The interaction of electromagnetic waves with artificial microwave chiral materials has drawn considerable attention in recent years. Since the chirality parameter provides an extra degree of freedom to control the scattering properties of targets, there have been many potential applications suggested for chiral materials. At microwave frequencies, it may be possible to use chiral materials to coat an object to achieve more effective control of its scattering properties. Moreover, chiral material has been considered for use in other applications including as substrates in microstrip antennas to reduce the resonance frequency and as polarization transformers.

Here, a set of mixed potential integral equations has been developed for computing the electromagnetic scattering of 3D arbitrarily shaped homogeneous chiral targets in free space and located above a lossy half space. The effects of the relative chirality parameter on the scattering cross section are examined by considering several canonical examples. Scattering from multiple chiral targets in the presence of a lossy half space was also investigated. These results indicate that the relative chirality can significantly change the scattering behavior of objects. This work represents an important step toward the fundamental understanding of how the scattering cross sections of chiral objects located above a half space can be controlled via the chirality parameter.