed binary data trans- fer via high-bandwidth optical waveguides is expected to solve various limitations of conventional metallic wires that are dom- inantly used in intrachip wiring in commercial chips. With ag- gressive device and interconnect scaling, metallic interconnect is witnessing several formidable problems, namely, increasing propagation delay on long global wires, increasing power dis- sipation due to wide-scale insertion of signal boosting buffers, and intrinsic coupling between wires causing signal-dependent time delays and logical faults. Optical interconnect, in contrast, offers very small interconnect delay, high bandwidth of data transfer, significantly reduces power consumption by obviat- ing the need of repeaters, and virtually eliminates the coupling Manuscript received October 20, 2006. First published September 19, 2008; current version published May 6, 2009. This work was supported in part by the Air Force Office of Scientific Research (AFOSR) grant. The review of this paper was arranged by Associate Editor H. Misawa. K. Song is with the Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2121 USA (e-mail: songk@umich.edu). P. Mazumder is with the Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2121 USA (e-mail: mazum@eecs.umich.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNANO.2008.2005493 noise and electromagnetic (EM) interference between various adjacent wires [1]. However, light cannot propagate along the conventional waveguide if it is smaller than the wavelength of the optical signal [2]. As an alternative to solving the diffraction limit of optical signals, surface plasmon (SP) is now being extensively pursued for fabricating nanoscale photonic devices [3]. Notably, a metal has a negative dielectric permittivity in the optical spec- trum, thereby enabling 1-D or 2-D SP wave to be propagated over subwavelength metallic structures [2], [4]. Especially, the selective optical absorption of a spherical-like metallic nanopar- ticle (MNP) allows us to develop the next-generation photonic devices such as subwavelength waveguides and SP biosen- sors. With the development of nanofabrication technology such as electron beam lithography (EBL) [5], the ordered metallic nanostructures can now be built to manipulate the efficient SP coupling between EM and the metallic surface [6], [7]. Some analytical calculations [7], [8] and numerical approaches [6], [9] have been developed to describe EM signal energy transfer along the MNPs. In addition, equivalent nanocircuit elements of MNP in the optical domain have been recently developed [10], [11]. These equivalent nanocircuit elements allow us to investigate future MNPs applications such as subwavelength imaging [12], quantum optics [13], nanoscale waveguide [6], [7], and near- field optics [14]. However, these models [10], [11] have some limitations to describe damping terms such as radiation damping and host matrix coupling effects. Furthermore, applied current element from optical signal interaction has not been presented analytically. In this paper, we focus on rigorous way to develop the equiv- alent circuit modeling of an MNP and an equispaced linear MNPs array based on the electric dipole moment (EDM). First, to develop the inductance and capacitance elements, the internal oscillation energy and EM near-field energy can be calculated based on the EDM. Second, to describe the resistance elements and the applied signal, four main power flows including re- laxation loss, radiation outflow emission, host matrix coupling, and applied signal interaction are calculated by using the rigor- ous EM analysis. Third, the conservation of energy law leads to computation of the relaxation, radiation, and surrounding matrix damping frequency. Fourth, the resonant behavior of SP modes in a single MNP is represented by a lumped SP resonant circuit model. The lumped resonant circuit parameters such as capaci- tance, inductance, and conductance are calculated by using the equation of motion of the EDM, electric potential, and EM near- field energy. Finally, nanoelements of an MNP are extensible to the equivalent circuit modeling for a closely equally spaced MNPs array as a voltage-controlled voltage source (VCVS) 1536-125X/$25.00 © 2009 IEEE