TABLE OF CONTENTS Periodic structures also find many applications in the design of various scatterers and antenna arrays. For example, frequency selective surfaces (FSS) consisting of periodic dipoles or slots are used as radomes for large antenna systems [32]. Planar reflectarray antennas, which are built from hundreds or thousands of antenna elements arranged in a periodic lattice, are installed in spacecraft for Earth remote sensing and deep space exploration programs [33]. Recently, periodic dielectric rods and metal patterns are designed to realize electromagnetic band gap (EBG) structures and double negative metamaterials [34]. In this section, the FDTD/PBC algorithm is implemented to calculate the scattering properties of periodic structures.
For scattering analysis, the goal is to calculate the radar cross section (RCS) of an object. That is to find the strength of scattered fields in different directions. However, the presence of periodicity in the scatterer limits the existence of scattering angles. This can be understood from the array theory.
Assume that the scattered pattern of a single element is F e( ?) and the excitation on the element is I n . Using the array theory, the total scattering pattern F( ?) of the structure is
where ? s denotes the scattering angle. According to the Floquet theorem, the excitation I n satisfies the following equation:
Here, ? i is the incident angle. Substitute (2.60) into (2.59),
For an infinite array, the scattered fields focus on several discrete...
