Comparison of absorbing boundary conditions for numerical analysis of periodic structures

Periodic structures like gratings or frequency selective surfaces are widely met in antenna design and applications. Some problems require calculating reflectivity in a wide frequency band. Time domain methods like FDTD are beneficial in such problems since they provide the whole spectrum in a single simulation. A periodic structure is modeled as a Floquet waveguide. In FDTD the simulation region needs to be bound with absorbing boundary condition that imitates a semi-infinite waveguide. We tested several such conditions, which are widely used, and reveal that none of these performs well near cutoff frequencies. The problem is demonstrated on a simple illustrative diffraction problem. Some possible ways of improving ABC to overcome the difficulty are discussed.