602 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 49, NO. 4, APRIL 2001 Time-Domain Equivalent Edge Currents for Transient Scattering Ayhan Altıntas ¸, Senior Member, IEEE, and Peter Russer, Fellow, IEEE Abstract—Time-domain equivalent edge currents (TD-EEC) are developed for the transient scattering analysis. The development is based on the Fourier inversion of frequency domain equivalent edge current expressions. The time-domain diffracted fields are ex- pressed in terms of a contour integral along the diffracting edges for any arbitrary input pulse shape, thereby yielding finite results at the caustics of diffracted rays. The approach also eliminates the need for the evaluation of a convolution integral in the time domain geometrical theory of diffraction (GTD) analysis. The results are compared with the first order GTD results for the transient scat- tering analysis for a circular disk. Index Terms—Electromagnetic transient scattering, equivalent edge currents, high-frequency techniques in electromagnetics, time-domain methods. I. INTRODUCTION F OURIER inversion of high-frequency fields gives a clear picture of the scattering mechanism when the object size is large compared to the wavelength at the lowest frequency considered. Ray optical techniques have been commonly ap- plied for the determination of scattered fields at high frequen- cies [1]–[3]. Equivalent edge currents are employed when the ray optics fail due to the observation point being at or around the caustics of the rays, or even when there is no ray reaching the observation. In addition, they are useful when the input field has spatial variations along the edge [4]. Recently, direct use of physical optics (PO), geometric theory of diffraction (GTD) and uniform theory of diffraction (UTD) in the time domain has been of interest [5]–[7]. The advantages are several. Efficient and faster computation, more suitable solutions when the pulse width is narrow compared with the geometrical dimensions of the scattering object, feasibility to implement a hybrid solution by combination with various numerical time domain methods such as finite difference time domain (FDTD) and TLM. As in the frequency domain, the problem of PO is the limited accuracy yet the simplicity makes it still a desirable approach in certain applications. The time-domain GTD and its extensions have better accuracy and are suitable for multiple diffraction analysis, however, in addition to becoming invalid at caustics of diffracted rays, they require a convolution integral of the input pulse with the so-called “time-domain diffraction coefficients.” In the proposed time-domain equivalent current approach, diffracted fields are obtained by an integration of Manuscript received February 11, 1999; revised June 20, 2000. A. Altıntas ¸ is with the Department of Electrical and Electronics Engineering, Bilkent University, 06533 Ankara, Turkey. P. Russer is with the Institut für Hochfrequenztechnik, Technische Universität München, D-80333 Munich, Germany. Publisher Item Identifier S 0018-926X(01)03183-0. the input pulse over the edge contour and thereby remain finite at caustic regions. In addition, arbitrary pulse inputs can be applied without further processing. When the optical distance is stationary at discrete points over the edge contour satisfying generalized Fermat’s principle (the observation point being on the Keller cone), the time-domain equivalent edge currents (TD-EEC) integration recovers the GTD ray optical solution. The approach will, therefore, prove to be useful especially for the transient scattering analysis from plate structures. It is noted that the accuracy of high-frequency based solutions is increased if the low-frequency content of the input pulse is weak [2]. This paper deals with the development of the TD-EEC for transient scattering applications. First, a brief review of the time- domain GTD is given. Followed by a description of the TD-EEC approach. Finally, transient scattering from a circular disk is an- alyzed using the TD-EEC and the results are compared with the Fourier inversion of the GTD analysis. It is noted that a time-do- main version of the physical theory of diffraction is reported very recently [8], however, the numerical results are presented only for two-dimensional (2-D) structures. II. BACKGROUND For scatterers with edges, the geometrical optical incident and reflected rays are complemented with the edge-diffracted fields of the GTD or the UTD. Analytical time-domain solutions based on the GTD and the UTD are obtained by the Fourier inversion of the corresponding GTD and UTD diffraction coefficients. These are called the “time-domain diffraction coefficients.” For an impulse excitation, the scattered fields are proportional to the time-domain diffraction coefficients. However, for a general pulse excitation, a convolution integral of the excitation with the time-domain diffraction coefficients is required to get the scat- tered field as follows: (1) where distance from the diffraction point to the observa- tion; speed of light; time when the excitation reaches ; spreading factor for the diffracted rays; time-domain dyadic diffraction coefficient obtained by the inverse transform of frequency domain dyadic diffraction coefficient. 0018–926X/01$10.00 © 2001 IEEE