Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer

An efficient algorithm for implementing the perfectly matched layer (PML) is presented for truncating finite-difference time-domain domains. The algorithm is based on incorporating the auxiliary differential equation method into the PML formulations. Simple, unsplit-field and material independent PML formulations are obtained. Two dimensional numerical examples are included to validate the proposed formulations.     

Extension and validation of a perfectly matched layer formulation for the unconditionally stable D-H FDTD method

In this letter, a modification to the recently proposed unconditionally stable D-H ADI FDTD method is presented that considerably reduces the late-time error induced by the corner cells. The PML boundary is derived from the direct discretization of the modified D-H Maxwell's equations rather than the superposition of uniaxial PML boundaries. An optimal choice of the PML conductivity profile coefficients is proposed. Results show that the reflection error of the PML is limited for increased time step size beyond the Courant-Friedrichs-Lewy stability bound, and maximum reflection errors are 15 to 20 dB lower than the original formulation.     

Physical limitations of antennas in a lossy medium

The dissipated power and the directivity of antennas in a homogeneous, lossy medium are systematically analyzed in this paper. The antennas are ideal and located inside a lossless sphere. In the lossy space outside the sphere, the electromagnetic fields are expanded in a complete set of vector wave functions. The radiation efficiency, the directivity, and the power gain are defined for antennas in a lossy medium, and the optimal values of these quantities are derived. Simple relations between the maximal number of ports, or channels, an antenna can use and the optimal directivity and gain of the antenna are presented.     

Perfectly matched layer for transmission line modelling (TLM)method

The authors present a development of Berenger's perfectly matched layer (PML) for direct application to the transmission line modelling (TLM) method of electromagnetic simulation     

A revised formulation of modal absorbing and matched modal sourceboundary conditions for the efficient FDTD analysis of waveguidestructures

A revised formulation of modal absorbing and matched modal source boundary condition is proposed for the efficient analysis of a waveguide circuit with the finite-difference time-domain (FDTD) method. The formulation is based on a suitable translation operator modeling, in time domain, the propagation in a uniform hollow waveguide. By applying this operator, a multimodal absorbing boundary condition is obtained. Moreover, a source algorithm is developed that generates a given incident wave, while absorbing each modal component reflected from a discontinuity. The source is capable of separating incident and reflected waves without requiring any presimulation of long uniform waveguides. The validity and effectiveness of the formulation is verified by means of three numerical experiments. The first two refer to waveguide discontinuities. In these cases, the FDTD results are compared to mode-matching results. The third example is a transition from waveguide to printed circuit transmission line. The numerical simulation is compared with published experimental results. The presented examples show that the generalized scattering matrix of a waveguide circuit can be evaluated accurately in the smallest computational space allowed by the structure     

Quasiparticle description of pulse propagation in a lossy dispersive medium

It has been known from extensive saddle point analysis that pulses propagating in a lossy dispersive Lorentzian medium exhibit a high frequency forerunner and frequency chirping. The quasiparticle approximation permits an accurate and numerically efficient calculation of the forerunner frequency chirping with a simple physical explanation. For the case of a Gaussian incident pulse, the error in the second order quasiparticle approximation becomes smaller as the pulse propagates; hence one may apply the quasiparticle method for a wide range of propagation distances with error estimates that can be readily calculated.     

Magnetic dipole excitation of a long conductor in a lossy medium

A formulation is presented for the excitation of currents on an infinitely long conductor by electric or magnetic dipoles of arbitrary orientation. The conductor can be either insulated or bare to model ungrounded or grounded conductors. Specific calculations are presented for a vertical magnetic dipole source because this source produces the appropriate horizontal polarization and could be used in a borehole-to-borehole configuration. Numerical results for the induced current and secondary magnetic field indicate that long conductors produce a strong anomaly over a broad frequency range. The secondary magnetic field decays slowly in the direction of the conductor and eventually becomes larger than the dipole source. Results have been presented for frequencies from 20 kHz to 2 MHz, and the entire frequency range appears to be useful     

Thermal noise emission of a lossy material for a TEM propagation

New methods of computation of the thermal noise signals emitted by homogeneous and multilayered lossy materials, for a TEM propagation are presented. In particular, the noise contribution of the different subvolumes and the case of non-uniform temperature repartition are studied, taking into account correlation and refractive-index variation effects.     

Propagation characteristics of a heaviside absorbing layer for TLM

The perfectly matched layer for use with the finite-difference time-domain method is adapted to our transmission-line matrix simulation as what we call a heaviside absorbing layer (HAL). It is shown that the reflection coefficient for the wave incident on a HAL is less than that of the wave incident on a matched-load termination at all angles of incidence. Furthermore, the dispersion relation of a transmission-line matrix mesh of a symmetrical condensed node with both electric and magnetic loss stubs is derived. It provides guidance on how to choose the losses of HAL and other simulation parameters properly     

Modeling of thin wires in a lossy medium for FDTD simulations

An equivalent radius of a thin wire in a lossy medium, represented by the finite-difference time-domain method, is derived using the concept that was proposed to derive an equivalent radius of a thin wire in air. Then, a simple technique to specify an arbitrary radius of a thin wire in a lossy medium is proposed. The proposed technique does not employ locally fine or nonuniform subgrids, but is based on an orthogonal and uniform-spacing Cartesian grid. The validity of the proposed technique is investigated in a transient state, as well as in a quasisteady state, and shown to be satisfactory.     

The perfectly matched layer (PML) boundary condition for the beam propagation method

The perfectly matched layer (PML) boundary condition for the Helmoltz equation is developed and applied to the finite-difference beam propagation method. Its effectiveness is verified by way of examples.     

Distortion of a short quasi-monochromatic signal in a resonantly absorbing medium

Propagation of a short quasi-monochromatic electromagnetic (light or radio) signal (wave packet) is considered. The carrier frequency of the signal is close to the frequency of the absorption spectral line (or group of lines) of a medium, and the spectrum width is large relative to the width of this spectral line (or group of lines). Analytic formulas for the temporal dependence of the signal are derived and numerically confirmed for paths of various lengths. It is shown that the signal is substantially distorted long before it noticeably decays owing to absorption. The signal’s temporal dependence turns out to be rather universal with respect to the form factor of the spectral line, the optical thickness of the substance layer, and the initial temporal dependence of the signal.     

Calculated admittance of an idealized drill rod antenna in a lossy medium

Some calculated results for the input admittance of both insulated and uninsulated drill rods immersed in a lossy medium are given. The source can be either a voltage gap or a thin toroidal coil. For this input admittance calculation the drill rod is assumed to be of infinite length. Even a very thin insulating layer is found to greatly decrease the real part of the input admittance or the input power.     

A hybrid computational electromagnetics formulation for Simulation of antennas coupled to lossy and dielectric volumes

A heterogeneous hybrid computational electromagnetics method is presented, which enables different parts of an antenna simulation problem to be treated by different methods, thus enabling the most appropriate method to be used for each part. The method uses a standard frequency-domain moment-method program and a finite-difference time-domain program to compute the fields in two regions. The two regions are interfaced by surfaces on which effective sources are defined by application of the Equivalence Principle. An extension to this permits conduction currents to cross the boundary between the different computational domains. Several validation cases are examined and the results compared with available data. The method is particularly suitable for simulation of the behavior of an antenna that is partially buried, or closely coupled with lossy dielectric volumes such as soil, building structures or the human body.     

Optical interference effect of a thick absorbing LT-GaAs layer on a Bragg reflector

Near-infrared reflectance spectra of 5 μm thick low-temperature (LT) GaAs films on GaAs/AlAs Bragg reflectors (BRs) have been studied by model calculations as a function of the linear absorption coefficient of the films α_f. With increasing α_f, the reflectance of the stop band decrease monotonously. In contrast, the interference modulation due to the LT-GaAs layer on the BR inside of the stop band increases with increasing α_f until 1×10³ cm⁻¹ and decreases for larger α_f. This unusual behavior of the Fabry–Perot features in the stop band is explained by the attenuation of the light in the film as well as by the interference in the case of destructive superposition between the partial waves, which are strongly reflected at the film/BR interface, and those partial waves, which are much more weakly reflected at the air/film interface.     

Analysis of transient interaction of electromagnetic pulse with an air layer in a dielectric medium using wavelet-based implicit TDIE formulation

The interaction of transient electromagnetic pulse with an air layer in a dielectric medium is formulated in terms of a time-domain integral equation and solved numerically via the method of moments. Previous related works pointed to the inherent inadequacy of the marching-on-in-time method in this case, but suggested no remedy. This paper explains why an implicit modeling scheme would work effectively in this case. It is also noted that the use of an implicit scheme would normally involve a solution of a very large and dense matrix equation. To alleviate this drawback of the implicit scheme, the use of a wavelet-based impedance-matrix-compression technique, which has facilitated in the very recent past solutions of time-domain problems with greater efficiency, is described.     

The fundamental electromagnetic wave of a single-wire line in a weakly absorbing medium

An approximate dispersion equation valid over a wide frequency range is obtained from the dispersion equation for the symmetric E ₀₀ wave (the Sommerfeld wave) propagating along a finite-conductance metal wire embedded in a lossy dielectric. The boundaries of this frequency range are determined. A technique is developed for solution of the obtained approximate dispersion equation in the frequency band where the pronounced skin effect is observed. The ratio of the wire radius to the thickness of the skin layer is assumed to be no less than 10. This technique is applied to calculate the longitudinal and transverse propagation constants for 1.0-and 2.5-mm-radii copper wires over the frequency range 0.5 MHz to 1000 GHz.     

The diffraction of an inhomogeneous plane wave by an impedancewedge in a lossy medium

The diffraction of an inhomogeneous plane wave by an impedance wedge embedded in a lossy medium is analyzed. The rigorous integral representation for the field is asymptotically evaluated in the context of the uniform geometrical theory of diffraction (UTD) so that the asymptotic expressions obtained can be employed in a ray analysis of the scattering from more complex edge geometries located in a dissipative medium. Surface wave excitations at the edge and their propagation along the wedge faces are discussed with particular emphasis on the effects of losses     

Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the /spl Delta/t time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to /spl Delta/t, and as such, increasing /spl Delta/t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.     

Generalisation of the partial-power law (Brown's identity) to waveguides with lossy media

The partial-power law, otherwise known as Brown's identity, which relates the product of the phase velocity of a mode on a lossless waveguide to the time-average power and momentum carried by the mode, is generalised to be applicable to lossy waveguides as well.