Finite-Difference Time-Domain Study of Guided Modes in Nano-plasmonic Waveguides

TL;DR

This paper develops a novel conformal dispersive FDTD method for modeling 1-D plasmonic waveguides with curved nano-structures, enabling accurate simulation of guided modes in silver cylinder arrays at optical frequencies.

Contribution

It introduces the first conformal dispersive FDTD scheme for curved plasmonic structures, combining effective permittivities with ADE for stable, accurate modeling.

Findings

Dispersion diagrams match frequency domain results.

Adding elements or changing geometry alters dispersion.

Silver cylinders can effectively guide light via surface plasmons.

Abstract

A conformal dispersive finite-difference time-domain (FDTD) method is developed for the study of one-dimensional (1-D) plasmonic waveguides formed by an array of periodic infinite-long silver cylinders at optical frequencies. The curved surfaces of circular and elliptical inclusions are modelled in orthogonal FDTD grid using effective permittivities (EPs) and the material frequency dispersion is taken into account using an auxiliary differential equation (ADE) method. The proposed FDTD method does not introduce numerical instability but it requires a fourth-order discretisation procedure. To the authors' knowledge, it is the first time that the modelling of curved structures using a conformal scheme is combined with the dispersive FDTD method. The dispersion diagrams obtained using EPs and staircase approximations are compared with those from the frequency domain embedding method. It is shown that the dispersion diagram can be modified by adding additional elements or changing geometry of inclusions. Numerical simulations of plasmonic waveguides formed by seven elements show that row(s) of silver nanoscale cylinders can guide the propagation of light due to the coupling of surface plasmons.