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UPML-ABC of dispersive materials for the unconditionally stable 2-D WLP-FDTD method
摘要： In this paper, uniaxial anisotropic perfectly matched layer (UPML) absorbing boundary condition (ABC) of dispersive materials is presented for 2-D finite-difference time-domain (FDTD) method with weighted Laguerre polynomials (WLP). Taking advantage of the auxiliary differential equation (ADE) technique, our proposed algorithm avoids not only the complicated formulations but also the convolution integral. Using ADE scheme, the relationship between field components and auxiliary differential variables is derived in Laguerre domain. Substituting auxiliary differential variables into UPML-ABC, the electric field E of order q can be expressed directly by magnetic field H in Laguerre domain. Inserting magnetic field H of order q into electric field, and using central difference scheme, the formulations of uniaxial anisotropic dispersive media PML are obtained. One numerical example of wave propagation in 2-D dispersive materials is simulated. Numerical results validate the efficiency of the presented method.
关键词： finite-difference time-domain (FDTD),weighted laguerre polynomials (WLP),uniaxial anisotropic dispersive materials,perfectly matched layer (PML),Auxiliary differential equation (ADE)
更新于2025-09-23 15:23:52
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[IEEE 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Rome, Italy (2019.6.17-2019.6.20)] 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring) - Spectrally Tunable Germanium-on-silicon Photodetectors: Design and Simulations
摘要： To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity. Two situations are considered. 1) The skin depth is smaller than the thickness of the conductive volume. 2) The skin depth is larger than the thickness of a thin conductive sheet. For the first situation, a surface impedance boundary condition (SIBC) is employed, wherein the surface impedance usually exhibits a complex relation with the frequency. To incorporate the SIBC into DGTD, the surface impedance is first approximated by rational functions in the Laplace domain using the fast relaxation vector-fitting (FRVF) technique. Via inverse Laplace transform, the time-domain DGTD matrix equations can be obtained conveniently in integral form with respect to time t. For the second situation, a transmission IBC (TIBC) is used to include the transparent effects of the fields. In the TIBC, the tangential magnetic field jump is related with the tangential electric field via the surface conductivity. In this work, a specifically designed DGTD algorithm with TIBC is developed to model the graphene up to the terahertz (THz) band. In order to incorporate the TIBC into DGTD without involving the time-domain convolution, an auxiliary surface polarization current governed by a first-order differential equation is introduced over the graphene. For open-region scattering problems, the DGTD algorithm is further hybridized with the time-domain boundary integral (TDBI) method to rigorously truncate the computational domain. To demonstrate the accuracy and applicability of the proposed algorithm, several representative examples are provided.
关键词： finite integral technique (FIT),surface/transmission impedance boundary condition (SIBC/TIBC),vector-fitting,time-domain boundary integral (TDBI) algorithm,Auxiliary differential equation (ADE),graphene,discontinuous Galerkin time-domain (DGTD) method
更新于2025-09-23 15:19:57
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Stability-Improved ADE-FDTD Method for Wideband Modeling of Graphene Structures
摘要： A stability-improved auxiliary differential equation (ADE) finite-difference time-domain (FDTD) method is developed for broadband modelling graphene-based devices in this paper. By introducing an electric polarization term characterized with an auxiliary equation, the graphene sheet is incorporated into the FDTD method without decreasing the Courant–Friedrich–Levy (CFL) number. The stability condition is analyzed and numerical experiments are carried out to validate the proposed method with analytical results. It is further applied to investigate some properties of metal-graphene Split-Ring Resonator (SRR).
关键词： Auxiliary differential equation (ADE),split-ring resonator (SRR),wideband,graphene,finite-difference time-domain (FDTD)
更新于2025-09-04 15:30:14