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...

Optical activity is the ability of chiral materials to rotate linearly polarized electromagnetic waves. A knotted chiral metamolecule is introduced here that exhibits strong optical activity corresponding to a 90° polarization rotation of the incident waves. More importantly, the torus knot structure is intrinsically chiral and multifold axisymmetric. Consequently, the observed polarization rotation behavior is found to be independent of how the incident wave is polarized. The metamolecule is fabricated through selective laser melting and experimentally validated in the microwave spectrum. This work represents the first ever metamolecule to be reported that is intrinsically axisymmetric and capable of simultaneously exhibiting…

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

The quarter-wavelength matching technique is widely used because it minimizes the reflection while it maximizes the transmission. The recently introduced antireflection temporal coatings (ATCs) [Optica7, 323 (2020)10.1364/OPTICA.381175] have been considered as its temporal analog. However, our study shows that by introducing an ATC, not only will the reflection be reduced but also the transmission. This phenomenon is opposite its spatial counterpart, which indicates that ATCs are more than simply a temporal dual of quarter-wavelength matching. This is a direct consequence of the different physical phenomena that are manifested in the temporal and spatial domains. Read more Wending Mai,* Jingwei Xu,…

It is well known that control over the polarization of electromagnetic waves can be achieved by utilizing artificial anisotropic media such as metamaterials. However, most of the related research has been focused on time-invariant systems. Inspired by the concept of temporal boundaries, we propose a method to realize polarization conversion in real time by employing time-variant materials, whose permittivity or permeability switches between isotropic and anisotropic values. The criteria for complete polarization conversion are studied for several polarization angles, both analytically and numerically. Read more Jingwei Xu,* Wending Mai, AND 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…

Prism DGTD simulation toolkit with GDM for pixelized metasurface This simulation package is the prism-based Discontinuous Galerkin Time Domain method with General Dispersion Model for analysis of gold pixelized metasurfaces. How to use it: Open "runme.m" in MATLAB. Modify the time span and the Geo matrix "A". The geometry is a 2-fold symmetric unit cell with a period of 400 nm. The unit cell can be patterned by several gold pixels, measures 50 nm × 50 nm × 20 nm. In order to add gold padding, one could input the number of padding, and then the index numbering. The index…

Planar photonics technology is expected to facilitate new physics and enhanced functionality for a new generation of disruptive optical devices. To analyze such planar optical metasurfaces efficiently, we propose a prismatic discontinuous Galerkin time domain (DGTD) method with a generalized dispersive material (GDM) model to conduct the full-wave electromagnetic simulation of planar photonic nanostructures. Prism-based DGTD allows for triangular prismatic space discretization, which is optimal for planar geometries. In order to achieve an accurate universal model for arbitrary dispersive materials, the GDM model is integrated within the prism-based DGTD. As an advantage of prismatic spatial discretization, the prism-based DGTD with…

Stroke is a dangerous disease with a high recurrence rate. Therefore, postoperative patients need timely monitoring of stroke conditions in their rehabilitation stage for early treatment. Recent studies in biomedical imaging have shown that strokes produce variations in the electric permittivity of brain tissues, which can be detected by microwave imaging techniques. Assuming that we have obtained the image of electromagnetic parameters in previous treatment, we can use differential imaging to detect the bleeding points when stroke recurs. However, the computational cost of traditional methods could be prohibitively large, as the bleeding points are small in the early stages of…

Planar periodic structures are widely utilized in microwave applications. The prism-based Discontinuous Galerkin time domain (DGTD) method is optimal to cope with the modeling challenges associated with these planar structures. In this work, we modified the prism based DGTD to take lossy materials into account. A ring-shaped frequency selective surface (FSS) is studied as a representative numerical example. When submerged into water, the operating frequency of the FSS is lowered dramatically. We test the algorithm with distilled and tap water of different conductivity. Results of both examples compare well with references of commercial software, which validates the accuracy of the…

The Discontinuous Galerkin Time-Domain (DGTD) method has gain great popularity for its capability of obtaining highly accuracy, flexibility, efficiency and parallel-computing. Different basis functions have their own merit in their advantageous applications. In this work, we focus on reseaches of DGTD’s basis functions and their advantageous applications. We firstly designed a nodal high-order based DGTD algorithm and studied its improvement on accuracy. As we known, an ultra-dense-mesh h-refinement will lead to the low-frequency breakdown which has been studied for decades. However, for highorder p-refinement, it is conventionally regarded that the accuracy is only limited by the basis orthogonality. While in…

Power integrity (PI) problem is essential when analyzing high speed signal passing through power ground. The fundamental mode in power ground is the zero-order parallel plate mode, which is capable for 2D simplification. However, in areas around anti-pads and other z-axis discontinuities, 3D algorithm has to be adopted to improve the accuracy. A hybrid 2D／3D discontinuous Galerkin time domain (DGTD) method has advantage on both accuracy and efficiency, thus is effective to cope with such full wave simulations. The 2D and 3D domains share the same triangular prism mesh. With appropriated basis functions, different domains can couple with each other…

Chiral mirrors are a class of metamaterials that reflect circularly polarized light of a certain helicity in a handedness-preserving manner, while absorbing circular polarization of the opposite handedness. However, most absorbing chiral mirrors operate only in a narrow frequency band, as limited by the causality principle. Instead of absorbing the undesired waveform, here we propose a transparent chiral mirror that allows undesired waves to pass through. In particular, the handedness-preserving band of the transparent chiral mirror is free of the causality limit, thus enabling broadband functionality. Furthermore, since electromagnetic waves outside the handedness-preserving band may transmit through the proposed chiral…

In this letter, we develop a prism-based discontinuous Galerkin time-domain (DGTD) algorithm with simplified periodic boundary conditions (PBCs) to analyze infinite doubly periodic frequency selective surfaces (FSS). Most FSS structures contain patterned planar conductive layers and supporting dielectric layers. These layers are very thin compared to the wavelength. Therefore, general tetrahedral discretization of space will unnecessarily increase the number of mesh elements, as well as the number of unknowns. Instead, we propose using prismatic elements, which are more optimal for planar structures, resulting in less unknowns, less memory usage, and higher efficiency. The accuracy of the proposed prism-based DGTD method…

The zeroth-order parallel-plates mode dominates in most parts of the power-ground plates pairs. Domains with such mode distribution can be solved by a simplified 2D algorithm, while only higher-order modes require 3D computation. For DGTD method, different domains can be decoupled with each other by the numerical flux. To distinguish 2D and 3D domains properly, the field distribution has to be known before it is actually solved. This paradox is walked around by a predictive criterion which roughly predicts tn's field distribution based on tn-1's results. Here we introduce an adaptive criterion based on the CFL condition to realize such…

The 2-D/3-D hybrid discontinuous Galerkin time-domain (DGTD) method is efficient to deal with structures that contain elements capable of 2-D simplification. To separate 2-D elements from 3-D ones, a criterion for approximation error manipulation is required. However, in the latest reported technique, this kind of criterion is derived from the causality principle and the Courant–Freidrichs–Lewy constraint, and thus is indirect and inessential to 2-D simplification. As a result, some elements capable of 2-D simplification are unnecessarily flagged as 3-D ones, deteriorating efficiency dramatically. Moreover, controlling absolute error, the traditional criterion is not flexible for structures with complex mode distribution. In…

The 2-D/3-D hybrid discontinuous Galerkin time domain (DGTD) method is efficient to deal with power-ground structures that contain elements capable of 2-D simplification. To generalize the capability of the 2-D/3-D DGTD method to deal with various complex structures in engineering design, a criterion is proposed to differentiate 2-D and 3-D elements adaptively. For domain decomposition criterion at time steptn, the electromagnetic field distribution at the previous time steptn-1is analyzed to identify the zeroth-order parallel-plates mode domain. Compared with the classical static distance criterion, this new adaptive criterion makes the approximation error under control, thus enhancing the stability. The 2-D simplification…

A hybrid 2-D and 3-D discontinuous Garlerkin time-domain (DGTD) method is proposed for transient analysis of multiple arbitrarily shaped antipads in a dispersive parallel-plate pair. In the proposed hybrid method, the domains where only the zeroth-order parallel-plate mode exists are modeled by the 2-D DGTD, and the remaining domains are modeled by the 3-D DGTD. Each element is independent with others, thus easily parallelizable. Because higher order modes will propagate in the parallel-plate pair, the spatial domain decomposition should be time-dependent. For domain decomposition criterion at time step $\text t_\text n$ , the electromagnetic field distribution at the previous time…

Electromagnetic radiation for a printed circuit board (PCB) midplane connector is studied in this paper. By applying integral-equation (IE) based method and characteristic mode (CM) analysis, the current is split into radiating and non-radiating ones. The radiated power from each part of the structure can be quantified using the radiating current. Therefore, the radiation hot spot can be identified for both edge-side coupled and broad-side coupled connectors. Furthermore, the radiation characteristics for these connectors are compared. Read more Ying S. Cao, Xu Wang, Wending Mai, Yansheng Wang, Lijun Jiang, Albert E. Ruehli, Shiquan He, Huapeng Zhao, Jun Hu, Jun Fan,…

An efficient hybrid 3D and 2D discontinuous Garlerkin time-domain (DGTD) methods is proposed for signal/power integrity analysis of multiple arbitrarily shaped anti-pads in power-ground. The entire structure is decomposed into anti-pad-domain (3D) and plate-domain (2D). Complicated fields exist around anti-pad, yet, in plate domain, only zeroth-order parallel-plate mode exists. Therefore, triangular prism element (3D) could be simplified as triangle element (2D), which has fewer unknowns. The accuracy of the hybrid method has been validated by comparison with commercial software. Its flexibility, and enhancement of efficiency, are also demonstrated. Read more Wending Mai, and Jun Hu

A FSS filter with shorting stubs will be designed in this paper. This filter provides compact design and sharp frequency selectivity by using transmission-zeros, and it is designed for a compact E-plane duplexer. It can be fabricated in a simple and economical way. We simulate the filter with CAD tool, and the tested results show good agreement with the design target. Read more Bin Wang, Qingyuan Wang, Ao Liao, Lifeng Chen and Wending Mai