A fan-beam antenna is a directional antenna producing a main beam having a narrow beamwidth in one dimension and a wider beamwidth in the other dimension. This pattern will be achieved by a truncated paraboloid reflector or a circular paraboloid reflector. Since the reflector is narrow in the vertical plane and wide in the horizontal, it produces a beam that is wide in the vertical plane and narrow in the horizontal. (The larger the antenna dimension, the narrower the beam.)
Figures: A truncated paraboloid reflector and its antenna pattern (a: lateral view, b: frontal view)
Fan beam antennas are used in radar sets. Those in height finders have the beam oriented horizontally.