Development of Three-Dimensional Legendre Pseudospectral Time-Domain Method for Electromagnetics and Metal-Nanoparticle Plasmonics

• Main Authors: Bang-Yan Lin, 林邦彥
• Other Authors: 張宏鈞
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/00454250287236089659

博士 === 國立臺灣大學 === 電信工程學研究所 === 97 === In this study, a three-dimensional (3-D) Legendre pseudospectral time-domain (PSTD) algorithm for solving the Maxwell equations is developed to analyze optical properties of single silver nanoparticles and two-dimensional (2-D) silver nanorod arrays. An in-house PSTD parallel program along with three commercial softwares provides a thorough solution from the construction of mesh grids to data post-processing. Our approach starts by conducting an analysis for finding well-posed boundary operators for the Maxwell equations. We then derive equivalent characteristic boundary conditions for common physical boundary constraints. These theoretical results are then employed to construct a pseudospectral penalty scheme which is asymptotically stable at the semidiscrete level. Through verified by a number of cases with exact solutions, the expected convergence patterns of the proposed scheme are observed. Due to inadequacy of the classical Drude model in the visible spectra, a more precise Drude-Lorentz model with carefully chosen parameters is used to characterize the linear dispersive nature of silver form visible to near infrared regime. Numerical validations are conducted based on solving both the near-field and far-field of Mie scattering problem, and expected convergence is observed. With a systematic comparison of near- and far-field behaviors of single silver nanoparticles, the significant differences in peak wavelengths increase and represent red-shifted, and their bandwidths become broader, as particle size increases and the relative permittivity of the surrounding medium has a larger value than the vacuum does. Taking into account such differences provides useful suggestions in designing plasmonic structures. Based on this numerical scheme, a program equivalent to the experimental procedure is constructed for investigating both near- and far-field electromagnetic characteristics of 2-D silver-nanorod quasi-hexagonal arrays embedded in a substrate of anodic aluminum oxide, and the simulated far-field scattering spectra agree with the experimental observations. We show that enhanced electric field is created between adjacent nanorods and, most importantly, far-field scattered light wave is mainly contributed from surface magnetic field, instead of the surface enhanced electric field. The identified near-field to far-field connection produces an important implication in the development of more efficient surface-enhanced Raman scattering substrates.