Analytic Fields With Higher-Order Compensations for 3-D FDTD TF/SF Formulation With Application to Beam Excitations

The total-field/scattered-field (TF/SF) formulation is widely used to initiate incident waves for scattering problems in finite-difference time-domain (FDTD) simulations. An important aspect of the TF/SF formulation is the calculation of incident fields at the TF/SF boundary by methods that account for the numerical nature of the incident wave in the FDTD grid. Failure to do so can lead to high levels of field leakage errors across the TF/SF boundary. This paper presents an improved analytic time-domain method for accurately computing incident fields in the TF/SF formulation. Using analytic field expressions with higher-order dispersion and polarization compensations, the proposed method compensates for 1) the FDTD numerical dispersion; and 2) the lack of orthogonality between the frequency-dependent field polarizations and the wavevector, which was not accounted for in existing analytic time-domain methods. The higher-order compensations result in further suppression of field leakage errors in the SF region. In addition to exciting a plane wave, the proposed method can be employed to excite an incident beam. To demonstrate this, numerical experiments that source both 3-D plane wave and focused beam into a free space FDTD grid are presented and compared with existing methods.