Opening a new door to tailoring electromagnetic (EM) waves, temporal boundaries have attracted the attention of researchers in recent years, which have led to many intriguing applications. However, the current theoretical approaches are far from enough to handle the complicated temporal systems. In this paper, we develop universal matrix formalism, paired with a unique coordinate transformation technique. The approach can effectively deal with temporally stratified structures with complicated material anisotropy and arbitrary incidence angles. This formulation is applied to various practical systems, enabling the solution of these temporal boundary related problems in a simple and elegant fashion, and also facilitating…

Temporal boundary value problems (TBVPs) provide the foundation for analyzing electromagnetic wave propagation in time-varying media. In this paper, we point out that TBVPs fall into the category of unbounded initial value problems, which have traveling wave solutions. By dividing the entire time frame into several subdomains and applying the d’Alembert formula, the transient expressions for waves propagating through temporal boundaries can be evaluated analytically. Moreover, unlike their spatial analogs, TBVPs are subject to causality. Therefore, the resulting analytical transient solutions resulting from the d’Alembert formula are unique to temporal systems. Read more Wending Mai and Douglas H. Werner

Various dispersion models can be expressed as special cases of the Generalized Dispersion Model (GDM), which is composed of a series of Pade polynomials. While important for its broad applicability, we found that some materials with Drude dispersive terms can be accurately modeled by mixing a 1st order Pade polynomial with an extra conductivity term. This conductivity term can be separated from the auxiliary differential equation (ADE). Therefore, the proposed mixed-order model can achieve the same accuracy with fewer unknowns, thus realizing higher computational efficiency and lower memory consumption. For examples, we derive the model parameters and corresponding numerical errors…

Materials with time-varying permittivity are an emerging research area in the electromagnetics and optics communities. From Maxwell's equations, the electric displacement (D) must be continuous in the time domain. However, this requirement is not satisfied for some conventional time domain solvers, which were developed for time-invariant simulations. Here we briefly review several commercial and open-source software packages. Some of them employ a so-called time-static simplification, which works well for time-invariant materials but will fail for time-varying materials. Read more Wending Mai*, Jingwei Xu, Douglas H. Werner

We develop a discontinuous Galerkin time domain (DGTD) algorithm with an experimentally validated modified Debye model (MDM) to take metal dispersion into consideration. The MDM equation is coupled with Maxwell’s equations and solved together through the auxiliary differential equation (ADE) method. A Runge-Kutta time-stepping scheme is proposed to update the semi-discrete transformed Maxwell’s equations and ADEs with high order accuracy. Then we employ the proposed algorithm to analyze an infinite doubly periodic frequency selective surface (FSS) operating in the optical regime that exhibits transmission enhancement due to the surface plasmatic effect. The accuracy and the efficiency enhancements are validated through…

We proposed a new methodology to detect the neurological degenerative diseases in the early stage. These neurological degenerative diseases often occur along with some mark proteins. Instilled by golden nanoparticles, these protein cells can demonstrate optical activity because of their helical structure. In order to detect these mark proteins, we developed a numerical method to simulate the electromagnetic response upon chiral (bi-isotropic) material. The chiral proteins in human head can therefore be detected. The primitive simulation results suggest that the proposed method would be capable of carrying out in vivo detection of neurological degenerative disease using microwaves. Read more Wending…