These axially symmetric antennas have radiation patterns with a similar symmetry, called omnidirectional patterns; they radiate equal power in all directions perpendicular to the antenna, with the power varying only with the angle to the axis, dropping off to zero on the antenna's axis.
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Because an antenna's far field radiation pattern is a Fourier Transform of its aperture distribution, most antennas will generally have sidelobes, unless the aperture distribution is a Gaussian, or if the antenna is so small, as to have no sidelobes in the visible space.