An ADI-FDTD Formulation With Modified Lorentz Dispersion for the Study of Plasmonic Structures

Abstract

This letter presents an alternating-direction implicit finite-difference time-domain scheme for the efficient study of plasmonic systems. The material dispersion is described by generalized modified Lorentzian terms and it is implemented via the auxiliary differential equations technique employing an order reduction. The computational domain is backed by a properly designed convolution perfectly matched layer. The efficiency of the proposed method is validated in benchmark examples and its unconditional stability is evidenced by the Fourier method.Index Terms-Alternating-direction implicit finite-difference time-domain method, auxiliary differential equations, dispersive media, plasmonic circuitry.

Implementation of the Crank‐Nicolson Douglas‐Gunn finite‐difference time domain with complex frequency‐shifted perfectly matched layer for modeling unbounded isotropic dispersive media in two dimensions

“…where ( ) r ε ω is the complex relative permittivity of the isotropic dispersive media. In the following, the implementations of the CNDG-CFS-PML based on the ADE method [34][35][36] 5and 8- (14) in [32].…”

An HIE‐FDTD algorithm for dispersive media with modified Lorentz model

“…[6][7][8][9][10] Recently, a general model for dispersive media, the modified Lorentz model 11,12 that can cover the common models such as the Debye model, Drude model, and Lorentz model for dispersive media was proposed and has attracted great attention. [11][12][13][14][15][16][17][18] In this letter, we extend the HIE-FDTD method to simulate dispersive media with modified Lorentz model based on auxiliary difference equations (ADEs). The correctness and computational efficiency of the proposed method are verified by numerical experiments.…”

A unified 3‐D ADI‐FDTD algorithm with one‐step leapfrog approach for modeling frequency‐dependent dispersive media

“…In Shibayama et al, a locally one‐dimensional (LOD) scheme is introduced for the modeling of metal‐insulator‐metal (MIM) plasmonic circuits with Drude mode while in Jung and Teixeira, the ADI‐FDTD method is developed to study the surface plasmon resonance utilizing the Drude‐Lorentz model. Additionally, a novel ADI‐FDTD method with modified Lorentz model is proposed to simulate the plasmonic structures . Simultaneously, a more efficient auxiliary differential equations (ADE) technique, which uses two first‐order differential equations instead of one second‐order differential equation to describe the constitutive relation between the electric polarization ( P ) and the electric field ( E ).…”

“…Additionally, a novel ADI-FDTD method with modified Lorentz model is proposed to simulate the plasmonic structures. 14,15 Simultaneously, a more efficient auxiliary differential equations (ADE) technique, which uses two first-order differential equations instead of one second-order differential equation to describe the constitutive relation between the electric polarization (P) and the electric field (E). Thus, the instability problems due to previous time step field components are avoided in each update cycle.…”