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A unified view of direct-integration (DI) and exponential-time-differencing (ETD) methods to incorporate Drude media, such as isotropic plasma and microwave graphene, into finite-difference time-domain (FDTD) simulators is provided. To this end, the Drude constitutive relation is expressed in integral form and the DI integrators are obtained by applying quadrature rules. Analogously, the ETD integrators are obtained by starting from the variation of constants formula and applying the same quadrature rules as in the DI case. This approach allows one to directly compare the two families of methods. In addition, the accuracy of each integrator is discussed and the stability condition of the resulting FDTD schemes is derived in exact closed form by applying the von Neumann method. [ABSTRACT FROM AUTHOR]

The radial basis function-generated-finite-difference (RBF-FD) method is applied to the analysis of homogenous waveguides. To this end, the Helmholtz equation and the boundary conditions are collocated on the waveguide cross section. At each collocation node, derivatives are locally approximated by the RBF-FD formulas based on the polyharmonic splines supplemented with high-degree polynomials. As a result, a sparse matrix eigenvalue problem is obtained, which allows cutoff wavenumbers and axial fields to be calculated. To illustrate the accuracy of the method, we consider a semicircular and an eccentric circular waveguide. [ABSTRACT FROM AUTHOR]

The electric field computed by the locally 1-D finite-difference time-domain (FDTD) method at dielectric interfaces is investigated. To this end, two comprehensive problems are considered, namely a dielectric step in a rectangular waveguide and a dielectric-loaded metallic cavity. We found that, in both problems, the electric field patterns exhibit an unexpected phase shift at the dielectric interface. By contrast, the alternating-direction implicit FDTD method does not present this unphysical behavior. [ABSTRACT FROM AUTHOR]

The magnetoelectric coupling that appears in the constitutive relations of Tellegen media makes formulating unconditionally stable finite-difference time-domain (FDTD) extensions a challenging problem. In this letter, we present an alternating-direction implicit (ADI)-FDTD approach for modeling transient wave propagation in Tellegen media. In the proposed formulation, the discretization of the governing equations is performed introducing weighted average parameters. The numerical features are then carefully examined and the weighted discretization parameters conveniently chosen to yield an unconditionally stable scheme. Moreover, the resulting approach presents second-order accuracy and preserves the tridiagonal structure of the data matrices. Finally, the numerical dispersion relation is given in a closed form. The new method has been validated by means of numerical experiments and has shown good agreement. [ABSTRACT FROM AUTHOR]

While the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method preserves the second-order temporal accuracy of the conventional FDTD technique, the locally one-dimensional (LOD)-FDTD method exhibits a first-order in time splitting error. Despite this difference, the numerical dispersion analyses of these methods reveal that both present similar accuracy properties. For this reason, the characteristic noncommutativity error of the LOD-FDTD scheme has not received much attention. In this letter, we determine the closed form of the local truncation error for the 3D-LOD-FDTD scheme. We find that it presents error terms that depend on the time-step size multiplied by the spatial derivatives of the fields. Numerical results confirm that these terms become a significant source of error that is not revealed in the dispersion analyses. [ABSTRACT FROM AUTHOR]

In recent years, split-step finite-difference time-domain (SS-FDTD) methods have attracted much attention and many implementations have been developed to improve their accuracy and efficiency. In this communication the equivalence between some of these recently reported techniques and conventional schemes is shown. More specifically, we prove that there are four-stage split-step (4SS)-FDTD algorithms that can be reinterpreted as classic two-stage split-step (2SS)-FDTD schemes yielding the same local truncation errors and numerical dispersion relationships. The analytical results are validated by numerical simulations. [ABSTRACT FROM PUBLISHER]

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the x-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general Mth-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency. [ABSTRACT FROM AUTHOR]

A numerical dispersion analysis of the alternating-direction implicit finite-difference time-domain method for transverse-electric waves in lossy materials is presented. Two different finite-difference approximations for the conduction terms are considered: the double-average and the synchronized schemes. The numerical dispersion relation is derived in a closed form and validated through numerical simulations. This study shows that, despite its popularity, the accuracy of the double-average scheme is sensitive to how well the relaxation-time constant of the material is resolved by the time step. Poor resolutions lead to unacceptably large numerical errors. On the other hand, for good conductors, the synchronized scheme allows stability factors as large as 100 to be used without deteriorating the accuracy significantly. [ABSTRACT FROM AUTHOR]

This paper introduces an extension of the original finite-difference time-domain (FDTD) method for modeling double-negative media characterized by high-order frequency-dependent permittivity and permeability. The approach basically consists of adding electric and magnetic current densities to Maxwell's curl equations and considering Ohm's law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohm's law by applying the Mobius transformation technique. The extended FDTD formulation is validated and its numerical features are carefully examined. More specifically, analytical stability conditions are derived for several types of double-negative media and the numerical dissipation issue is discussed. In addition, the numerical dispersion equation for general high-order double-negative media is given and the order of accuracy of the scheme is studied. Finally, the definition of numerical refractive index is addressed and it is shown that, when the discretization parameters of the problem are not properly chosen, a negative refractive index may become a positive one in the discrete world, thus changing the physics of the problem. [ABSTRACT FROM AUTHOR]

A multiresolution in time domain method is used to model the propagation of transient signals through dispersive chiral media. The modeling of these media requires the computation of convolution integrals, whose resolution level may be increased by introducing wavelets in the time dependence of the fields. [ABSTRACT FROM AUTHOR]

A transmission-line matrix model suitable to model the propagation of electromagnetic (EM) waves in hi-isotropic media is presented. The main characteristic of the EM response of such complex media is the cross coupling of the EM field vectors in their constitutive relations. In this study, the angle tilt between electric and magnetic field vectors, the intrinsic impedances, the effective parameters of the medium, and the rotation of the polarization plane are computed. The results are in very good agreement with the theoretical solution. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel finite-difference time-domain model of transient wave propagation in general dispersive bi-isotropic media with losses. The special properties of these materials may lead to new applications in microwave and millimeter-wave technology. While their frequency-domain properties have been well described in the literature, their time-domain behavior has only been modeled thus far for special sub-classes and monochromatic time dependence. We have validated our method by first computing time-harmonic wave propagation through a bi-isotropic medium and comparing it with analytical results. Agreement is typically better than 1%. We have then computed transient field propagation in a general lossy dispersive bi-isotropic medium. [ABSTRACT FROM AUTHOR]