FDTD modeling of wave propagation in dispersive media by using theMobius transformation technique

This paper introduces a technique for finite-difference time-domain modeling of wave propagation in general Mth-order dispersive media. Ohm's law in the Laplace domain with an Mth-order rational model for the complex conductivity is considered as a constitutive relation. In order to discretize this model, the complex conductivity is mapped onto the Z-transform domain by means of the Mobius transformation. This leads finally to a set of difference equations that is consistent with Yee's scheme. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The numerical stability problem is discussed and the numerical dispersion equation for Mth-order media is given     

A ray-tracing method for modeling indoor wave propagation andpenetration

A ray-tracing method for waves inside buildings is presented. Ray tubes are used to model the wave propagation and penetration and all the significantly reflected and transmitted ray tubes from interfaces are included. Also, the cross sections of the ray tubes at the field points are evaluated to find the spreading factors of the waves and then the geometrical optics (GO) contributions at the locations of the receiving antenna. A program has been developed according to this ray-tracing technique that can be applied to simulate waves transmitted through and reflected from electrically large complex 2D and 3D bodies. To verify this ray-tracing program, 2D moment method (MM) solutions for wave propagating in a two-room structure and also through a stair-shaped wall above a lossy ground are used to compare with those obtained from the ray tracing. Besides, comparisons of field measurements and ray-tracing simulations at 900 and 1800 MHz performed in a corridor on different floors and inside a staircase are shown. The effective complex dielectric constants of the buildings determined from a free-space method are employed in the simulations and a vector network analyzer is used for the field measurements. Good agreements are obtained. In addition, measured results for waves penetrating an exterior wall with metal-framed windows at 1290 MHz are employed to test the ray-tracing solutions, which indicate that scattering from the metal frames may be significant for field points near the windows. This ray-tracing program can be applied to evaluate the channel characteristics for the indoor wireless communications     

A novel dispersive FDTD formulation for modeling transient propagation in chiral metamaterials

Chiral media engineered for applications at microwave frequencies can be described as metamaterials composed of randomly oriented helices (with sizes typically less than a wavelength) embedded within an achiral background that is characterized by its permittivity and permeability. Chiral metamaterials embody properties of magnetoelectric coupling and polarization rotation. Chiral media are also highly dispersive and no effective full-wave time domain formulation has been available to simulate transient propagation through such an important class of metamaterials. A new finite-difference time-domain (FDTD) technique is introduced in this paper to model the interaction of an electromagnetic wave with isotropic dispersive chiral metamaterials, based on the implementation of a wavefield decomposition technique in conjunction with the piecewise-linear recursive convolution method. This formulation represents the first of its kind in the FDTD community. The FDTD model is validated by considering a one-dimensional example and comparing the simulations with available analytical results. Moreover, the FDTD technique is also used to investigate the propagation of electromagnetic waves through multilayered metamaterial slabs that include dispersive chiral and double-negative media. Hence, this model enables the investigation of complex dispersive metamaterials with magnetoelectric coupling and double-negative behavior as well as facilitates the exploitation of their unique properties for a variety of possible applications.     

FDTD modeling of scatterers in stratified media

The FDTD technique is well suited for calculating the fields scattered by buried objects when the sources are close enough to the air/ground interface so that they can be incorporated into the solution space. Difficulties arise, however, when the sources are far from the interface since the total fields in the solution space are not all outgoing waves. Using well-known formulas for the fields transmitted and reflected by stratified media, this paper discusses a method whereby the fields scattered by a buried object can be easily calculated by the FDTD technique when the incident field is a plane wave     

BI-FDTD: a novel finite-difference time-domain formulation for modeling wave propagation in bi-isotropic media

This paper presents a newly developed finite-difference time-domain (FDTD) technique, referred to as BI-FDTD, for modeling electromagnetic wave interactions with bi-isotropic (BI) media. The theoretical foundation for the BI-FDTD method will be developed based on a wavefield decomposition. The main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium, which makes it possible to readily apply conventional FDTD analysis techniques. The BI-FDTD scheme will also be extended to include the dispersive nature of chiral media, an important subclass of bi-isotropic media. This extension represents the first of its kind in the FDTD community. Validations of this new model are demonstrated for a chiral half-space and a chiral slab.     

A hybrid technique based on combining ray tracing and FDTD methodsfor site-specific modeling of indoor radio wave propagation

The paper presents a hybrid technique based on combining ray tracing and finite-difference time-domain (FDTD) methods for site-specific modeling of indoor radio wave propagation. Ray tracing is used to analyze the wide area and FDTD is used to study areas close to complex discontinuities where ray-based solutions are not sufficiently accurate. The hybrid technique ensures improved accuracy and practicality in terms of computational resources at the same time since FDTD is only applied to a small portion of the entire modeling environment. Examples of applying the method for studying indoor structures and penetration of wave from outdoor to indoor are given at 2.4 GHz. Numerical results are compared with known exact solutions or results of the full wave analysis or traditional ray model to demonstrate the accuracy, efficiency, and robustness of the novel method. Numerical results are also compared with reported measurement results for waves at 1.29 GHz penetrating an external wall with metal-framed windows. Cumulative distributions of field envelope obtained from the hybrid method show close resemblance to the Rayleigh distribution, which conforms to the reported measurement results     

A higher order FDTD method for EM propagation in a collisionlesscold plasma

A fourth-order in time and space, finite-difference time-domain (FDTD) scheme is presented for radio-wave propagation in a lossless cold plasma. As with previously reported fourth-order schemes, the methodology is founded on the principle that correction derivatives (i.e., three derivatives in time) can be converted into vector spatial derivatives. From the error analysis and phase-velocity data, it is argued that this approach will significantly minimize the dispersion errors while still maintaining minimal memory requirements. This claim is also supported by data obtained from FDTD simulations. Using a one-dimensional plasma slab problem as the test case, we show that the bandwidth and dynamic range associated with this fourth-order scheme are significantly improved with respect to its second-order counterpart. The impact of other error mechanisms, namely material boundary-related errors, is also discussed     

FDTD analysis of wave propagation in nonlinear absorbing and gainmedia

An explicit finite-difference time-domain (FDTD) scheme for wave propagation in certain kinds of nonlinear media such as saturable absorbers and gain layers in lasers is proposed here. This scheme is an extension of the auxiliary differential equation FDTD approach and incorporates rate equations that govern the time-domain dynamics of the atomic populations in the medium. For small signal intensities and slowly varying pulses, this method gives the same results as frequency-domain methods using the linear susceptibility function. Population dynamics for large signal intensities and the transient response for rapidly varying pulses in two-level (absorber) and four-level (gain) atomic media are calculated to demonstrate the advantages of this approach     

在时域内计算色散媒质中光脉冲的传输

得到了时域内色散媒质中光脉冲传输的计算公式，并提出了时域内色散媒质中显式的光束传播法。计算了短脉冲在具有二阶色散效应的定向耦合器内的传输、计算结果同参考文献中的一致，但本文的计算方法简单、方便、实用。     

Numerical mode-matching method for the multiregion verticallystratified media [EM wave propagation]

The response of a source in the presence of an N-region, vertically stratified media is solved using the numerical mode-matching method. By treating the fields propagating in the direction parallel to the subboundaries of the stratified media in terms of the propagators, and by introducing the concepts of reflection operators, transmission operators, and generalized reflection operators, the two-dimensional problem is reduced to several one-dimensional problems, which are solved by the one-dimensional finite-element method (FEM). The one-dimensional method saves computer storage and computation time compared to the two-dimensional version. A formulation valid for a general N-region vertically stratified medium is derived. When there are only three regions, the results compare well with those in the literature. Some typical numerical results for N>3 are also shown     

A fictitious domain method for conformal modeling of the perfectelectric conductors in the FDTD method

We present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors (PEC) in the finite-difference time-domain (FDTD) method. The idea is to extend the electromagnetic field inside the PEC and to introduce a new unknown, the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the PEC. This requires the use of two independent meshes: a regular three-dimensional (3-D) cubic lattice for the electromagnetic field and a triangular surface-patching for the surface electric current density. The intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density. An interesting property of this method is that it provides the surface electric current density at each time step. Furthermore, this method looks like FDTD with a special model for the PEC. Numerical results for several objects are presented     

FDTD等效入射波法分析PSTM

本文提出一种简捷有效的方法，即等效入射波法分析光子扫描隧道显微镜(PSTM)。作为验证，计算了3维情况下，形貌起伏样品和嵌埋的不同折射率样品，S和P极化情况下，等高扫描面上的场分布的PSTM图像，并与其他方法进行比较。比较表明，时域有限差分法(FDTD)等效入射波法与其他方法已有的结果符合相当好，并具有简捷，降低对吸收边界的要求，减小网格数和计算时间等优点。     

Electromagnetic wave propagation in almost periodic media

The problem of electromagnetic wave propagation in almost periodic media is investigated, and a solution is obtained directly from Maxwell's equations. The evaluation of this solution involves a generalization to almost periodic media of the Brillouin diagram of periodic media. The Brillouin diagram is used to place in evidence similarities and differences of wave propagation in periodic and almost periodic media. It is shown that although the periodic and almost periodic theories agree in many cases of interest, there exist cases in which distinct differences appear. In particular, these distinctions become apparent for media with closely spaced tones.     

Three-dimensional FDTD modeling of impulsive ELF propagation about the earth-sphere

This paper reports the application of an efficient finite-difference time-domain (FDTD) algorithm to model impulsive extremely low frequency (ELF) propagation within the entire Earth-ionosphere cavity. Periodic boundary conditions are used in conjunction with a three-dimensional latitude-longitude FDTD space lattice which wraps around the complete Earth-sphere. Adaptive combination of adjacent grid cells in the east-west direction minimizes cell eccentricity upon approaching the poles and hence maintains Courant stability for relatively large time steps. This technique permits a direct, three-dimensional time-domain calculation of impulsive, round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities/anisotropies of the excitation, ionosphere, lithosphere, and oceans. The numerical model is verified by comparing its results for ELF propagation attenuation with corresponding data reported in the literature.     

A novel FDTD formulation for dispersive media

A novel FDTD formulation for dispersive media called piecewise linear JE recursive convolution (PLJERC) finite-different time-domain (FDTD) method is derived using the piecewise linear approximation and the recursive convolution relationship between the current density J and the electric field E. The high accuracy and efficiency of the PLJERC method is confirmed by computing the reflection coefficients of an electromagnetic wave through a collision plasma slab in one dimension.     

A higher order electron wave propagation method

A finite-difference propagation scheme for simulating electron currents through arbitrary quantum structures is presented in this paper. It is shown that due to the strong interaction of external fields and electrons, the trajectories predicted using higher order propagation operators are a significant improvement over that of lower order schemes, especially in cases where the longitudinal electron momentum is not accurately known. A novel boundary condition based on the popular transparent boundary condition is used for minimizing unphysical reflections off the computation boundaries even in the presence of strong lateral electric fields. The application of this scheme is illustrated through a few examples     

Cavity losses modeling using lossless FDTD method

The impulse response of a lossless resonant system, usually obtained using the finite-difference time-domain method, permits us to determine the resonant frequencies through the Fourier transform. However, the obtained spectrum has no physical meaning since the losses have not been implemented. Rather than modeling physically the losses, we propose to apply a specific time-domain window to the already simulated signal of the lossless system. This Losses window depends on a user-defined quality factor. The advantage of this postsimulation losses implementation is a capability of parametric study of composite losses. Losses of various physical origins are found for example in the case of reverberation chambers.     

Electromagnetic wave propagation in spherically stratified isotropic media

The general electromagnetic field can be resolved into two components represented by electric and magnetic Hertz vectors, both vectors being parallel to the radial direction. Very few exact solutions for the radial variation of fields of the electric type have been found hitherto. Generalised refractive-index profiles permitting exact transcendental solutions are presented.