Efficient Plane Wave Injection For FDTD Method

The finite-difference time-domain (FDTD) method, as one of the main methods of numerically solving electromagnetic problems, requires the introduction a volume source into FDTD computational domain, which should has a very low noise level, especially when observing weak scattering. And many practical problems of interest involve the use of plane wave sources, for example, one often needs to calculate the radar cross-section (RCS) of an object where it is assumed that the source is far away, allowing the use of the plane wave approximation.For efficient simulation of a plane wave, the total-field/scattered-field (TF/SF) formulation as outlined in Taflove is such a well-developed method for introducing volume source into FDTD. The mathematical principle of this formulation is rooted at the field discontinuity equations and the equivalence principle, which in electromagnetic theory often manifests in different forms. In a sense, the formulation can solve many scattering problems only by remodeling the scatter. If required, the resulting scattered fields can also be transformed to investigate their far-field properties. An efficient time-domain technique is an auxiliary 1D incident field array (IFA) which is used to propagate a plane wave source concurrent with the main simulation domain, being used as a lookup table to populate the Huygens' surface. Unfortunately, depending on the formulation used for this source, errors are introduced as a result of interpolation and numerical dispersion mismatches—or equivalently the grid anisotropy—between the source and the main FDTD grid, as this causes a nonphysical scattered field to corrupt results and reduce the dynamic range.For a 2D problem, we present a new but efficient method for introduction of plane wave source, which based on the split-field:the method of splitting the plane-wave FDTD (SP-FDTD), which fundamentally eliminates the error of interpolation and phase velocity mismatch, achieving a perfect TF/SF separation with leakage error around -300dB. In addition, its feasibility is confirmed by the nature of numerical plane wave in FDTD and the SP-FDTD method can also be extended to 3D FDTD and higher-order FDTD (M24) method.Specific studies include the following:(?) Aimed at the traditional method of introducing plane wave source, its deficiency is presented through theoretical analysis, and we propose the way of eliminating leakage error.(?) For the 2D TMZ model, we present a new but efficient method for introduction of plane wave source, which based on the split-field:the method of splitting the plane-wave FDTD (SP-FDTD). By the research on the nature of the numerical plane wave in FDTD, the feasibility of the method is confirmed in theory, and its effectiveness is also confirmed by numerical examples in 2D.(?) Making using of the nature of the numerical plane wave in FDTD and a split-field formulation, the corresponding SP-FDTD is presented for FDTD problems in 3D and M24 method. According to the numerical examples, there both are perfect total-field/scattered-field separations with leakage error around-300dB.(?) Finally, the paper elaborates the advantages and disadvantages of the SP-FDTD method. The paper also makes a prospect to many aspects such as extending the method to symplectic algorithm, ADI-FDTD and so on.