In this paper, the physics that determines the performance limits of a diffractive optical element based on a liquid-crystal (LC) optical phased array (OPA) is investigated by numerical modeling. The influence of the fringing electric fields, the LC material properties, and the voltage optimization process is discussed. General design issues related to the LC OPA configuration, the diffraction angle, and the diffraction efficiency are discussed. A design for a wide-angle LC OPA is proposed for high-efficiency laser beam steering. This work provides fundamental understanding for a light beam deflected by a diffractive liquid-crystal device.