Abstract
The finite difference time domain (FDTD) method is a grid-based, robust, and straightforward method to model the optical properties of metal nanoparticles (MNPs). Modelling accuracy and optical properties can be enhanced by increasing FDTD grid resolution; however, the resolution of the grid size is limited by the memory and computational requirements. In this paper, a 3D optimized FDTD (OFDTD) was designed and developed, which introduced new FDTD approximation terms based on the physical events occurring during the plasmonic oscillations in MNP. The proposed method not only required ~52% less memory than conventional FDTD, but also reduced the calculation requirements by ~9%. The 3D OFDTD method was used to model and obtain the extinction spectrum, localized surface plasmon resonance (LSPR) frequency, and the electric field enhancement factor (EF) for spherical silver nanoparticles (Ag NPs). The model’s predicted results were compared with traditional FDTD as well as experimental results to validate the model. The OFDTD results were found to be in excellent agreement with the experimental results. The EF accuracy was improved by 74% with respect to FDTD simulation, which helped reaching a near-unity OFDTD accuracy of ~99%. The λLSPR discrepancy reduced from 20 nm to 3 nm. The EF peak position discrepancy improved from ±5.5 nm to only ±0.5 nm.
Highlights
When an external electric field, such as the one associated with the electromagnetic spectrum, is applied, the electrons and positively charged nuclei are polarized. This displaces the electron cloud from positively charged nuclei, and, as a result, forms a dipole, which creates a restoring force and oscillates with a certain frequency known as plasmon frequency. It is known as the electromagnetic excitation and oscillation of the conduction electron, which is characterized by the resonance frequency of the metal nanoparticles (MNPs), referred to as surface plasmon resonance (SPR) [2]
This confines the electromagnetic excitation electric field in the subwavelength range and, induces a remarkable local amplification in electric field intensity. This enhanced electric field strength decay from MNP surface is broadly divided into near-field and far-field response of MNPs. The latter is responsible for macroscopic properties such as the color resulting from the MNP, while the near-field
The finite difference time domain (FDTD) method is an excellent numerical algorithm to solve Maxwell’s equations, its required memory, calculation, and accuracy are dependent on the Yee grid properties of the modelled device
Summary
When an external electric field, such as the one associated with the electromagnetic spectrum, is applied, the electrons and positively charged nuclei are polarized This displaces the electron cloud from positively charged nuclei, and, as a result, forms a dipole, which creates a restoring force and oscillates with a certain frequency known as plasmon frequency. It is known as the electromagnetic excitation and oscillation of the conduction electron, which is characterized by the resonance frequency of the MNP, referred to as surface plasmon resonance (SPR) [2]. In small and sub-wavelength MNPs, plasmonic resonance is confined locally, and known as LSPR This confines the electromagnetic excitation electric field in the subwavelength range and, induces a remarkable local amplification in electric field intensity. The latter is responsible for macroscopic properties such as the color resulting from the MNP, while the near-field
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