A novel finite-difference time-domain (FDTD) method is proposed in this article for electromagnetic (EM) wave propagation in time-varying plasma. It is formulated based on the fundamental Newton’s equation of motion, which governs the relationships among the time-varying electron density, current density and electric field. Utilizing the auxiliary differential equation (ADE) FDTD scheme, the method is aptly referred to as the Newton-ADE FDTD method for time-varying plasma. Traditionally, the previous ADE FDTD methods directly apply the time-varying electron density for the plasma frequency in the update equations of current density and electric field. This is inadequate and incorrect in general time-varying plasma conditions. The formulation of the Newton-ADE FDTD method is provided and compared to that of the traditional ADE FDTD method. It is found that the key difference lies in the new compact term being the time-derivative of logarithm of electron density. Two discretization schemes for this term are provided. The Newton-ADE FDTD method is validated based on the matrix exponential method. Novel stability and convergence analyses are provided for the proposed method in time-varying dispersive media. These analyses show that our proposed method is stable and achieves second-order temporal accuracy. Numerical results are presented for various time-varying plasma conditions. It is demonstrated that when the absolute value for time-derivative of logarithm of electron density is large, e.g., greater than the collision frequency, the Newton-ADE FDTD method can provide correct results, while the traditional ADE FDTD method yields significant differences.

The unconditionally stable multiple one-dimensional alternating direction implicit finite-difference time-domain (M1-D ADI-FDTD) method for coupled transmission lines is presented. The differential equations for coupled transmission lines are formulated in compact matrix form. Proper 4 x 4 split matrices are introduced, which feature unconditional stability for the ADI procedures. These matrices also lead to update equations with the left-hand sides involving tridiagonal matrices that can be solved efficiently. The update equations of the M1-D ADI-FDTD method are given, which comprise one implicit and three explicit updates in each procedure. The analytical proof of unconditional stability is also provided based on the von Neumann method. The M1-D ADI-FDTD method allows quick simulation and visualization of electromagnetic fields everywhere along the coupled transmission lines. To demonstrate the usefulness of the M1-D ADI-FDTD method, various coupled line structures for filter and filtering antenna are analyzed using the method.

This letter presents a finite-difference time-domain formulation to model electromagnetic wave propagation in dispersive media using matrix exponential method. The Maxwell's curl equations and the time domain relations between electric fields and auxiliary variables are formulated as a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. Numerical results show that this formulation yields higher accuracy compared to many other previous methods, without incurring additional auxiliary variable and complexity.

The classical impulse invariance method in Z-transform theory is found to be incorrect and inaccurate when the impulse response is discontinuous at initial time t = 0 . Such inaccuracy results in higher numerical errors if it is used to develop the update equations for frequency-dependent finite-difference time-domain (FDTD) methods. In this paper, thorough discussions of corrected impulse invariance method in the realm of Z-transform theory for dispersive media are presented. The correction is shown to be necessary for dispersive media which exhibit discontinuity at t = 0 in the time domain susceptibility function. A (corrected) Z-transform table is provided to facilitate the conversion from frequency to Z domain. With the aid of the table, various formulations of frequency-dependent FDTD update equations using both corrected and classical impulse invariance methods are carried out conveniently. Detailed performance measures such as numerical permittivity, leading error term, dispersion relation, normalized phase and attenuation errors as well as memory storage requirements are included along with some extensive numerical comparisons.

This paper presents the 3-D dispersion analysis of flnite- difierence time-domain (FDTD) schemes for doubly lossy media, where both electric and magnetic conductivities are nonzero. Among the FDTD schemes presented are time-average (TA), time-forward (TF), time-backward (TB) and exponential time difierencing (ETD). It is flrst shown that, unlike in electrically lossy media, the attenuation constant in doubly lossy media can be larger than its phase constant. This further calls for careful choice of cell size such that both wavelength and skin depth of the doubly lossy media are properly resolved. From the dispersion analysis, TF generally displays higher phase velocity and attenuation errors due to its flrst-order temporal accuracy nature compared to second-order ETD and TA. Although both have second-order temporal accuracy, ETD has generally lower phase velocity and attenuation errors than TA. This may be attributed to its closer resemblance to the solution of flrst-order difierential equation. Numerical FDTD simulations in 1-D and 3-D further conflrm these flndings.

The wide avai lability of smart handheld and mobile devices has provided educators with another opportunity to aid the teaching of electromagnetics (EM) courses with touchbased interactivity, allowing seamless teaching and learning. This article explores how mobile devices may be used to enhance students' grasp of EM polarization concepts through a special app designed to provide interactive visualization. It also helps instructors to effectively illustrate many wave polarization topics through various interactive features. By using the app, various polarizations can be better explained with two-dimensional (2-D) and three-dimensional (3-D) animations. Users are allowed to input various wave parameters to see, in real time, how they change the polarization ellipse and/or handedness.