Classical theories such as the uniform geometrical theory of diffraction (UTD) utilize analytical expressions for diffraction coefficient for canonical problems such as the infinite perfectly conducting wedge [1]. In this paper, we present a numerical approach to this problem using the finite-difference timedomain (FDTD) method. We present results for the diffraction coefficient of the two-dimensional (2-D) infinite perfect electrical conductor (PEC) wedge, the 2-D infinite lossless dielectric wedge, and the 2-D infinite lossy dielectric wedge for incident TM and TE polarization and a 90 wedge angle. We compare our FDTD results in the far-field region for the infinite PEC wedge to the well-known analytical solutions obtained using UTD. There is very good agreement between the FDTD and UTD results. The power of this approach using FDTD goes well beyond the simple problems dealt with in this paper. It can, in principle, be extended to calculate diffraction coefficients for a variety of shape and material discontinuities, even in three dimensions.
IIntroduction In this paper, we apply the FDTD method of [1,2] to numerically obtain the dyadic diffraction coefficients for several infinite 3-D right-angle material wedges over a range of observation angles and frequencies. This method exploits the temporal causality inherent in FDTD modeling, as discussed in [2] for the infinite perfect electrical conductor (PEC) wedge case. Fig.1 shows the 3-D geometry of the scatterer, the ray-fixed coordinate system (described in [2,3] for PEC wedges), and the coordinate system used in the FDTD model. The figure shows the edge-fixed plane of incidence (i',i) and difhction (i,;); the ray-fixed coordinates for the incident field (i',4',bo') and diffracted field (;,$,bo); and the edge-fixed spherical angles made by the incident ray (Bo', @') and the diffracted ray (Po, 4).
II
Description of the methodIn order to obtain the FDTD-calculated soft (DJ and hard (Dh) diffraction coefficients, we illuminate the scatterer with a pulsed plane wave 2Ern and compute the diffracted field & ! ; from edge BC at the observation points of interest. The observation points and the side lengths of the scatterer are chosen such that 2 ; ; can be causally isolated in time from all the other fields. ir has a center frequency of 850 MHz and a Gaussian spectrum of 600 MHz (full-width at half-maximum). We use cubic lattice cells of side length u 2 5 , where & is the wavelength at 850 MHz in air, and the PML absorbing boundary condition. Our numerical convergence studies indicate that the FDTD data for the cases studied are essentially converged under these conditions. D, and Dh are obtained using 0-7803-
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