markFDTD: Near-to-Far Field Transformation For Two Dimension FDTD

Using the near-field data obtained in a single FDTD modeling run, this transformation efficiently and accurately calculates the complete far-field bistatic scattering response of an illuminated structure for a single illumination angle, or the complete radiation pattern of an antenna. In other words, these is no need to extend the FDTD lattice to the far field to obtain far-field data.
In fact, the equivalent electric and magnetic currents tangential to any closed contour surrounding a two-dimensional TM electromagnetic wave interaction structure is sufficient to obtain the far field via a simple integration of these currents around the contour. This idea, illustrated in Fig.1, forms the basis of the surface equivalence theorem.

(a) Original interaction geometry (b) equivalent problem
Fig.1 Definition of electromagnetic fields and equivalent electric and magnetic virtual currents for the surface equivalence theorem.

Applied this concept, the program fd2d_004 calculated the RCS for three structures respectively.
Case 1: Metal square with a=2*lamda , lamda=1.e-6m , and dx=dy=lamda/40. The plane wave incident from the left, that is the incident angle is 0 degree.

Case 2: Metal square with a=2*lamda, lamda=1.e-6m, and dx=dy=lamda/40. The plane wave incident from the left, that is the incident angle is 45 degree.

Case 3: Dielectric circle with r=2*lamda, lamda=1.e-6m, epsr=3.5 and dx=dy=lamda/40 . The plane wave incident from the left, the incident angle is 0 degree.