Ana Grande

FDTD Modeling of Chiral Media by Using the Mobius Transformation Technique

This letter introduces a new technique for finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation in frequency-dispersive chiral media. First, Maxwells curl equations are discretized according to Yees scheme. Then the constitutive relations, expressed in the Laplace domain, are discretized using the Mobius transformation technique and appropriate digital-processing methodologies. The resulting formulation is explicit and preserves the second-order accuracy of the conventional FDTD technique. To show the validity of the method, the reflection and transmission coefficients of a chiral slab are computed and compared to the exact results, with good agreement being obtained

Two-dimensional extension of a novel FDTD technique for modeling dispersive lossy bi-isotropic media using the auxiliary differential equation method

This letter describes a two-dimensional (2-D) extension of a recently developed finite-difference time-domain (FDTD) scheme to model wave propagation in bi-isotropic media. To our knowledge this method is the only one successfully generalized to modeling transient microwave signals in general lossy dispersive bi-isotropic media. The new 2-D cell built and computational procedure of the FDTD algorithm developed is described. Condon and Lorentz dispersion models have been included for modeling the frequency dependence of the medium parameters and the auxiliary differential equation (ADE) method is considered to deal with dispersion in order to avoid defining complex back-stored numbers to compute the convolutions recursively. Finally the oblique incidence of a wave on a chiral medium and the propagation in a general lossy bi-isotropic medium have been successfully simulated.

The 1D ADI-FDTD Method in Lossy Media

A stability and numerical dispersion analysis for the one-dimensional alternating-direction implicit finite-difference time-domain method in lossy media is presented. To conduct a general study, the conduction term is approximated by a weighted average in time. The stability analysis is based on the von Neumann method and the numerical dispersion relation is derived in a closed-form. The analytical results are validated by numerical simulations, showing that errors for both the attenuation and phase constants can be very high if the weighted-average coefficients are not properly selected.

On the Equivalence of Several FDTD Formulations for Modeling Electromagnetic Wave Propagation in Double-Negative Metamaterials

Recently, several approaches have been proposed to incorporate double-negative media into finite-difference time-domain simulators. In this letter, a rigorous comparative study of the formulation introduced by Karkkainen and Maslovski and the bilinear frequency approximation technique applied by Feise (IEEE Trans. Antennas Propag., vol. 52, pp. 2955-2962, Nov. 2004) is presented. Although these two formulations are based on different approximation principles, we show that both lead to equivalent difference schemes. Moreover, these two methods are equivalent to a third one, previously published for dispersive dielectrics, which is based on a different approach. The stability of these formulations is also analyzed by means of the von Neumann method.

Accuracy Limitations of the Locally One-Dimensional FDTD Technique

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.

Stability and Accuracy of a Finite-Difference Time-Domain Scheme for Modeling Double-Negative Media With High-Order Rational Constitutive Parameters

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 Maxwells curl equations and considering Ohms law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohms 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.

Combining the FDTD Method and Rational-Fitting Techniques for Modeling Active Devices Characterized by Measured

Most extensions of the original finite-difference time-domain (FDTD) method to incorporate lumped components are based on equivalent-circuit models. However, for active components, most manufacturers provide only the measured S-parameters of the device. This letter proposes the combination of the two-port lumped-network FDTD method and rational-fitting techniques to incorporate linear active devices characterized by measured 5-parameters into FDTD simulators. To this end, first the Y-parameters are obtained, which are then approximated by rational functions of the frequency over the band of interest. The polynomial coefficients resulting from the rational fitting are directly used to feed the FDTD simulation. The approach proposed here is applied to the calculation of the S-parameters of a microstrip amplifier. The results obtained are compared with those provided by the commercial simulator advanced design system and with measurements.

S

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.

-Parameters

In recent years, the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method has been extended to dispersive media. To this end, a constitutive relation is appended to Maxwells curl equations. A common feature of all of the existing formulations is that the integration over a full time step, of Maxwells equations and the constitutive relation, is split into two sub-steps.

Reinterpreting Four-Stage Split-Step FDTD Methods as Two-Stage Methods

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.