Time-domain fields exterior to a two-dimensional FDTD space

A transformation algorithm for the near-zone and far-zone fields exterior to a two-dimensional (2-D) finite-difference time-domain (FDTD) field lattice has been developed entirely in the time domain. The fields are found from a surface integration of the convolution of the time derivative of equivalent currents and charges along a contour that encloses the scatterer or radiator of interest. The kernel of the convolution integral has a square-root singularity for which an efficient numerical integration rule is presented. Using this technique, a very accurate solution is obtained; however, convolution integrals are computationally expensive with or without singularities. As an alternative, a rapidly convergent approximate series expansion for the convolution integral is presented, which can be used both in the near and far zone. Results using the new 2-D transform are compared with analytical expressions for the fields generated by a modulated Gaussian pulse for TE and TM line sources. In addition, the 2-D transform solution for the near-zone fields scattered from an open-ended cavity for a TE incident modulated Gaussian pulse plane wave is compared against a full-grid FDTD solution for accuracy and efficiency. The 2-D transform far-zone fields are compared against an alternative technique, which uses a double Fourier transform to perform the convolution in the frequency domain.