Wide band circular polarized (CP) antennas behind extended hemispherical lenses suitable for polarization sensitive THz detector and wireless communication have been designed and characterized using numerical simulation. Two novel, compact and CP dipole antennas are designed and studied for this purpose. CP property of planar antennas is achieved by geometrical modifications of antennas without any complicated feeding structure. Due to compact dimensions, wideband performance and CP behavior, these designs have applications in circular dichroism (CD) spectroscopy and terahertz detectors. This numerical study deals with polarization diversity with substrate lens, effect of off axis displacement on CP behavior of lens antenna which determines number of pixels for any application, far field patterns variation due to lens's internal reflection, directivity variation attributed to internal reflection and losses. Radiation efficiency variation of antenna by antenna dimensions is also studied carefully to design appropriate lens from application's point of view. Off axis performance of antenna on hemisphere lens is also studied and redesigning of antenna by some geometric modification has been carried out to improve far field patterns.