Abstract-An axial-mode helical antenna backed by a perfect electric conductor (PEC reflector) is optimized to radiate a circularly polarized (CP) wave, using the finite-difference time-domain method (FDTDM). After the optimization, the PEC reflector is replaced with a corrugated reflector. The effects of the corrugated reflector on the current distribution along the helical arm and the radiation pattern are investigated. A reduction in the backward radiation is attributed to the reduction in the current flowing over the rear surface of the corrugated reflector. A spiral antenna backed by a PEC reflector of finite extent is also analyzed using the FDTDM. As the antenna height decreases, the reverse current toward the feed point increases, resulting in deterioration of the axial ratio. To overcome this deterioration, the PEC reflector is replaced with an electromagnetic band-gap (EBG) reflector composed of mushroom-like elements. Analysis reveals that the spiral radiates a CP wave even when the spiral is located close to the reflector (0.06 wavelength above the EBG surface). The input impedance for the EBG reflector is more stable over a wide frequency band than that for the PEC reflector.Index Terms-Corrugated reflector, electromagnetic band-gap reflector, finite-difference time-domain method (FDTDM), helical antenna, spiral antenna.