A General FDTD Algorithm Handling Thin Dispersive Layer

Abstract

Abstract-A novel general technique for treating electrically thin dispersive layer with the finite difference time domain (FDTD) method is introduced. The proposed model is based on the modifying of the node update equations to account for the layer, where the electric and magnetic flux densities are locally averaged in the FDTD grid. Then, based on the characteristics that the complex permittivity and permeability of three kinds of general dispersive medium models, i.e., Debye model, Lorentz model, Drude model, the permittivity and permeability can be formulated by rational polynomial fraction in jω; the conversion equation from frequency domain to time domain (i.e., jω replaced by ∂/∂t) and the shift operator method are then applied to obtain the constitutive relation at modified electrical points, and the time-domain recursive formulas for D and E, B and H available for FDTD computation are obtained. Several numerical examples are presented, indicating that this scheme possesses advantages such as fine generalization, EMS memory and time step saving, and good precision.Corresponding author: B. Wei (bwei@xidian.edu.cn). 244Wei et al.

Subcell Modeling of Frequency-Dependent Thin Layers in the FDTD Method

“…This is a situation currently encountered in bioelectromagnetism where thin layers are placed between thick media. Such problems cannot be addressed with [11], [12] that deal with only one dispersive layer surrounded with a vacuum. The proposed method relies on the application of the integral form of the Maxwell-Ampere equation and the solution of a set of auxiliary equations.…”

“…They can address dielectric and lossy materials where the real permittivity and the conductivity are not frequency dependent, and they assume that the layer is thin with respect to the wavelength and the skin depth. More recently, methods relying on the same assumption have been reported [11], [12] to account for layers where the permittivity and the permeability are frequency dependent complex numbers. And to address the opposite situation of [6]- [12], that is the case where the skin depth in the layer is shorter than its thickness, there exist other thin layer methods based on the surface impedance boundary condition concept, as the recent work [13].…”

Implementation of the FDTD Method Based on Lorentz-Drude Dispersive Model on Gpu for Plasmonics Applications

“…In order to model them accurately, different dispersive models have been incorporated into Maxwell equations [13,[16][17][18][19][20][21][22][23][24][25][26][27][28]. Most of the available dispersive models are in frequency domain, so as to make them consistent with time domain methods different approaches such as recursive convolution (RC), piecewise linear recursive convolution (PLRC), z-transform and auxiliary differential equation (ADE) [13,18,[24][25][26] are used.…”

Specialty Fibers Designed by Photonic Crystals

“…PWE is also a good numerical method for calculating photonic band gap in periodic structures. Therefore, we have analyzed and modeled the PCF structures by the FDTD and the PWE methods [26][27][28][29][30][31][32].…”