Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures

Periodic structures, e.g., frequency selective surfaces (FSSs), are used in applications such as the design of bandpass radomes for missiles, subreflectors for dual frequency reflector antenna systems and filters for optics and infrared. In this work, complex periodic structures are analyzed using the finite difference time-domain algorithm (FDTD) in combination with the Floquet boundary condition. The Floquet type of phase shift boundary condition is incorporated in the time-domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step. With this approach, the FDTD method can be applied to a frequency selective surface (FSS) geometry of arbitrary shape illuminated by a plane wave at an arbitrary angle of incidence, without the need to store large amounts of data to model the time advance or delay between the periodic cells. The application of the technique will be demonstrated on a thick, doubly-concentric square loop FSS.