Antennas and other transducers for use in transmitting and receiving twisted waves are disclosed. A reflector includes numerous parabolic segments having focal lengths that decrease monotonically with azimuth angle. A feed is used that is located at a focal length associated with one of the segments. Thus, each segment has a phase delay that is related to a difference between the primary focal length and the focal length of the segment. This variation of phase delay with azimuth allows twisted waves to be transmitted and received.